This is it, the moment you have been waiting for, the math. You know the crunchy bits that make your game run. Mostly this is dice-based and has a few charts. You can decide how crunchy you want it to be. For ease of use we are going to split the system into 3 phases. Phase 1: dice and system. Phase 2: test and combat. Phase 3: character creation and advancement.
Your System: Phase One
When attempting to figure out your system, start with your goals in mind. Are you going to build an extensive system with long-term gameplay in mind or a simple system with short-term (one-shot type) play.
While not necessary for an RPG they are the most common way of deciding the outcome of an action in a Table Top Role Playing Game. So we will assume that you are using some as the center of your system. You probably already know that dice are made in many different varieties and shapes. The different shape produce a random number in a different range. So a pyramid shaped 4 sided die produces a result between 1 and 4 with each possible result having a %25 chance of happening. Traditionally the 6 sided and 20 sided dice are the most common in use. If you are working on a game with a long character progression cycle then I suggest a larger die so that you will have smaller increases for each digit on a die.
In Space Pirates the Musical, I chose to go with a 2d6 spread for the main part of the system with some smaller variations of d6 for damage and character creation. I like the steep bell of 2d6 with the center of the curve having the highest probability. For the light and simple system/game, I decided that the small amount of movement it gave was acceptable.
For this one, I highly recommend looking at what others have done before you. Only this time, look at the math that is involved in it. If you have problems with probability then check out some math text and read up.
If it ain’t broke, don’t fix it. Check other games and see what they did, then follow in their footsteps. You don’t need to steal from others, but most games have used the same dice and math for a reason. Make your own decision and use what you think works best.


The Message of GOD, The Book of GOD, The Quran, 666 and its Proof, 19.
The Quran is a gift from GOD to humanity that it guides to the right path which leads to Heaven.
The proofs shall be the evidences that this Quran is the 666 that Satan, his religions, his temples especially the Church are afraid of.
The Quran is the 666 and GOD preserves the 666 with the number 19.
6 is the first perfect number in mathematics.
It is the only number that the sum of its factors and also the product of its factors equal to the number itself.
1 + 2 + 3 = 6
1 x 2 x 3 = 6
We read in the Quran that GOD created the Heavens and the Earth and all in between in 6 days.
Sura 111 has 100 letters and the Gv of letter Qaf is 100.
Sura 111 has 6 verses ; 111 x 6 = 666 , The Quran
Sura 6 verse 111 is 666 th verse in the Qaf table.
The number 666 is written mathematically as : 6 x 100 , 6 x 10 , 6 x 1
Adding the factors gives the result of the number 111 (100+10+1).
We say “ALLAHUAKBAR” 111 times in daily contact prayers.
Adding all the factors gives the result of 18 (6+6+6) and 111 (100+10+1).
Sura 18 has 111 verses and 18 x 111 = 1998 (666×3)..The Year that The Message “This Quran” delivered.
The creation of biological life on this earth is based on Carbon. Carbon has 6 electrons.
Carbon is the 6th element in the Periodic table.
Additional note from an Islamiat student I talked to:
There are 666 verses, or ayats, in the Quran.
What do you think?
Either the number 666 is the number of the beast [evil], as the Bible describes,
it is the holy number of the Quran.
You cannot believe the 666 is both good and evil. You have to make a choice as to what you believe.
Is the Bible correct, or is the Quran correct, on this? Your eternal destiny depends on the choice you make.


This post may contain affiliate links. Please read my disclosure here.
Math can look and sound like a foreign language to kids.Try some of these learning strategies for math to help your child view the wondrous world of math through new eyes! (and understanding!)
Anytime you can put something into your child’s hands to help them learn- DO IT! Learning new things can be an overwhelming experience as our kiddos are trying to wrap their minds around many different concepts. Giving them physical objects to use that can represent the concepts they are learning can be a game changer.
Imagine asking a 5 year-old to add 5 and 3 together without using your fingers, objects, or a story. Tough, right? Try it again and this time help them count out 5 beans then add 3 more beans to the pile, one at a time. Makes a lot more sense!
Manipulatives are tools/objects used to help teach a concept.
Pretty awesome stuff, if you ask me! Some manipulatives I loved using in my classroom (that could certainly be used at home as well) include Unifix Cubes (or linking cubes), Base 10 Blocks, and Pattern Blocks.
Below are some ideas on how to use each type of manipulative.
Count Practice counting by 1s, 2s, 5, 10s, etc. It is a great way to count because each cube is equal to one!
Link them up in sets of 2 and your child can practice skip counting by 2s. Apply that same principle to skip count by any other number as well.
Solve addition and subtraction problems- link cubes together and take them apart. Use two different colors to represent both sides of the addition equation.
Sort the colors into groups.
Create patterns with the colors, linking the cubes together. There are a bunch of pattern variations you can use. ABAB, ABCABC, ABBABB, etc. It offers a great opportunity to be creative!
Base 10 Blocks
*Tip- if you don’t have the actual blocks at home/school, draw a representation of each size.
A small cube for the ones, a stick for the tens, a square for the hundreds, and a large cube for the thousands.
Learn Place Value These blocks are an awesome way to teach place value! Going along with the hands-on idea, your child can hold the blocks representing 1s, 10s, 100s, and 1000s. Each time they add ten 1s blocks together they can ‘trade’ it in for a 10s block. The same method continues as they add ten 10s to make 100.
Show the number Use the blocks to show a specific number. For example, if you ask your child how many hundreds, tens, and ones are in 357 they could show (or draw) this by using 3 hundreds blocks 5 tens blocks and 7 ones blocks.
Add and Subtract all kinds of numbers! This could be a fun way to practice adding and subtracting, using the different blocks to physically move the numbers represented to solve the latest problem.
Watch the video below to see how to use base- 10 blocks to multiply!
Watch the video below to see how to use base- 10 blocks to divide!
Create pictures using various pattern blocks, let your child fit them together to create whatever comes to mind. This is something they can get caught up doing for hours, endless possibilities! You may just find yourself joining in on the creations! I always liked pairing this with a writing activity, invite your child to write about the picture they created. They could also trace the shapes to recreate their picture on paper.
Learn the shapes Talk about the name of each shape and how many sides and corners (vertices) it has. Look around your house, inside and outside, to find real-life things that look like the shapes.
Compose and Decompose Shapes
Put the shapes together and take them apart to create other shapes. This helps solidify how the shapes are ‘composed’ and ‘decomposed’ into other shapes. For example you can use 3 triangles to create a trapezoid. Or 2 trapezoids to make a hexagon.
Symmetry Draw a line down the middle of a page and ask your child to create a picture off to one side of the line. When they are finished, have them mirror the same thing across the line of symmetry. Talk about lining up each shape to match the other one across the line. A fun way to show this is to put your hands together then open them up with your pinkies touching to see how they ‘mirror’ each other.
Take a look at this article for more fun ideas with Unique and Creative Building Blocks for Kids!
Most children are visual learners, makes sense as to why children’s books are dominated by pictures! There are tons of awesome math picture books available that teach concepts in a fun and engaging way. Pictures can help your child visualize what the math looks like outside of just numbers and symbols.
Make Connections to the Real World
“Is there a point to all of this?” Likely a question that has gone through the minds of many kids!
Sometimes math concepts can seem so abstract and disconnected from kid’s lives. Tying in some familiarity through story-telling can go a long way.
Going back to our example above, ask your 5 year-old the question “what is 5+3?” They may be able to answer it right away, but some may not.
Now try asking them the same question with a little story mixed in. If mom has 5 cookies and dad has 3 cookies, how many cookies would they have altogether?
(Bonus points if you have real cookies they can count with and enjoy after!) Which version of that question would you want to hear?!
Another story example for older children: Meg had 3 boxes of apples. Each box had 5 apples in it. How many apples did she have altogether?
Teach Someone Else
After your child has learned something new, have them teach it back to you! Or they could teach a sibling, grandparent, or friend.
It gives them the opportunity to think through how they would solve a math problem (in this case) and figure out how to explain it with words, objects, and numbers.
Not only are they solidifying their own understanding but they are building confidence!
True mastery is shown when you can correctly teach it to someone else.
Build Math Vocabulary
Kids hear many unfamiliar words and ideas as they continue learning new math concepts. You can help ease the pain of the unknown! Help them build their math vocabulary using these ideas.
This strategy works well for any type of words you’d like to help your child learn. In this case, for math words, choose a few words to put on a poster, whiteboard, etc. When possible, include the word, a picture, a child-friendly definition (in their own words is fabulous!) and examples.
When your child comes across an unfamiliar word, explain the meaning of the word in words they can understand.
Gather or print weekly ads from various stores. There are several activities you could do with these ads!
1. Using play currency like monopoly money (or cut up pieces of paper for dollars and beans for coins), give your child a certain amount of “money” and have them shop for a list of items while staying within the budgeted amount.
Teach them how to compare the same products on different ads looking at the price and quantity. Then switch roles and have them create a budget amount for you.
1. Using play currency like monopoly money (or cut up pieces of paper for dollars and beans for coins), give your child a certain amount of “money” and have them shop for a list of items while staying within the budgeted amount. Teach them how to compare the same products on different ads looking at the price and quantity. Then switch roles and have them create a budget amount for you.
2. Give them a list of ingredients for a recipe and let them choose the best-priced ingredients off of the ads.
Use Treats to Count and Learn
It’s pretty much a universal thing, kids love treats! Anytime food is offered as part of a learning activity, they are all ears (or all mouths?!).
Skittles/ M&Ms- Give your child an individual pack or small handful of skittles/M&Ms. Ask them to sort them into colors. Add up the total.
Create addition and subtraction problems by adding just two colors (ie. red and blue) or subtracting the amount of one color from the other. Create a pattern using the different colors.
Graham crackers are great for teaching parts/whole. Give your child a graham cracker and talk about it as being one whole. Have them break it into 2 halves. Then break the 2 halves into 4 fourths. Show how the 2 halves come back together to make 1 whole and 2 fourths make 1 half. Then enjoy the graham crackers with frosting!
Look around your house and find other yummy treats you could use to make math even more fun!


3rd-8th Math and Sciences
Welcome to the Home Learning Toolkit Math and Science resources for your young learner! Our resources are designed to provide a fun and engaging learning experience for young learners. Let's get started on this exciting learning journey together!
Dive into the fun-filled world of Math Playground, where math comes alive with a colorful mix of problem-solving adventures, mathematical art, real-life math mysteries, and brain-tickling thinking games!
If your child needs help with their math homework, check out Plainmath to ask a question and find a solution.
Khan Academy–3-6th grad math and science; Algebra, geometry, biology, chemistry and more! Watch these video for instructions about getting started: getting started for kids 12 and under; getting started for kids 13 and up.
Math Game Time offers engaging math games for pre-K to 7th graders, focusing on key concepts with games like Integer War and Jet Ski Addition, tailored to their grade and Common Core Standards for quick engagement.
Math activities and entertaining games for children, educators, and parents, covering lessons from kindergarten through sixth grade, along with quizzes, brain teasers, and additional content.
Children of all ages and abilities will love the math games, lessons, quizzes, hands-on tools, and puzzles on this engaging website, designed to both educate and entertain.
For over ten years, GCFLearnFree has been empowering millions globally with vital 21st-century skills. Offering tutorials in 190+ topics, including Microsoft Office, email, reading, and math, it's your go-to for essential learning.
Free educational videos for kids! Flashcard-style learning covering math (addition, subtraction), sight words, spelling, shapes, time, months, days, reading, the alphabet, colors, and more.
Ready for your kiddos to thrive in the digital classroom? Explore video content from our online courses and discover how we support students, parents,


|Also, energy costs vary from region to region. If you want to know how much
electricity your space heater uses, you'll need a recent electric bill to work along
with the example.
You'll need two pieces of information from your bill; the amount due for the
current month and the number of kWh (kilowatt hours) used. You can find the
kWh usage in the meter reading section of your bill.
The amount of electricity used by a space heater is measured in watts and
expressed on your utility bill as kilowatt hours (kWh). Technically speaking,
kilowatt hours is the product of power in kilowatts (1000 watts) and time in
hours - not kilowatts per hour. But for the purposes of this explanation,
kilowatts per hour is sufficiently accurate.
Step 1. Determine cost per kWh (kilowatt hour)
The easiest way to do this is divide your total current monthly bill by kWh
Monthly bill ÷ kWh usage = Cost per kWh
This isn't the most accurate way to determine the cost per kWh because all
electric bills include a customer service charge of $6 or more which in effect
increases the cost per kWh by 5-10% depending on the amount of your bill. So
it's up to you, you can either use the full billing amount or subtract the service
charge before you divide it by the kWh usage.
For the examples here I'm going to include the monthly service charge because
you really don't have the option to pay it. I typically spend around $69 a
month for 438 kWh of electricity. When I plug the numbers into the formula
above it looks like this:
69 ÷ 438 = 0.158 So my cost per kilowatt hour is slightly less than 16¢.
Not coincidentally, your cost per kWh equals the cost to run a 1,000 watt
space heater for one hour.
Step 2. Determine the cost to run any wattage space heater per hour
Cost to run space heater per hour = heater watts x .001 x cost per kWh
For a 1,500 watt space heater at a rate of $0.158 per kWh, the formula looks
1,500 x .001 x .158 = .237, or 24¢ per hour rounded up.
Some personal space heaters, like the Toasty Toes Footrest heater, use only
90 watts of power and cost practically nothing to run:
90 x .001 x .158 = .014 or 1½¢ per hour rounded up.
Step 3. Estimate monthly cost to run
Let's say I plan on running my 1,500 watt space heater every day of the month
for 6 hours. This is how to figure out how much to budget for:
$0.24 (per hour) x 6 (hrs) x 30 (days) = $43.20.
How much will you pay?
Electric rates in New England are some of the highest in the country. The
national average according to the EIA is 12½¢ per kWh. So whatever the rate
is in your area, you now have the know how to budget for monthly space
heater use and avoid an unpleasant surprise when you open your electric bill.
How Much Does It Cost To Run A 1,500 Watt Space Heater?
Most electric space heaters and
electric fireplaces are rated at
1,500 watts. This would be the
"high" setting on the heater.
However, most space heaters
also have a "low" setting or a
thermostat, so for the sake of
simplicity we'll assume the
space heater in this example is
operating continuously at the
full power setting of 1,500


Non-Parametric Modeling of Longitudinal Data
Longitudinal data or repeated measurements taken on each of a number of subjects arise frequently in many biomedical applications. The key difference between longitudinal data and cross-sectional data is that longitudinal data are usually correlated within a subject and data analysis must account for the within-subject variation. Linear and nonlinear regression models such as mixed-effects models have been very popular for longitudinal data analysis. However, in many applications, the functional form describing the time patterns of longitudinal data or relationship between a longitudinal response and covariates may not be available, such as for some preliminary data analyses or long-term follow-up studies. In the past decade, semiparametric and nonparametric regression models (including functional or time-varying coefficient models) have been developed for longitudinal data to deal with this problem. Standard nonparametric smoothing techniques such as kernel smoothing, regression splines, smoothing splines and penalized splines have been proposed and adjusted to estimate the nonparametric components or functional coefficients in the semiparametric/nonparametric models for longitudinal data. Functional data analysis techniques with some modifications can also be applied to longitudinal data analysis. Some difficulties in longitudinal data analysis such as missing data issues, lost follow-ups, data truncation and censoring, measurement errors in covariates, and data sparseness from individuals need to be carefully addressed. Other unresolved problems in the area of nonparametric modeling of longitudinal data include hypothesis testing, pattern classification and clustering, model selection and evaluation, and other statistical inferences. Our research group has made great strides in introducing ideas of mixed-effects modeling to semiparametric/nonparametric models for longitudinal data analysis with practical application to biomarker data analysis from AIDS clinical trials. Currently we are trying to develop more practical and useful statistical inference methods for longitudinal data under nonparametric model settings.


This section is a brief digession to illustrate that dummy variables are not the only means of sesonally adjusting data it is interesting to compare this method with. Bradford s jones, uc-davis, dept of political science today: dummy variables and multiplicative regression dummy variables i begin with garden variety regression. Multiple regression with categorical variables dummy coding - making many variables out of one dummy coding with three levels using spss to dummy code variables. Econometrics | chapter 10 | dummy variable models | shalabh, iit kanpur 1 chapter 10 dummy variable models in general, the explanatory variables in any regression.
I have dummy variables (dv) which measure policy reforms (eg independence of the judiciary, barriers-to-entry in a market etc) these can be either “0,1” or. For quick questions email [email protected] no appts necessary during walk-in hrs note: the dss lab is open as long as firestone is open, no appointments. Chapter 7, dummy variable 1 a dummy variable takes on 1 and 0 only the number 1 and 0 have no numerical (quantitative) meaning the two numbers are used to.
How to create dummy variables in spss master it quickly with this simple step-by-step example and try it yourself on a downloadable practice data file. Muitos exemplos de traduções com dummy variable – dicionário português-inglês e busca em milhões de traduções. Pol242 lab manual: exercise 9b regressions with dummy variables and interaction terms part 1: dummy variables purpose to learn how to create dummy variables. The number of dummy variables necessary to represent a single attribute variable is equal dummy variable which is simply the product of the two individual dummy. Pandasget_dummies ¶ pandasget_dummies dtype=none) [source] ¶ convert categorical variable into dummy/indicator variables parameters: data: array-like.
This matlab function returns a matrix d containing zeros and ones, whose columns are dummy variables for the grouping variable group. A dummy variable is a variable that takes on the values 1 and 0 1 means something is true (such as age 25, sex is male, or in the category “very much”. The dummy variable eviews page explains what is a dummy variable while also giving examples of how dummy variables are used. Dummy variables may 29, 2018 1 dummies in regressions (not regressions for dummies) let us remember the unfortunate econometrician who, in. Effects coding in the effects coding system, data are analyzed through comparing one group to all other groups unlike dummy coding, there is no control group.
Dummy variablesintroduction • discuss the use of dummy variables in financial econometrics • examine the issue of normality an. A variable that appears in a calculation only as a placeholder and which disappears completely in the final result for example, in the integral int_0^xf(x. As stated earlier, to consider a categorical variable as a predictor in a regression model, we create indicator variables to represent the categories that.
Chapter 09 - dummy variablespptx - download as powerpoint presentation (ppt / pptx), pdf file (pdf), text file (txt) or view presentation slides online. In situations where we have categorical variables (factors) but need to use them in analytical methods that require numbers (for example, k nearest. Create dummy variables in spss fast with this easy-to-use and freely downloadable tool. Sas example -- dummy variables in regression for both ordinal and nominal variables filename: regress2sas / /use permanent.
We get asked questions on dummy variable creation in eviews fairly regularly, so i thought i'd write up a quick all-inclusive guide simple dummies. The main purpose of “dummy variables” is that they are tools that allow us to represent nominal-level independent variables in statistical techniques like. 5 regression analysis in excel, we want the regression of price on conditions by using two dummy variables x 1 and x 2 i will label them as excellentand good.


Calculus Help Derivatives | Differential Calculus Help
Assignments Help Tutors has employed highly qualified and experienced tutors, experts, professionals and professors from IITs and other prestigious colleges to provide Calculus Help Derivatives. The Calculus Help Derivatives Assignment service provided by Assignments Help Tutors has been acknowledged and appreciated worldwide by students for its 24x7 quality service at a very reasonable Management.
Our tutors of Calculus Help Derivatives Assignment are splendid in their respective domain with experience of working on hundreds and thousands of Calculus Help Derivatives Assignment. Experts of Calculus Help Derivatives Assignment at Assignments Help Tutors use tables, graphs and coordinated data to make the solution more accurate and complete. We are determined to help students understand the core concepts and improve their grades in Calculus Derivatives Help.
In mathematics, differential calculus is a subfield of calculus concerned with the study of the rates at which quantities change. It is one of the two traditional divisions of calculus, the other being integral calculus.
Differential Calculus Types:
Change of variables
The primary objects of study in differential calculus are the derivative of a function, related notions such as the differential, and their applications. The derivative of a function at a chosen input value describes the rate of change of the function near that input value. The process of finding a derivative is called differentiation. Geometrically, the derivative at a point equals the slope of the tangent line to the graph of the function at that point. For a real-valued function of a single real variable, the derivative of a function at a point generally determines the best linear approximation to the function at that point.
Differential calculus and integral calculus are connected by the fundamental theorem of calculus, which states that differentiation is the reverse process to integration.
Ours assignments are backed by authentic writing skill, with complete referencing and are completely plagiarism free. We provide proper in- text citation to cater the requirements of all students in United States, United Kingdom, Australia, UAE and others.
Students who have taken our help in solving Calculus Derivative Help, greatly admire us for offering quality service within given Deadline and Reasonable Management. Experts of Calculus Derivative Help at Assignments Help Tutors are available 24x7 to help students. To get the solution of your Calculus Derivative Help you just need to submit your Differential Calculus Assignment at our '' Submit your Assignment/Homework here '' form.
You can also contact us at " firstname.lastname@example.org " for further clarification and understanding our procedure . We ensure you to offer quality service while dealing with your help with derivatives in calculus. We believe in providing 100 % satisfaction guarantee.
Other recommended pages :
We value our customers and their feedback means the world to us
Best Online Homework Assignment Help service with Best Quality Assignment Solutions at a very Reasonable Price, is what they say and Yes! is what they do. Kudos to AHT for their amazing service. - Victoria, Houston, US


One challenge every baker faces sooner or later is adapting on the fly when the pans a recipe calls for aren't the ones you have on hand. For home bakers, that means you'll need to figure out how to fit your batter into the pans you've got at your disposal. This is a routine calculation for professional bakers, though they come at it from the opposite direction: they'll work backward from the number of cakes they need to the quantity of batter needed and scale the recipe up or down accordingly.
Making the recipe larger or smaller can be complicated for home bakers, so choosing an appropriate pan is usually the easy option. To do that, you'll need to know what the standard measurements are for cake pans and how they relate to each other. I'm a trained chef and sometimes commercial baker, and I have also been a prolific home baker for decades, so I have the background to help you with that. Here's what you need to know.
Read more: 30 Types Of Cake, Explained
Round Cake Pans
The standard round cake pans most recipes call for come in 8- and 9-inch versions, and they're usually 1½ or 2 inches deep. You should never fill cake pans more than ⅔ of the way with batter or half-full for sponge cakes (which rise a little more aggressively), or they may overflow and make a mess.
Since the depth of the batter will be the same regardless of whether it's an 8- or 9-inch pan, you only need to work out its area. For a circle (buckle up, we're going back to geometry class!), you're going to cut the pan's diameter in half to get the radius, multiply the radius by itself, and then multiply that number by pi. It's all coming back to you, right? An 8-inch pan works out to be just over 50 square inches, and a 9-inch pan to 64.
Two 8-inch pans add up to about 100 square inches. Two 9-inch pans total just under 130 inches. If your recipe calls for two 9-inch pans, then three 8-inch pans will hold about the same quantity of batter (it's not exact, but close enough). If the recipe calls for two 8-inch pans and you have 9-inch, you'd need to increase the recipe by about 50 percent.
Square Cake Pans
Like their round siblings, the most common square cake pans are 8 and 9 inches. Figuring out the area for these is easier because you just have to multiply those numbers by themselves. That gives us 64 square inches for 8-inch square pans and 81 square inches for 9-inch pans. In other words, an 8-inch pan is about ¾ the size of a 9-inch. You could bake an 8-inch recipe in a 9-inch pan, but it will be a thinner layer and would bake more quickly. A 9-inch recipe will over-fill an 8-inch pan, but you can keep back part of the batter to make yourself a cupcake or two on the side as a "chef's treat."
It gets more interesting when you adapt between round and square pans. A 9-inch round and an 8-inch square are the same size and can be substituted for each other. A recipe making two 8-inch rounds will yield one 9-inch square cake, with leftover batter for cupcakes.
You may occasionally encounter oversized round or square cakes. You can apply the same math to those to find out how much of your favorite recipe (or box mix) will be needed to fill them. For these oversized cakes, you might find that a heating core helps them bake evenly.
Rectangular Cake Pans
Rectangular cake pans for home bakers come in two main sizes: 7x11 inches and 9x13 inches. To work out their area in square inches, simply multiply their length by their width. This gives us an area of 77 square inches for the 7x11 and 117 square inches for the 9x13 cake pan.
A 9x13, then, is about 50 percent larger than a 7x11. If you're making a recipe written for a 9x13 pan in a 7x11, you'll have enough batter left over for cupcakes or even a thin 8-inch round. If you're scaling up a recipe meant for a 7x11 pan, you'll need 1½ batches to fill a 9x13 instead.
If you're converting between rectangular pans and smaller round or square pans, the neatest substitution to know is that a 7x11-inch cake pan (77 square inches) equals a 9-inch square or 1½ 8-inch round pan. Meanwhile, a 9x13-inch cake pan (117 square inches) is equivalent to two 9-inch rounds or two 8-inch squares and is also equal to one and one-half 9-inch square pan.
These aren't exact equivalents, but they're close enough. The differences in pan size won't usually have a meaningful effect on your baking time, but it's always prudent to check before you think your cake should be done: every oven performs differently, especially when the thermometers are unreliable.
Sheet pans are among the most versatile tools at your disposal, with many uses other than baking. Commercial suppliers list five standard sizes: a full sheet at 18x26 inches, a two-thirds sheet at 16x22 inches, a half-sheet at 13x18, a quarter-sheet at 9½ x 13, and an eighth-sheet at 6½ x 9½. The two-thirds sheet is the largest that will fit in most home ovens, but half-sheets are much more common.
Sizing these, as with rectangular pans, means multiplying their length by their width. For the three sizes you're likely to see in home-baking recipes, that gives us 234 square inches for a half-sheet, 123½ for a quarter-sheet, and 61¾ for an eighth-sheet. Substituting between sheet pans is simple; a half-sheet makes two quarter-sheets or four eighth-sheets, and vice versa (not exactly, but close enough). Most department-store sheet pans are quarter-sheet-sized.
A jelly roll pan (midway between a cake pan and a sheet pan) is 10x15 inches or 150 square inches, so you can use a quarter-sheet as a substitute and have just a little batter left over. A quarter-sheet matches a 9x13 cake pan, so those are direct equivalents. To make a sheet cake from a recipe calling for square or round pans, just multiply the recipe until it matches the size of the sheet pan you plan to use. A half-sheet is about four 9-inch rounds, for example, so you'd double your recipe.
Volume Provides Another Useful Measurement For Cake Pans
Calculating the area of a pan in square inches is a useful way to judge their sizes: for pans small enough or large enough not to show up on your favorite site's conversion charts, it's often the only way to compare. But for common sizes, you may sometimes find it more convenient to adjust by volume.
This is especially useful when you're converting between normal pans and deeper pans, between flat pans and loaf pans, or tube-style pans. You can work out the volume by multiplying the area of a pan by the depth of the batter (two-thirds of its height for most cakes, half-full for sponge cakes) and then dividing by 14.44 (the number of cubic inches in a cup). That takes a bit of "math-ing," but for the most common sizes, you can simply look them up on a chart.
8-inch rounds hold 4 cups (or 6 cups if they're 2 inches deep). 9-inch rounds hold 6 cups (or 8 cups at 2 inches deep). An 8-inch square is the same as a 9-inch round, and a 9-inch square holds 8 cups at 1½ inches' depth (or 10 cups at 2 inches). A rectangular pan at 11x7 also holds 10 cups, and a 13x9 holds 14 cups. With that knowledge in hand, it's easy to work out which size pan to use (or how much to adjust the size of your recipe).
Muffin pans, like loaf pans or Bundt pans, are easiest to work with when we measure in cups rather than working out the cumulative number of square inches in a pan. There are three sizes: standard, jumbo, and mini. A pan may give you as few as six or as many as 24 cups (pro tip: muffin tins have many uses).
The cups of a standard muffin pan have a capacity of 3½ ounces to 3⅘ ounces or almost ½ cup, but — because you need room for your cupcakes to rise — their batter capacity is ¼ cup to ⅓ cup. Mini muffin pans hold about 1½ ounces per cavity or 3 tablespoons, so their batter capacity is 1 to 1½ tablespoons. Jumbos are more variable and can be as small as a 5-ounce capacity to over 8 ounces. The most common size lands at around 7 ounces, or double the capacity of a standard muffin pan (per cup).
A recipe that makes 12 standard muffins or cupcakes will make 6 jumbos. That same recipe can produce up to 36 or 40 minis (you'll get more if your muffins have lots of add-ins). That's also the capacity of a round 8-inch cake pan, approximately 4 cups. A recipe that makes two pans would yield roughly 24 cupcakes.
Bundt Pans And Tube Pans
Bundt and tube pans both form a doughnut shape around a central chimney, which neatly solves the question of how to ensure an evenly baked deep cake. They come in small, medium, and large sizes, typically 7½, 9, and 10 inches in diameter for Bundt pans and 8, 9, and 10 inches for tube pans. Tube pans and the largest Bundt pans are 3 inches deep; smaller Bundt pans are shallower at 2½ inches.
Small, medium, and large tube pans hold 9, 12, and 16 cups of batter, respectively. With Bundt pans, it's 6, 9, and 12 cups (Bundt pans are tapered and patterned, which reduces their capacity). Medium and large Bundt pans correspond to the small and medium tube pans. Remember that 8 and 9-inch rounds hold 4 and 6 cups, respectively, so a recipe that makes 2 layers should fit (respectively) a medium or large Bundt.
It's important to note that while a recipe meant for a Bundt pan can bake in the corresponding tube pan, the opposite isn't always true. Some types of batter aren't "Bundt-friendly" because they'll tear when you try to unmold them.
Character And Other Specialty Pans
When kid birthdays roll around, you may find yourself frantically figuring out how to meet your youngster's request for a cake in the shape of a specific, well-loved character from a cartoon, movie, or TV show. Manufacturers like Wilton have your back with a catalog of pans in character shapes (believe us when we tell you it's easier than sculpting one from scratch!).
For convenience, most of these special-purpose cake pans are sized to hold a standard box-mix cake, which would otherwise make a 9x13 cake pan. A few require two boxes.
If you're a scratch baker, you can treat these special-character pans as a 9x13 for conversion purposes. A recipe sized for a 9x13, two 9-inch round pans, or two 8-inch square pans should do the job, but if the pan looks larger or deeper than most, you might opt to scale up the recipe or make a second batch. Any surplus batter can go to cupcakes.
If you've ever scraped and cussed while coaxing a stuck-on cake out of a pan, then you'll understand why springform pans are a godsend. It's much easier to loosen the sides of a springform and lift out your cake on the removable bottom.
Springforms come in a range of sizes, with 9- and 10-inch pans the most common. You'll also see smaller 6- and 8-inch pans, used mostly for cheesecakes, and occasionally a square or a 9x13 springform, though they're harder to find. A 9-inch springform holds 10 cups of batter, a 10-inch holds 12, but you can also fit 12 cups into a 9-inch springform if it's extra-deep, meaning 3 inches or more.
A recipe that calls for two 9-inch round pans can be baked in a 10-inch springform or a deep 9-inch. A recipe that calls for two 8-inch round pans can be baked in a 9-inch springform. A recipe meant for a conventional 9x13 cake pan can fit a 10-inch springform. In each case, the cake will need to bake longer because of the pan's depth, and you'll usually need to turn down the heat by at least 25 degrees Fahrenheit so the edges won't overbake.
Most loaf pans fall into three standard sizes: 8x4, 8½x4½, and 9x5. A standard bread pan is the middle size, which will bake a 1-pound loaf. The larger 9x5 can bake a loaf using 3½ to 4 cups of flour, again depending on the type of loaf.
The smaller 8x4 size is typically used for loaf cakes rather than bread and holds the same 4 cups of batter as an 8-inch round cake pan. The middle size holds 6 cups, and the larger 9x5 holds 8. If you're switching between loaf cakes and conventional cakes, you can substitute an 8x4 for an 8-inch round, an 8½x4 ½ for a 9-inch round, and a 9x5 for two 8-inch rounds.
You may also have mini loaf pans, usually measuring 5¾x3 ¼ or 5⅝x3 ⅛. These make a ⅜ pound loaf, about 40 percent of a standard 8½-inch bread pan's capacity, or up to 1½ cups of batter. Finally, serious bread bakers might own a so-called Pullman loaf pan. These are longer, at 9 or 13 inches, and are 4 inches wide and high. They have a lid, and they're meant for baking square sandwich bread. A 9-inch Pullman pan holds as much dough as a 9x5 loaf pan, and a 10-inch will hold as much dough as two standard pans
Tart And Quiche Pans
If you've mastered a pie crust (or at least mastered buying them), you can make a tart or quiche just as easily. Tart pans are shallow, usually an inch deep and most are 9¼ or 11 inches in diameter. Quiche pans are deeper, at 1¾ to 2 inches, and are usually in 9- and 10-inch diameters. You may find the deeper pans also labeled as tart pans, though it's quiches that really benefit from the extra depth.
For these, like round cake pans, it's the physical area of the pan that matters, and the math is the same. Pans at 9 inches' diameter check in at just under 64 square inches, 9¼-inch pans at about 67, 10-inch pans at 78½, and 11-inch pans at 95. To make a quiche in a 10-inch pan rather than a 9-inch, then, you'd need about 25 percent more crust and filling. Going the other way you can cut back your recipe by about 15 percent or cook the extra filling as homemade egg bites.
With tarts, if you're scaling up from the smaller pan to the large 11-inch version, you'll need to increase your recipe by about half. Going the other way, reduce it by ⅓ or use the excess pastry and filling to make individual tartlets. For larger or smaller tart pans, the same simple math applies, though the smaller your pan, the more pastry you'll need relative to the amount of filling.
Pie Pans, Aka Pie Plates
A quick visit to a bakers' supply website will show pie pans in sizes up to 12 inches, but the standard-sized ones you find at department stores are most often 8, 9, or 10 inches. Modern recipes are typically written for a 9-inch pie plate, but family recipes are unpredictable. Unless you inherited her own pie plate, you'll have to play it by ear.
To complicate things further, some pie pans are deeper than the standard 1 inch, and their actual diameter can vary significantly from one manufacturer to another. Your best bet is to measure the real diameter of your pan with a measuring tape, and then do the math to see how it compares to the 64 or 78 square inches of standard 9-and 10-inch pans. You can increase or decrease your recipe accordingly.
If math makes your head hurt, don't worry: adapting your plans to match your pan size is a relatively low-stakes game with pies. Fruit pies can simply be piled higher, and with custard pies, you can pinch up your pastry to make a high rim to contain any extra filling. When all else fails, you can also pour any surplus into ramekins and make individual custards. Other factors have a bigger impact, like your choice of material (many experts prefer metal pie tins).
Measuring Non-Standard Pans
Some pans don't fit neatly into these standard categories. Think heart-shaped Valentine's pans, oversized and undersized pans, or vintage pans that may not conform to modern-day standards. To work with those, you'll need to get hands-on and measure them directly.
The simplest way to do this is to fill the pan to an appropriate depth with water or a dry ingredient, like sugar — ⅔ full for most cakes, ½ for sponge cakes. Pour that out into one or more large measuring cups, and that tells you the pan's volume.
If you don't have large measuring cups, you can work with a 1-cup measuring cup and start from the opposite direction: carefully measure 1 cup at a time and pour it into your pan until it reaches the right depth. Write this down for the next time you use that same pan. It's also helpful to make a note of which conventional pan size it corresponds to, so the next time you want to use it, you'll know which size of recipe is appropriate.
Read the original article on Tasting Table


Cars Maths in Motion is online software which simulates the setting up of Formula 1 style racing car. Your students, working in small teams of 4, must complete a series of mathematical challenges in an effort to produce the perfect car. This 'virtual' car is then entered into competitive races against teams from other local schools followed by entry into the summer national competition.
The Maths in Motion project has a proven track record of enhancing attainment and engagement in Mathematics in Year 6 (and able Year 5 pupils) covering areas including:-
The cost for schools to join the Bradford Online League for the 2019-20 season will include: 22.10.19 : Launch & initial training 14.01.20 : Winter face to face race meeting 07.07.20 : Celebration / summer event 4 online races against local schools Access to phone and email support from a consultant Excellent preparation for entering the national competition
- Addition, subtraction, multiplication & divsion
- Decimals, rounding & context
- Ratios,chance, risk & strategy
- Speed, distance& time
- Angles, measurement & scale
- Data handling
- Interpreting graphs & statistics
- Maths modelling...what happens if?
Pupils and teachers will need to attend 3 sessions at the Innovation Centre Bradford on the following afternoons from 12.30-3.00:-
22.10.19 : Launch & initial training 14.01.20 : Winter face to face race meeting 07.07.20 : Celebration / summer event
Primary school staff with 4 pupils


(A) 20 m/s. Horizontal velocity is constant. CORRECT 25. A projectile is fired at an angle of 60 o with an initial speed of 60 m/s. The speed of the projectile at the top of its motion is _____. A. 9.8 m/s B. 30 m/s C. 48 m/s D. 60 m/s JASMINE
(y component of final velocity) 4.What is the magnitude of its velocity when it hits the ground? 5.What is the angle that it hits the ground from the horizontal? A ball is launched from the edge of a 15.0m tall cliff at 16 m/s at an angle of 60 degrees from the horizontal.
Initial angle θ: degree, 0＜θ＜90 ... a projectile is fired vertically upward and reched at height of 125m.find the velocity of projection and time it takes to ...
On a 30-degree slope, subtract 10% of the distance to target. A 300-yard shot would then have the drop component of a 270-yard shot. On a 45-degree slope, subtract 30%. A 300-yard shot would be the drop equivalent of a 210-yard trajectory. A 60-degree angle (almost unheard of when hunting) requires a 50% reduction. Just cut the range in half.
on the fly. The ball is thrown at an initial velocity of 32 m/s and at an initial angle of 27° with respect to the horizontal. If the ball is caught by Todd Zeile at third at the same height as where it was thrown, and the ball is in flight exactly 3.0 seconds,
A bullet is fired horizontally at a height of 1.3 meters at a velocity of 950 m/s. ... at a 45.0° angle and an initial velocity of 625 m/s. ... speed of 70.0 m/s at ...
Elasticsearch search by id


Moved By Maths - 13 ACTIVE Ways to Teach Number Skills
According to one of the most extensive studies on active learning ever conducted, short bursts of physical activity in lessons can increase pupils' fact retention. There are many reasons for this, but the most compelling is the fact movement accelerates the flow of oxygen to the brain. Contrary to centuries of belief that stillness equals focus, it seems the human body enters a sort of 'standby' mode after prolonged sitting. To maximise its potential for learning, it needs to be active.
When children move, their cells get flooded with oxygen. They are more alert, give faster responses and find it easier to engage with challenging concepts. This is particularly evident in maths lessons which require critical thinking and the ability to grasp abstract ideas. It's why child development experts strongly recommend teachers use dynamic activities to teach number skills.
Try these active math games to give your pupils a burst of inspiration and show them numbers can be lots of fun!
1.Simon Says 'Spin!'
How to Play: Put a twist on the traditional game of Simon Says by having pupils respond to directional instructions. Use 'full turn,' 'half turn' and 'quarter turn' to test children's knowledge of basic geometry. If they're confident with this, introduce the words 'clockwise' and anti-clockwise.' Increase the pace of your commands when as children get better at this.
Progression: Older children (KS2 and KS3) may be able to play this game with basic angles such as 90°, 180° and 360°. If your pupils need help, display pictures of these angles so they can use their knowledge of full turns, half turns and quarter turns to figure out the instructions.
2. Hot Potato - Maths Edition!
How to Play: Ask your pupils to stand in a circle. Then, propose a maths question with multiple answers. For example, you might ask pupils to recite the two times table. Or you could ask them to name geometric shapes. Start the game by giving one child a softball or any easily passable object. As soon as he/she passes the ball to the next person in line, the 'clock' starts ticking. This child must provide an answer to the question before the ball makes it all the way around the circle and back to them. When the answer is given, the 'clock' stops. The child holding the ball must now pass the object to restart it and give an answer before it comes back to them.
Progression: Make this game more challenging by requiring pupils to catch and throw the ball. Every time the 'clock' restarts, reverse the direction of play. You could even add a second ball and have two children trying to beat the 'clock' at the same time.
3. Catch It, Count It
How to Play: Use a permanent marker or stickers to write numbers across the surface of a beach ball. Throw the ball to a pupil and ask them to shout out the number their right thumb is touching. They must then throw it to another pupil who repeats the process. However, they must also add their number to the first. Repeat until all of the children have taken a turn or, for a greater challenge, play for five minutes. Continue for five minutes and record the sum. Each time you play the game, add the sum to a graph.
Progression: Every time your class finishes the game, ask them to add the day's total to a week long graph. On which day did you reach the highest number? What about the lowest number? Is there any reason for this or are the numbers random? Could you do anything to influence the total?
4. Student Vote
How to Play: Ask your class an interesting question with multiple potential answers (for example, what is your favourite colour?) Invite pupils to 'vote' by placing a straw in one of several plastic cups, each labelled with one of the answers. The children should then count the votes, record the results and turn them into a pie chart.
Progression: Add even more activity to your lesson on proportions by splitting pupils into pairs - with one counting and one competing. The question: how many lunges can you do in 30secs? Once all the results are in, your pupils can work on turning them into graphs.
5. Messy Maths
How to Play: If you don't mind getting a little messy, use shaving cream to create a 'whiteboard' on pupils' desks. Each child should have enough space (and cream) to solve your maths questions by finger writing them on the desk. This is a great way to get younger pupils excited about counting!
Progression: Ask each pupil to 'reset' their desk (by wiping away the previous answers). They should then write a maths problem on their desk. Instruct each child to move to a different desk or allocate them a desk. They must solve the maths problem on the new desk. Don't forget to check the answers before starting another round.
6. High Rollers
How to Play: Divide pupils into pairs. Give each pair a regular six sided die and two pieces of paper. On their respective pieces of paper, they should draw four squares for the digits they're about to roll. Before playing, decide if the highest or lowest number will win the game (you can alternate between rounds). The pupils take turns rolling the die and filling in the blank squares in any order they choose. Once a number is written, it cannot be changed! The rolling continues until both children have filled their squares. When finished, compare the numbers. If time permits, have students subtract to find the difference between their numbers.
Progression: Set the pairs some challenges to complete with their numbers. Can they add them together? Can they subtract them to find the difference between the two?
7. Shifting Shapes
How to Play: Ask pupils to explore different ways to create and represent shapes. For instance, they could lie on the floor to make a triangle. Or they could use yarn to create a square shape on their desktop. Can they find examples of these shapes in the classroom?
Progression: Give each pupil several pieces of square paper. From their squares, they must form a triangle, a rectangle and a circle. They can draw on the paper but, the rule is they can only draw ONE line. They need to form their shapes using one continuous line on the paper (no lifting and replacing the pen). Encourage your pupils to pause and really think about their strategies. Once decided, they can use folds (no scissors) or cuts (with safety scissors) to create the shape.
8. Listen to the Leader
How to Play: This activity is best played in the playground or school gym where there's lots of space. Divide your pupils into small teams or pairs. One child from each team will be the Listener, the other(s) will act as the Leader. The Leader must direct the Listener along a prespecified route across the space and back to the rest of the group. However, they may only use turn based directions - 90°, 180°, 360°, clockwise, anti-clockwise.
Progression: If you're confident in the safety of the space and your pupils' movement skills, introduce some obstacles to the route or - for a serious challenge - blindfold the Listener.
9. Card Sharks
How to Play: Divide your pupils into pairs. Give each pair a deck of cards. Just like in any card game, each card corresponds to a number (2 through to 10, leave out the picture cards). Playing in pairs, each pupil takes two cards from the deck and lays them face up. They must subtract the lower number from the higher number. The pupil with the highest number wins and gets to keep all four cards. If the totals end up the same, the players take two more cards. Repeat until all the cards have been won.
Progression: If your pupils are confident with using and recognising the cards, bring back the ace, jack, queen and king. This should make the game a little trickier because it re-introduces some larger numbers.
10. One Meter Challenge
How to Play: Split your pupils into small groups of 3-4. Give each group a metre stick, a pencil and a piece of paper. Children get two minutes to look around the classroom and write down three items they think will add up to a metre in length (in total). They must not touch or handle the items before the teacher says it's allowed. On the call of 'Go,' they have five minutes to measure their three items, record the lengths (in cms) and add up the total. The group that comes closest to one metre wins.
Progression: Using their measuring stick as a guide, can your pupils find objects that are half a metre, a quarter of a metre, and three quarters of a metre?
11. Weighing In
How to Play: Arrange a variety of fruits and vegetables in your classroom - oranges, bananas, potatoes, grapes, tomatoes, etc. Ask pupils to write the names of the foods in order of weight, from lightest to heaviest. Then, use a small scale to weigh each item and reveal its actual density. Once finished, ask the children to rearrange the foods in the correct order.
Progression: Carefully cut each fruit or vegetable into two pieces. Ask your pupils to look inside and make notes about what they see. How do they think the inside of a fruit or vegetable affects its weight? What do the lightest items look like inside? Are they different from the heavier foods?
12. Round 'Em Up
How to Play: There are lots of playground games you can use to reinforce number skills. For instance, one activity is to get your pupils to run around in a large space and shout out various numbers. This might be the number of people you want them to get into a group with or the number of arms and legs you want in a group.
Progression: Extend this for skilled pupils by using challenging commands like 'get into a multiple of three' or even 'get into a squared number.'
13. Twister Math
How to Play: Attach labels with the names of numbers to a Twister mat. Each pupil who plays is given a number and must create it on the mat by placing their hands and feet in the correct spots. For this to work, you'll need several mats or you'll need to split pupils into teams and have a new team play each round.
Progression: Label the Twister mat only with numbers ending in zero. This time, the pupils have to identify the right sum to create the number called by the teacher. Then, they've got to round it up or down to the nearest zero-ending number on the mat.


Relatively Prime Numbers
This is a very simple method to find prime numbers. I use a mathematical function to find non prime numbers. Thus I have compared its efficiency with a code found on Matlab Central, Written by John D'Errico.
|License: Shareware||Cost: $0.00 USD||Size: 51.2 KB||Download (18): Method to find prime numbers Download|
this is a small basic file to generate the prime numbers within a given limit, starting from 3
|License: Shareware||Cost: $0.00 USD||Size: 10 KB||Download (19): generate prime numbers Download|
PrimeNumbersInformer is a small, simple, command prompt based application specially designed to help users learn the prime numbers.
Once you've opened the app, just enter the limit number and PrimeNumbersInformer will create a TXT file with the prime numbers.
|License: Freeware||Download (56): PrimeNumbersInformer Download|
How many do you know the prime number? Let's memorize prime numbers. How to play is easy. From among the numbers appear, touch the only prime numbers. When you touch the number that is not a prime number and miss a prime number, it becomes the mistake, and stars decrease. When a star is lost,...
|License: Freeware||Size: 2.4 MB||Download (7): 997 - Prime Numbers - Download|
Touch a quick prime numbers! "Touch the Prime Numbers" is a simple game! Prime Numbers 2,3,5 7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97 Let's try! Game Center introduction. Respect "Touch the Numbers"!! Requirements: iOS 3.1.3 or later. Compatible with iPhone, iPad,...
|License: Freeware||Size: 1.7 MB||Download (7): Touch the Prime Numbers Download|
Prime Validator validates prime numbers and finds prime numbers to a given upper limit. If you are searching for this kind of app, you already know about the importance of prime numbers ;-) The only one in the store. # - super fast # - best user interface # - supports biggest numbers # - no...
Platforms: Windows Phone
|License: Freeware||Size: 2 MB||Download (7): Prime Numbers Validator Download|
This is a fast prime number list generator using sieve algorithm. This function returns a list of prime numbers which are lower than a specified argument.
Platforms: Windows, Mac, *nix, Python, BSD Solaris
|License: Freeware||Download (43): A fast prime number list generator Download|
Lists all Prime Numbers, also allows you to enter a number and check if it is a prime number. If not - it will show all factors of the number.
|License: Freeware||Size: 1024 KB||Download (217): Prime Number Finder Download|
This utility will interest you if you like to work with prime numbers. It has two modes. Mode A finds primes starting at a number of your choice. Mode B finds all primes between a start number and a stop number. It calculates and displays the time it takes to complete your request.
|License: Freeware||Size: 2.5 MB||Download (84): Prime Number Generator Download|
A simple Cocoa application that finds, counts and lists all prime numbers from two to an arbitrary, user-inputed number. It is a universal binary and a timer is included: therefore, if nothing else, it may be used as a benchmarking utility.
|License: Freeware||Size: 86 KB||Download (89): Prime Finder Download|
PNGPython is a simple and useful program built using the Python programming language, that can help you calculate prime numbers.
The program will ask you the amount of prime numbers you want. Also displayed in the application is the amount of time it took the program to execute.
|License: Freeware||Download (58): PNGPython Download|
Prime2 was designed as a small, simple and accessible application that is able to calculate prime numbers using the new Fork/Join framework of Java 7.
You can also select the number of cores you want to use in order to calculate your prime numbers.
|License: Freeware||Download (97): Prime2 Download|
Prime95 is a program designed to be used to find Mersenne Prime numbers. Mersenne numbers can be proved composite (not prime) by either finding a factor or by running a Lucas-Lehmer primality test.
Prime numbers have long fascinated amateur and professional mathematicians. An integer greater...
|License: Freeware||Size: 3.7 MB||Download (123): Prime95 26.5 Build Download|
This is a card game where the objective is to win tricks by forming prime numbers on the table. The game is played with composite cards: 4, 8, 10, 20, 25, 26 each with respectively 10, 4, 4, 2, 2, 2 cards and operation cards: -2, +1, +7 each with 12 cards, making a total of 60 cards. At the start...
|License: Shareware||Cost: $0.00 USD||Size: 183.3 KB||Download (18): Prime Cards Download|
A program to find all factors of any positive integer less than 2^31 - 2, to decompose numbers into their prime constituents, to find prime numbers and pairs of primes, and to plot Erdos-Kac and Palmen Color histograms.
|License: Shareware||Cost: $15.00 USD||Size: 1.69 MB||Download (87): Factorizer Download|
Math, financials, stats, combinative, dates, y=f(x), series, units and calendars conversions, geometry, pi, Fourier, Taylor, Gamma, Bessel, Bernoulli, Fisher, prime numbers, fractionations, equations, electricity, chemistry, molar masses, currencies. Divx Bitrate Calculator. Advanced astronomy...
|License: Freeware||Size: 7.63 MB||Download (695): Khi 3 Download|
|License: Freeware||Size: 270 KB||Download (100): PrimeNumbers Download|
Powerful Calculator for Finance, Science, Math, Stats, Unit Conversions, Date and Time Calculations, Numeric Bases, Bit-Level Operations, Complex Numbers, Random Numbers, Prime Numbers, Fractions, Trigonometry, NIST Scientific Constants. Quick Popup Access. Selectable Keypads, Button Size, Font,...
|License: Shareware||Cost: $15.00 USD||Size: 367 KB||Download (80): AddUp Download|
Sprimer is a mathematical tool designed to look for prime number patterns. The exceptional qualities of prime numbers make searching for them a mathematical constant, and this program can help you do it.To do this, Sprimer plots numbers on a grid and makes spiral movements from the centre out....
|License: Freeware||Size: 1024 B||Download (100): Sprimer Download|
AP26 searches for Arithmetic Progressions of prime numbers. The code was written by Jaroslaw Wroblewski and Geoff Reynolds, with the Mac port by Iain Bethune. To date, the largest known progression contains 26 primes, and was found in 2010 by Benoat Perichon using the AP26 software as part of...
|License: Freeware||Size: 348.16 KB||Download (16): AP26 Download|


Online Sic bo in Sri Lanka
Sic bo has been around for many years first derived from the Chinese. Its popularity has ensured that it’s made its way to land based as well as online casinos. This Sic bo game is played with dice and depends a lot on the number sequences it lands on once rolled. Look on our website for a list of Sic bo online casinos suitable for Sri Lankan players. Only the best has been listed taking into consideration fast and secure banking transactions as well as loads of online casino bonuses and promotions to take advantage of.
At first glance you will see a board laced with numbers and dice faces. You might be turned off by the complex look of the game but that really could be further from the truth. This age old game is quite simple to grasp once you understand how to play the Sic bo game. Sic bo online is played with 3 dice; the dice will be scrambled in a virtual metal cage and released onto the board. The values that the dice land on are what predict your fate. Before the dice is rolled you will need to place a bet on what you think the outcome of the dice roll will be, if you’ve predicted correctly you have one the round.
|1||5/5||250% + 33 Free Spins|| Play now|
|2||4.9/5||$1000|| Play now|
|3||4.8/5||$1600|| Play now|
|4||4.7/5||$350|| Play now|
|5||4.6/5||$750|| Play now|
|6||4.5/5||$1000|| Play now|
The aim of the Sic bo game is to predict how much the dice will total up to once rolled. All 3 dice will land on a certain number, add those numbers up and that’s what you will bet on. You can bet on more than just that including the total value of all 3 dice, a single number, any 2 specific numbers, or a combination of numbers that the dice will land on. Online Sic bo pays out quite handsomely starting from 1:1 to 180:1 payouts. You can place more than one bet to increase your chances of winning.
Winning Online Sic bo Bets
Knowing the Sic bo odds when playing any online casino game is paramount when planning a big win. It’s said that betting on numbers 8, 10, 11 and 13 have the lowest payouts so you might want to skip these if you’re new to online Sic bo. The single bet is when you predict that the dice will land on one specific number, if its correct the payout is 1:1, if 2 of the dice land on that number the payout will be 2:1, and if by chance all 3 of the dice land on that number the payout will be 12:1. A double bet is when you predict that 2 of the dice will land on the same number; the payout in this case is 10:1. A triple bet is when you predict that all 3 of the dice lands on a set of numbers, the payout here is 180:1, if you place a bet that all 3 of the dice land on the same number i.e. a triple the payout will be 30:1. The ‘small and big’ bet is when you predict that the 3 dice will total an amount between 4 – 10 or between 11 – 17. If you bet on a combination bet which is predicting that the dice will land on 2 specific numbers the payout here will be 6:1. A total bet is when you predict that the total of all 3 dice will equal between 4 – 17.
Sri Lankan players should choose one of the best casinos listed on our website to play Sri Lanka online Sic bo and win big.


6th grade students who have a passion for math are encouraged to join Math Masters Club! We will have weekly practices from October-March and will attend 2 local Math Masters meets during the season with potential to advance to the Regional meet in March. Students will practice and utilize problem-solving, critical thinking & collaboration skills to solve challenging math problems. Coaches will foster a passion for math and will promote positive collaboration and friendly competition with HMS peers and students from other schools in Wisconsin. First meeting is October 12.
Mrs. Juneski and Mrs. Engstrom-Yde
Room 135 Raider White (Mrs. Juneski's Room)
- First meeting is October 12, 2018
- Meets weekly on Fridays from 3:00 p.m. – 3:40 p.m.


How Much Is $700 Billion?
It's a big number, but everyone was so concerned with who was supporting or opposing it, and panicking about potential bank failures (that and we're used to large sums of money being thrown around by the government) that no one stopped to ask how big it was. I decided to ask Google, and ran across an article that broke things down:
It is one third of the total amount of money received by the federal government in 2007, including social security, income tax, corporate tax, and all other receipts.
It is $140 billion more than has been spent on the Iraq war since the invasion.
It is $120 billion more than that spent on social security benefits.
It is almost 3 billion nonrefundable bus fares from Durham to San Francisco, leaving tomorrow.
It is nine times the amount spent on education in 2007.
It could pay for 2,000 McDonald's apple pies for every single American.
It is 35 times the amount spent on all foreign aid in most years.
It is more zeros than the calculator that comes with my computer allows.
It is 7,000 times bigger than the Sierra club’s yearly budget.
According to some estimates, it is three times what it would cost, over 10 years, to reduce oil dependency by 20%.
Its over twice the amount of all money given to all charitable organizations in the United States in any given year.
It is more than $100 for every person in the world.
I did some calculating myself, to add to those numbers. $700 billion is approximately 1/14th of the national debt.
If I started giving you $100 every second, it would take you about 222 years to accumulate $700 billion. (31,556,926 seconds in a year times $100, then divide $700 billion by that number.)
It is 4,666 times larger than an estimated total of all the websites on the internet.
It takes ten million $100 dollar bills just to reach a billion, so it would take 7,000,000,000 $100 dollar bills, which would weigh about 6800 TONS.
If you spent a million dollars a day, it would take you 1,917 years to spend $700 billion.
You would have to have 661 MILES of hundred dollar bills stacked up to get $700 billion. (Based on calculations about Bill Gates' 20 billion here.)
Your federal government hard at play with your hard-earned money.
Aww, why so sad?
The Washington Post has a nice breakdown of the allocation


The kindergarten classes at IAA have been exploring the work of American Artist Jasper Johns, whose mixed media paintings greatly influenced American art. Johns often worked with images you might see around the classroom, such as letters, numbers, and the American flag. His paintings encourage us to look again at these familiar symbols, as if with new eyes. As a way to reinforce numeracy and to practice number formation students created number paintings in the style of Jasper Johns. Each student chose one number to paint repeatedly and used the entire surface of the paper. In some instances the brush strokes and the paint color camouflages the numbers making it even more fun to look at and find the numbers. Can you spy the number in each painting?
Vermont Standards -Visual Arts Skill Development
APK-K:10 Students show skill development when CREATING art by
• using line to create shape and image,
• handling art tools and materials (e.g. paint brushes)
• using elements of 2D design (e.g., create using color)
Vocabulary: artist, line, color, rhythm, repeated, texture, overlapping, abstract, painting
Common Core – Kindergarten- Counting and Cardinality
Know number names and the count sequence
• K.CC. 3 Write numbers from 0 to 20.
“I like to create an image that when looked at becomes something else.”


Asphalt calculator advanced does a really good job calculating your asphalt tonnage or concrete yards, the estimated tonnage calculated by the app uses a formula of how many square yards 1 ton of asphalt will cover, making it really accurate.
The concrete calculator has columns or sonotubes and triangle calculation, this app is a must have for your daily asphalt or concrete work. no database at the moment for concrete and more features coming soon!..
Asphalt Calculator Advanced by Soteksa is your number 1 calculator.
We will gladly answer any question you may have or if you want to report a bug in the app, feel free to contact us any time.


Strict Average versus Power-law
We would logically assume that students proficiency in a particular skill will improve over time. Thus, as their skill improves their score on assessments for that skill should increase.
The strict average weights all attempts equally, so that the first attempt is just as important as the most recent attempt; even though the student may have made great improvements in that particular area.
The power-law operates under the assumption that as students make improvements in the skill area, their summary score for that skill should improve and follow their assessment scores as they improve.
Consider a student who, on 4 assessments on the same skill scored 0, 2, 3, and 3.5 respectively. As we would expect, their score increased over time. The strict average for their 4 scores is 2.125. The question is: Does 2.125 summarize their current proficiency? It most certainly does not, when one takes into consideration their continuing improvement and their most recent score.
The power law, on the other hand, follows their improving scores and leads to a summary grade of 3.5.
On the graph below you can see the student's scores as blue boxes, the power-law curve in red, and the average in green.
The beautiful part about the power-law is that it not only summarizes the students current proficiency level, it also mathematically can be followed backward to show how the students proficiency has changed over time.
Why not just use one summative score as the student's proficiency level?
Two reasons: students don't always perform to the best of their abilities every day and in every measurement there is some amount of uncertainty. Tracking progress over time helps to smooth out the effects of both of these variables.
What if the student's scores aren't so predictable?
As I just mentioned, there are things that make scores vary. There is a certain amount of uncertainty in every measurement. We can assume that every assessment score is accurate within a certain amount of confidence. Thus, if we take the scores over time we can follow the trend and find the closest fitting power-law to summarize the student's proficiency.
The graph below shows another student who scored 1, 3, 3, and 2 on a series of assessments on the same skill. The student's strict average (shown in green) comes out to 2.25. The power-law, in blue, follows an exponential curve that most closely fits the student's scores, showing that over time the student's scores are improving and that we have mathematical evidence to report their proficiency in this skill as 2.75 (the red dot on the power-law curve). It also gives us a prediction that if the student were to attempt the skill again, we would expect them to score around 3.
What if a student's score decreases over time?
This does happen, unfortunately. In those cases the power-law follows their grade downward and gives them a less-than favorable summary. In these instances, the strict-average gives the student a better overall score. Progradebook.com gives you the option to summarize each individual standard by the Power-law, the strict average, or to choose which method gives the student the best outcome.


Mathematics Training and Talent Search Programme
The aim of the MTTS programme is to expose bright young students to the excitement of doing mathematics, to promote independent mathematical thinking and to prepare them for higher aspects of mathematics. The Mathematics Training and Talent Search Programme or MTTS is a summer training programme in India for mathematics, started at the B.Sc. (undergraduate) level, aimed to expose bright young minds to mathematics and equip them better for Ph.D. studies. It is funded by the National Board for Higher Mathematics, India. The organizer is Professor S. Kumaresan.
MTTS programme will be at three levels : Level 0, Level I and Level II.
- In Level 0 there will be courses in Linear Algebra, Analysis and Number Theory / Discrete Mathematics.
- In Levels I and II there will be courses on Algebra, Analysis and Topology. There will be seminars by students at all Levels.
MTTS Selection Process :
MTTS selection will be purely on merit, based on consistently good academic record and the recommendation letter from a mathematics professor closely acquainted with the candidate. Only selected candidates will be informed of their selection by the 14 - 20th March, 2012.
The list of selected candidates will be posted on the MTTS site.
Candidates selected for the MTTS programme will be paid sleeper class return train fare by the shortest route and will be provided with free board and lodging for the duration of the MTTS course.
Towards the Department of Mathematics, I will Coordinate MTTS programme for the year 2011-2012.
- We will select the student coordinators from each section and educate them about the MTTS programme.
- The student coordinators will explain and motivate their respective class students
- We will select the students for attending this programme based on their marks secured in Mathematics from 10th class onwards as per the eligibility criteria
- Also those students who are interested in doing research in mathematics
- We will select nearly 30 students for all levels both from UG & PG. We will train them from the beginning of the academic year. We assign some seminars in the regular classes and assign marks to their seminars. While sending the order of priority of the students to attend the Programme, we consider these marks.
Coordintor: P. Chandrakala


1 edition of Advanced Algebra found in the catalog.
by Scott Foresman Addison Wesley
|The Physical Object|
Experience our interactive, profoundly engaging digital publication! SAMPLER Table of Contents for the Digital Edition of Financial Algebra: Advanced Algebra with . Pre-algebra and algebra lessons, from negative numbers through pre-calculus. Grouped by level of study. Lessons are practical in nature informal in tone, and contain many worked examples and warnings about problem areas and probable "trick" questions.
Free textbooks (aka open textbooks) written by knowledgable scholars are a relatively new phenomenon. Below, find a meta list of Free Math Textbooks, part of our larger collection Free Textbooks: A Meta see our online collection, 1, Free Online Courses from Top Universities.. Abstract Algebra: The Basic Graduate Year by Robert B. Ash, University of . These values divide the number line into four intervals. Choose a test number from each interval and determine whether the product is positive or negative. For this problem, we will use -5, -1, 1, and 2 as test numbers. Substitute these values into the original polynomial. 4 (-5) 3 +10 (-5) 2 (-5) 4 (-1) 3 +10 (-1) 2 (-1).
Algebra and Trigonometry provides a comprehensive and multi-layered exploration of algebraic principles. The text is suitable for a typical introductory Algebra & Trigonometry course, and was developed to be used flexibly. The modular approach and the richness of content ensures that the book meets the needs of a variety of a and Trigonometry guides and supports /5(14). Traditionally, the study of algebra is separated into a two parts, Elementary and Intermediate Algebra. This textbook by John Redden, Intermediate Algebra, is the second part. Written in a clear and concise manner, it carefully builds on the basics learned in Elementary Algebra and introduces the more advanced topics required for further study /5(1).
Paris and environs
Expressing sympathy for the victims of the devastating earthquakes that struck El Salvador on January 13, 2001, and February 13, 2001, and supporting ongoing ... session, on H. Con. Res. 41, March 14, 2001
H.R. 4243, Government Waste, Fraud, and Error Reduction Act of 1998; H.R. 2347, the Federal Benefit Verification and Integrity Act; and H.R. 2063, the Debt Collection Wage Information Act of 1997
The Faces of Clio
Chinese Cooking for Busy People
The Oz Sound-Book
Pillow lace in the East Midlands.
Balance of intrigue
Sculptures of Śeṣaśāyī Viṣṇu
1978 census of agriculture, preliminary report, Bay County, Mich.
Rage in the Gate City
Cakes, cookies and cake icings for quantity cookery
Out of 5 stars great advanced linear algebra book. Reviewed in the United States on Novem Verified Purchase. This is a great linear algebra book for anyone who has already had an undergraduate course in linear algebra.
It would help even more if the reader has already had at least one semester of abstract algebra (modern algebra).Cited by: We would like to show you a description here but the site won’t allow more. Advanced Linear Algebra (Graduate Texts in Mathematics Book ) - Kindle edition by Roman, Steven.
Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Advanced Linear Algebra (Graduate Texts in Mathematics Book )/5(16). This is the table of contents for the book Advanced Algebra (v. For more details on it (including licensing), click here.
This book is licensed under a. $\begingroup$ @user see Roman's Advanced Linear Algebra. It's really nice for abstract linear algebra. If matrix theory is what you're after, perhaps Carl Meyer's text is a nice choice, I don't have a copy personally, but the folks who use it know better than I on these matters.
$\endgroup$ – James S. Cook Jul 1 '13 at Quickies in Advanced Algebra Tensor products and free modules 3 1. Tensor Products and Free Modules Modules. Deﬁnition Let Rbe a ring (always associative with unit element). A left R-module RM is an Abelian group M(with composition written File Size: KB.
Basic Algebra The Laws of Algebra Terminology and Notation. In this section we review the notations used in algebra. Some are peculiar to this book. For example the notation A:= B indicates that the equality holds by de nition of the notations involved.
Two other notations which will become important when we solve equations are =) and (). upper level math. high school math. social sciences. literature and english. foreign languages. The LibreTexts libraries are Powered by MindTouch ® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot.
We also acknowledge previous National Science Foundation support under grant numbers. Advanced Linear Algebra. Authors: Roman, Steven Free Preview. Contains topics that are not generally found in linear algebra books "This is the 3rd edition of a well written graduate book on linear algebra.
The book covers a wide range of topics in a moderate length and careful manner. The list of references has been enlarged Brand: Springer-Verlag New York.
"Advanced Algebra is a wonderfully useful and well-written book, characterized by clear and ‘user-friendly’ treatments of many important algebraic topics. Finally, Advanced Algebra contains a thorough coverage of Gröbner bases and continues the trend set in Basic Algebra of providing good, meaningful (and plentiful) exercises.
I Brand: Birkhäuser Basel. Every time I’ve taught the course (undergraduate), I’ve been saddled with someone else’s choice of text. And they’ve generally been isomorphic (the same) and not particularly inspiring. So I’m going with speculation here - in terms of what I think. Online books on:Free Algebra Books Download Free Algebra Ebooks Online downloadable e-books downloads zip chm rar.
Editor's Notes. J Our latest update saw the newest edition of Algebra For College Students, as well as the addition of McDougal Littell Algebra 2 at the expense of Algebra 2 Common Core. Algebra 2 Common Core is still a more than adequate selection, but we felt that as the McDougal Littell version is a classic among many school districts and a much.
Betst linear algebra books I would suggest starting with a basic level textbook and then put more effort on one or two intermediate level textbooks. Advanced level books may not be a good source for study. Basic Introduction to Linear Algebra 5th Edition by Gilbert Strang This is an erudite and discursive introduction to linear [ ].
Put 2 periods between the numbers and add a unit of measure: lb, $$, Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established.
Together, the two books give the reader a global view of algebra and its role in mathematics as a whole. Key topics and features of Advanced Algebra: *Topics build upon the linear algebra, group theory. When I studied algebra, my teacher told the class that we could reasonably expect to spend thirty minutes per page to master the material in the old algebra book we used.
With the book you are holding, you will need two reading speeds: slower when you're learning algebra and faster when y’ enjoying the life adventures of Fred. Advanced Algebra book.
Read reviews from world’s largest community for readers. Basic Algebra and Advanced Algebra systematically develop concepts and to 4/5(4). Hello Friends, Today we are going to share a book for our future Engineers who are preparing for IIT JEE Examinations, and the name of this book is SK Goyal Algebra Pdf Download For IIT JEE, Mains and Advanced is a very popular and useful book for IIT JEE, you can learn all the concepts of Algebra without any help of coaching center, SK Goyal sir provides all type of.
I'm taking an advanced linear algebra course and I'm a little confused about books. The teacher said we could use any book we wanted to, but he recomended just Hoffman and Kunze and also Kostrikin, however, those seem to be not quite sufficient since it seems he's teaching in a little more advanced way.that students have already arrived and so in contrast with more advanced texts this book is ﬁlled with illustrations of the theory, often quite detailed illustrations.Big Ideas Math A Common Core Curriculum Big Ideas Math: Modeling Real Life.
Big Ideas Math Algebra II: Virginia Big Ideas Math Course 2: Virginia Big Ideas Math Course 3: Virginia Big Ideas Math Course 1: Virginia Big Ideas Math: Modeling Real Life .


Personal Loan Calculator
Without a calculator, it can be tricky to figure out how expensive your loan will be. Use ours and see your rate and payment for each month.
Here’s a little information about how our calculator works.
You’re first asked to enter your Loan Amount, or what you hope to borrow minus the interest you’ll need to pay. For example, if you’re using the loan to make a home repair that will cost $10,000, then you would enter $10,000 into the Loan Amount field.
Next, you enter your Interest Rate.
If you haven’t found a loan provider yet, then you probably won’t know the interest rate associated with your loan. At LoanStart.com, we try to help you find lenders and lending partners who offer interest rates starting at 4.84 percent, and going up to 35.99 percent. Try entering numbers within that range to get an idea of how these rates would affect your loan payments.
The last number is your Loan Term. This is the years that your loan will last. At LoanStart.com, we work with lenders and lending partners who offer two to seven-year loans.
After you enter your Loan Amount, Interest Rate, and Loan Term information, you’ll be ready to hit the orange “CALCULATE” button.
Our personal loan calculator shows you your Monthly Payment, Total Paid, and the Total Interest Paid amounts based on the numbers you entered. Please note that your loan may have additional fees that are not represented by our totals. Because of this, you should use our calculator for educational purposes only.
Your Monthly Payment is the amount you would pay your loan provider each month throughout the life of the loan. The Total Paid shows how much you would have paid the lender (if you did not encounter any extra fees). The Total Interest Paid shows how much you would pay in interest over the life of your loan.
What is an Amortization Schedule Calculator?
Our personal loan calculator assumes that you will be using an amortizing loan. With an amortizing loan, each payment you make goes toward the interest and the principle. Throughout the life of your loan, the ratio will change, but your monthly payment should stay the same. At the beginning of your loan, most of your monthly payment will pay off the interest, but toward the end, the majority will pay off the principle.
To determine your monthly payment (MP), our calculator uses the following formula, where “i” is the monthly interest rate, “LA” is the original loan amount, and “N” is the number of total monthly payments:
MP = i x LA x (1 + i)N / (1 + i)N - 1
After you know your monthly payment, it’s easy to figure out everything else. To determine the total amount paid, you just multiply your monthly payment by the number of months in your loan term. Then, to figure out the total amount of interest paid, you subtract your original loan amount from the total amount paid. Or, just let our calculator do those things for you.
What if I Have More Data to Enter?
We offer a basic tool that helps you get a general idea of what you might pay for a loan. Your loan might include fees that cannot be entered into our calculator. You can still use our tool to compare loan interest rates quickly. Just know that you’ll need to consult your loan agreement to see your actual rates and fees.


“I can’t do maths” is all too common a sentiment, and any maths educator knows. I’m left wondering where the skills this country has built over the centuries have departed. In Birmingham we have a statue dedicated to Watt, Boulton and Murdoch, prime movers in the technology of the late eighteenth century. They also knew how to make money. They couldn’t do this without a solid grasp of mathematics.
This solid grasp eludes many people brought up via the education system current in this country. We know we have the highest pass rate ever in GCSEs, or so we are told, but looking at the actual exam scores there is a significant decline to achieve this pass rate. You may at this time hear the galloping of a hobby horse, but we are experiencing a significant number of students who have difficulty with understanding both mathematics itself and the necessity of being proficient in mathematics to be able to succeed in business.
I’ve been seeing this problem for many years, starting in industry before I joined the University. Many graduates younger than I seemed to have a lack of an innate understanding of quantity. It’s unsurprising that many universities (half, according to The Telegraph) have to run classes for first year student to remedy gaps in knowledge in Maths and English. “Initiatives” and “Intervention” do not, I believe, work. They are demonstrably not producing people who are proficient. Alleged numeracy hours in schools will take a long time to work though the system. But if numeracy is being taught by people who themselves have difficulty with maths, where are we heading? Ever decreasing circles seems a probability.
(This blog post was formerly known as “Hello World!”)


Round-robin is a pairing-system. It means you play against everyone in the tourney. The number of players determines how many rounds.
Example: 8 players would be 7 rounds.
To determine the final standings, the following tie-breaks are used:
- Sum of scores of opponents, but adjusted in the following way:
- If an opponent does not play a round, it counts as if he scored 0.5 in that round. This holds for latejoin rounds, bye rounds, forfeits or games set by the manager
- Average rating of opponents
- Random number given at start of tournament


1 the quality of nearness to the truth or the true value; "he was beginning to doubt the accuracy of his compass"; "the lawyer questioned the truth of my account" [syn: truth] [ant: inaccuracy]
2 (mathematics) the number of significant figures given in a number; "the atomic clock enabled scientists to measure time with much greater accuracy"
- The state of being accurate; freedom from mistakes, this exemption arising from
conformity to truth, or to a rule or model; precision; exactness; nicety; correctness
- The value of testimony depends on its accuracy.
state of being accurate
- Czech: přesnost
- Finnish: tarkkuus
- French: exactitude
- German: Genauigkeit
- Hungarian: pontosság, helyesség, precizitás
- Indonesian: ketelitian, ketepatan, kecermatan, keakuratan
- Interlingua: exactitude, precision
- Italian: esattezza
- Japanese: 正確性 (せいかくせい, seikaku-sei), 正確さ (せいかくさ, seikaku-sa), 精密性 (せいみつせい, seimitsu-sei), 精密さ (せいみつさ, seimitsu-sa), 確度 (kakudo)
- Maltese: eżattezza
- Norwegian: nøyaktighet
- Polish: dokładność
- Portuguese: exatidão, precisão, correção
- Romanian: precizie , acuratete
- Spanish: exactitud
- Swedish: noggrannhet
- Telugu: ఖచ్చితత్వం (khachchitatvam)
In the fields of science, engineering, industry and statistics, accuracy is the degree of conformity of a measured or calculated quantity to its actual (true) value. Accuracy is closely related to precision, also called reproducibility or repeatability, the degree to which further measurements or calculations show the same or similar results. The results of calculations or a measurement can be accurate but not precise; precise but not accurate; neither; or both. A result is called valid if it is both accurate and precise. The related terms in surveying are error (random variability in research) and bias (non-random or directed effects caused by a factor or factors unrelated by the independent variable).
Accuracy vs precision - the target analogy
In many cases precision can be characterised in terms of the standard deviation of the measurements, sometimes incorrectly called the measurement process's standard error. The smaller the standard deviation, the higher the precision. In some literature, precision is defined as the reciprocal of variance, while many others still confuse precision with the confidence interval. The interval defined by the standard deviation is the 68.3% ("one sigma") confidence interval of the measurements. If enough measurements have been made to accurately estimate the standard deviation of the process, and if the measurement process produces normally distributed errors, then it is likely that 68.3% of the time, the true value of the measured property will lie within one standard deviation, 95.4% of the time it will lie within two standard deviations, and 99.7% of the time it will lie within three standard deviations of the measured value.
This also applies when measurements are repeated and averaged. In that case, the term standard error is properly applied: the precision of the average is equal to the known standard deviation of the process divided by the square root of the number of measurements averaged. Further, the central limit theorem shows that the probability distribution of the averaged measurements will be closer to a normal distribution than that of individual measurements.
With regard to accuracy we can distinguish:
A common convention in science and engineering is to express accuracy and/or precision implicitly by means of significant figures. Here, when not explicitly stated, the margin of error is understood to be one-half the value of the last significant place. For instance, a recording of 843.6 m, or 843.0 m, or 800.0 m would imply a margin of 0.05 m (the last significant place is the tenths place), while a recording of 8436 m would imply a margin of error of 0.5 m (the last significant digits are the units).
A reading of 8000 m, with trailing zeroes and no decimal point, is ambiguous; the trailing zeroes may or may not be intended as significant figures. To avoid this ambiguity, the number could be represented in scientific notation: '8.0 x 10³ m' indicates that the first zero is significant (hence a margin of 50 m) while '8.000 x 10³ m' indicates that all three zeroes are significant, giving a margin of 0.5 m. Similarly, it is possible to use a multiple of the basic measurement unit: '8.0 km' is equivalent to '8.0 x 10³ m'. In fact, it indicates a margin of 0.05 km (50 m). However, reliance on this convention can lead to false precision errors when accepting data from sources that do not obey it.
Looking at this in another way, a value of 8 would mean that the measurement has been made with a precision of '1' (the measuring instrument was able to measure only up to 1's place) whereas a value of 8.0 (though mathematically equal to 8) would mean that the value at the first decimal place was measured and was found to be zero. (The measuring instrument was able to measure the first decimal place.) The second value is more precise. Neither of the measured values may be accurate (the actual value could be 9.5 but measured inaccurately as 8 in both instances). Thus, accuracy can be said to be the 'correctness' of a measurement, while precision could be identified as the ability to resolve smaller differences.
Precision is sometimes stratified into:
- Repeatability - the variation arising when all efforts are made to keep conditions constant by using the same instrument and operator, and repeating during a short time period; and
- Reproducibility - the variation arising using the same measurement process among different instruments and operators, and over longer time periods.
A common way to statistically measure precision is a Six Sigma tool called ANOVA Gage R&R. As stated before, you can be both accurate and precise. For instance, if all your arrows hit the bull's eye of the target, they are all both near the "true value" (accurate) and near one another (precise).
Something to think about: In the NFL, a place kicker makes 9 of 10 field goals, and another makes 6 of 10. Even if the 6 that the second kicker made were straight down the middle and the first kicker just made his in, he is still less accurate and less precise than the first kicker. This differs from the darts example because either you make it or you do not; there are not different levels of points that can be scored.
Accuracy in binary classification"Accuracy" is also used as a statistical measure of how well a binary classification test correctly identifies or excludes a condition.
That is, the accuracy is the proportion of true results (both true positives and true negatives) in the population. It is a parameter of the test.
An accuracy of 100% means that the test identifies all sick and well people correctly.
Accuracy may be determined from Sensitivity and Specificity, provided Prevalence is known, using the equation:
- =()() + ()(1-)
The accuracy paradox for predictive analytics states that predictive models with a given level of accuracy may have greater predictive power than models with higher accuracy. It may be better to avoid the accuracy metric in favor of other metrics such as precision and recall.
Accuracy and precision in psychometricsIn psychometrics the terms accuracy and precision are interchangeably used with validity and reliability respectively. Validity of a measurement instrument or psychological test is established through experiment or correlation with behavior. Reliability is established with a variety of statistical technique (classically Cronbach's alpha).
- Calculation of glass properties - Decreasing accuracy of experimental data in modern scientific publications for some glass properties
accuracy in German: Präzision
accuracy in German: Genauigkeit
accuracy in Spanish: Precisión y exactitud
accuracy in French: Calcul d'incertitude
accuracy in Dutch: Nauwkeurigheid en precisie
accuracy in Japanese: 正確度と精度
accuracy in Portuguese: Exactidão
accuracy in Russian: Точность
accuracy in Slovenian: točnost in natančnost
accuracy in Finnish: Tarkkuus
absoluteness, attention to detail, attention to fact, care for truth, circumstantiality, conscientiousness, correctness, criticality, criticalness, definiteness, delicacy, detail, exactingness, exactitude, exactness, exquisiteness, faithfulness, faultlessness, fidelity, fineness, finicality, finicalness, finickiness, finickingness, flawlessness, fussiness, literalism, literality, literalness, mathematical precision, meticulousness, minuteness, minuteness of detail, niceness, nicety, particularity, particularness, perfection, preciseness, precisianism, precision, punctiliousness, punctuality, refinement, right, rightness, rigidity, rigidness, rigor, rigorousness, scrupulosity, scrupulousness, severity, specificity, strictness, subtlety, textualism, the letter