And other valuable chunks of information about computer memory
This here is a list of the largest and smallest possible values in each n-bit type of numbers which are possible to be represented as 2s-complements :
n-bits (SMALLEST : LARGEST)
- 2-bits (-2 : 1)
- 3-bits (-4 : 3)
- 4-bits (-8 : 7)
- 5-bits (-16 : 15)
- 6-bits (-32 : 31)
- 7-bits (-64, 63)
- 8-bits (-128 : 127)
- 9-bits (-256 : 255)
- 10-bits (-512 : 511)
- 11-bits (-1024 : 1023)
- 12-bits (-2048 : 2047)
- 16-bits (-32,768 : 32,767)
- 32-bits (-2,147,483,648 : 2,147,483,647)
- 64-bits (-9,223,372,036,854,775,808 : 9,223,372,036,854,775,807)
- 70-bits (-590,295,810,358,705,651,712 : 590,295,810,358,705,651,711)
- 2-bits: smallest 2 bit integer is -2, largest 2 bit integer is 1
- 3-bits: smallest 3 bit integer is -4, largest 3 bit integer is 3
- 4-bits: smallest 4 bit integer is -8, largest 4 bit integer is 7
- 5-bits: smallest 5 bit integer is -16, largest 5 bit integer is 15
- 6-bits: smallest 6 bit integer is -32, largest 6 bit integer is 31
- 7-bits: smallest 7 bit integer is -64, largest 7 bit integer is 63
- 8-bits: smallest 8 bit integer is -128, largest 8 bit integer is 127
- 9-bits: smallest 9 bit integer is -256, largest 9 bit integer is 255
- 10-bits: smallest 10 bit integer is -512, largest 10 bit integer is 511
- 11-bits: smallest 11 bit integer is -1024, largest 11 bit integer is 1023
- 12-bits: smallest 12 bit integer is -2048, largest 12 bit integer is 2047
- 16-bits: smallest 16 bit integer is -32,768, largest 16 bit integer is 32,767
- 32-bits: smallest 32 bit integer is -2,147,483,648, largest 32 bit integer is 2,147,483,647
- 64-bits: smallest 64 bit integer is -9,223,372,036,854,775,808, largest 64 bit integer is 9,223,372,036,854,775,807
- 70-bits: smallest 70 bit integer is -590,295,810,358,705,651,712, largest 70 bit integer is 590,295,810,358,705,651,711
Thus, it is evident that for n-bits, the smallest possible value will be -(2^n) and the largest possible value would be ((2^n)-1).
Currently, our modern computers have operating systems running up to 64-bits. Exceeding 70-bits is going to cause a problem known as a ‘floating point precision error’ or ‘floating point bug’. You can search that term up for better and detailed explanations, if you are curious.
Byte addressable or word addressable ?
When referring to a memory location, if the size of a ‘word’ is 8 bits (a byte), then it is conventionally called “byte addressable”. It’s counterpart — word addressable — exists when the size of a word is greater than 8 bits (i.e. 16 bits, 32 bits, 64 bits), the location is then “word addressable”.
How to determine memory address bits ?
That’s easy (kind of). For illustrative purposes, let’s take a 1 GiB (gibibyte) module of RAM, that is composed of several smaller 64 MiB (mebibyte) pieces.
Firstly, we need to convert the memory to bytes for convenience. So, 1 GiB = 1073741824 bytes, 64 MiB = 67108864 bytes. Done! (Conversion processes will be explained later)
Now you take the logarithm of the main memory module’s (the total memory value) value — in bytes — to base 2. You would get :
log(2, 1073741824) = 30
That means the 1 GiB memory module will be using 30-bit memory registers.
Now, since the whole 1 GiB memory module is actually made up of 64 MiB pieces — just like smaller pieces of chocolate are manufactured joined up together to form a large chocolate bar — we need to find exactly “how many” of those 64 MiB tiny modules/RAM chips we need to add up to the total of 1 GiB.
So we calculate it like this (simple unitary method) :
1073741824/67108864 = 16
or if the large and overly-detailed numbers is uncomfortable for you, you can rely on good old powers of 2 for all your calculations :
2³⁰/2²⁶ = 16
Phew. Feeling tired already? Hang on in there!
We know 2⁴ = 16, so the first 4 bits of the whole 30-bit memory register needs to be used for selecting which ‘chip’ among the sixteen chips used to build up the 1 GiB module. And the remaining 26 bits is used for the memory addressing.
How to calculate highest and lowest memory addresses ?
Tough question. (Just joking)
Just remember this for now :
Regardless of how many bits the memory has, the lowest address for it will always be zero.Dewan M.I. Mukto
That answers 50% of your question.
As for calculating the highest possible memory address for a defined byte range of memory, you can rely on this trend :
Consider there are 2ᵡ (2^x) bytes in memory.
So, if the word size is 8 bits, then the memory is byte addressable (as explained above). The highest memory address would be = 2^x-1
If the word size is 16 bits, then the highest memory address would be = 2^(x-1)-1, because 16 bits is a 2-byte (2¹) word. And you’d be reducing the total number of available addresses by that amount. Thus, 1 is subtracted from the total x-bits.
If the word size is 32 bites, then the highest memory address would be = 2^(x-2)-1. The explanation is same as above. 32 bits is a 4-byte (2²) word. So the amount is subtracted from x-bits.
Once more, if the word size is 64 bits, the highest possible address is 2^(x-3)-1, as 64 is a 8-byte (2³) word.
This trend continues for as many increments of powers of 2 you need.
Voila! You’ve now understood the concept, I presume.
If you’ve read this far, it’s a word of advice to join us on Amrella. Create an account! You won’t regret it! 😄👍


Neng Fan is an associate professor in the Systems and Industrial Engineering Department at the University of Arizona. He obtained his bachelor’s degree in computational mathematics from Wuhan University in 2004 and master’s degree in applied mathematics from Nankai University in 2007. He obtained his master’s and PhD degrees from the Industrial and Systems Engineering Department at the University of Florida in 2009 and 2011, respectively.
Fan’s research interests include integer programming, stochastic and robust optimization methods, and their applications in data mining, combinatorial optimization, energy systems, water systems, and health care. He has been involved in organizing several conferences in the areas of optimization, smart grids, and health care, and also served as a reviewer for many journals. Currently, he is the associate editor for two journals, Optimization Letters and Energy Systems, published by Springer.
Fan is a member of the Institute for Operations Research and Management Sciences (INFORMS) and the Institute of Industrial Engineering (IIE).
- PhD Industrial and Systems Engineering - University of Florida, 2011
- MS Industrial and Systems Engineering - University of Florida, 2009
- MS Applied Mathematics - Nankai University, 2007
- BS Computational Mathematics - Wuhan University, 2004
Teaching Interests: Optimization, operations research, probability, statistics, data analytics, and machine learning
Research Interests: Methodologies in optimization: integer programming, combinatorial optimization, stochastic programming, robust optimization, multilevel programming, and large-scale optimization; applied operations research: energy systems, water systems, renewable energy integration, interdependent infrastructures, healthcare and sustainable agriculture; data analytics: data mining, machine learning, and high-dimensional data with uncertainties


C# Modulo Operator: Get Remainder From DivisionUse the modulo division operator to get remainders from dividing numbers.
Modulo. This operator gets a remainder. It provides a way to execute code once every several iterations of a loop. It uses the percentage sign character in the lexical syntax.
Modulo has some unique properties. As with all low-level operations, it has a specific cost. We analyze modulo division in the C# language.DivideOdd, EvenEvery Nth Element
Modulo division is expressed with the percentage sign. It is implemented with "rem" in the intermediate language. Rem takes the top 2 values on the evaluation stack.
Then: Rem performs the computation that returns the remainder of the division. It pushes that value onto the evaluation stack.
Here: This example demonstrates the math behind modulo. The expressions here are turned into constants during the C# compilation step.
Important: We see that 1000 and 100 divide into parts of 90 with a remainder of 10.
Note: If the first argument to the predefined modulo operator is 81 and the second operand is 80, the expression evaluates to a value of 1.
C# program that uses modulo operator
static void Main()
// When 1000 is divided by 90, the remainder is 10.
Console.WriteLine(1000 % 90);
// When 100 is divided by 90, the remainder is also 10.
Console.WriteLine(100 % 90);
// When 81 is divided by 80, the remainder is 1.
Console.WriteLine(81 % 80);
// When 1 is divided by 1, the remainder is zero.
Console.WriteLine(1 % 1);
You can apply modulo in a loop to achieve an interval or step effect. If you use a modulo operation on the loop index variable, you can execute code at an interval.
Note: This example shows how to write to the screen every ten iterations in the for-loop.
Important: The 3 numbers in the condition in the if-statement can have any values, but we cannot divide by 0.
C# program that uses modulo division in loop
static void Main()
// Prints every tenth number from 0 to 200.
// Includes the first iteration.
for (int i = 0; i < 200; i++)
if ((i % 10) == 0)
The time required for modulo division depends on hardware and other factors. Some analysis from Microsoft is helpful. This page provides a table listing times required.Writing Faster Managed Code: Microsoft Docs
Estimated costs of instructions:
Add: 1 ns
Subtract: 1 ns
Multiply: 2.7 ns
Divide: 35.9 ns
Error, divide by zero.
If you use modulo by 0, you will get a compile error or a runtime exception. The denominator must never be zero.DivideByZeroException
Modulo has several common uses in programs. You can use modulo division in loops to only execute code every several iterations. This can improve real code.
Note: We do not often need to compute numeric remainders for user consumption. The regular division operator may be more useful here.
Odd: You can use modulo to test for odd numbers and even numbers. You can define odd numbers as not-even numbers.
Modulo is slower than other arithmetic operators such as increment and decrement or even multiply. This is a hardware limitation on computers.
But: The total time required for individual modulo operations is tiny compared to other tasks such as disk reads or network accesses.
So: If you can reduce those operations with modulo division, you can improve overall performance.
You may rarely have a modulo division in a hot path and this can cause a loss of performance. This will almost always occur in a loop body or in a recursive method.
Tip: You can apply a technique called "strength reduction" manually to convert the modulo operation into a subtraction or addition.
And: To do this, add another field or local variable. Then, in each iteration of the loop, decrement it and test it against zero.
Then: When zero is reached, set it to its maximum value again. This resets the pattern.
A summary. The modulo operator is often useful. This is implemented in the CLI as a rem instruction. The C# compiler calculates modulo divisions of constants at compile-time.
Modulo division returns the remainder of the 2 operands. We use the "percent" symbol for modulo in the C# language. This is a powerful operator, but it has its nuances.
© 2007-2020 Sam Allen. Every person is special and unique. Send bug reports to email@example.com.


Our results are uploaded to our website as soon as nationally available. We currently have results from the end of our KS1 but will not have results from the end of KS2 until July 2018.
Changes to 2016 Performance Data
Key Stage 2 national curriculum test outcomes will no longer be reported using levels, and instead will be reported as scaled scores. Key Stage 2 national curriculum teacher assessments will be reported against the new interim frameworks for teacher assessment.
The headline measures will be:
- the percentage of pupils achieving the expected standard in reading, writing and mathematics
- the percentage of pupils achieving the higher standard in reading, writing and mathematics
- the school’s progress score in each of reading, writing and maths
- the pupil’s average scaled score in each of reading and mathematics
A school will be above the floor standard if:
- 65% of pupils meet the expected standard in reading, writing and mathematics (i.e. achieve that standard in all three subjects) or
- the school achieves sufficient progress scores in all of reading, writing and mathematics.


Calculator Guide Volume of topsoil is calculated using length (m) x width (m) x depth (m). The next stage is to convert this volume into metric tonnes. We base our calculations on 1 cubic metre = 1.8 metric tonnes. Therefore we multiply the volume x 1.8 to give us the tonnage of topsoil required.
Custom Topsoil provides Topsoil, Mulch, Wood Chips, Compost, Fill (Nubbies) to customers throughout the Buffalo area. Pick up or Delivery in WNY. Calculate the number of cubic yards of material you will need.
You can't convert the two. One is measurement of weight, and the other is a measurement of mass. ... Soil. How do you convert cubic yards of soil to metric tons? Wiki User. ∙ 23:20:44. Study now. See Answer. Best Answer. Copy. You can't convert the two. One is measurement of weight, and the other is a measurement of mass.
CONVERSION TABLE Listed below are conversion factors compiled by the Solid and Hazardous Waste ... Yard Material WEIGHT/UNIT UNITS/TON 17-Brush-Chipped 500 lbs/cy 4 cy = 1 ton 17-Brush-Unchipped 250 lbs/cy 8 cy = 1 ton 18-Grass 1,111 lbs/cy 1.8 cy = 1 ton Compacted 18-Grass 741 lbs/cy 2.7 cy = 1 ton ...
Plastic =1 cubic yard 22.55 lbs Soil, Dry =1 cubic yard 2,025 lbs Soil, Wet =1 cubic yard 2,106 lbs Stone or Gravel 1 cubic yard = 2,632.5 lbs Rock, Loose 1 cubic yard = 2,570 lbs Metal Scrap 1 cubic yard = 906 lbs Wood Scrap, Loose 1 cubic yard = 329.5 lbs Conversion factors are those used by the California Integrated Waste Management Board.
Re: converting cubic yards to tons Gravel, loose, dry - 1.28 tons/cubic yard Gravel, w/sand, natural - 1.61 tons/cubic yard Gravel, dry 1/4 to 2 inch - 1.41 tons/cubic yard Gravel, wet 1/4 to 2 inch - 1.69 tons/cubic yard Depends on the type of gravel. I will show an example using loose dry gravel from the above list...
How do you convert tons to yards? To convert Tons to Cubic Yards*: Tons ÷ 1.4 = Cubic Yards. How much does a dump truck load of gravel cost? The cost of gravel ranges from $10 to $50 per ton, $15 to $75 per yard, $1 to $3 per square foot, or $1,350 per truck load depending on the rock type, volume, and travel distance.
Convert cubic feet to pounds by multiplying by the bulk density of topsoil, and then converting from cubic feet to tons. This is 83 pounds per cubic foot by 108 cubic feet, for a mass of 8,964 pounds. There are 2,000 pounds per ton, so the conversion from yards to tons is 8,964 divided by 2,000, or 4.5 tons. Click to see full answer
nutrient there is in terms of pounds per dry ton. For % to decimal : divide by 100 (or use % button on calculator) Calculating Nitrogen . 0.045 (TKN) X 2,000 lbs/ T = 89.0 lbs TKN/ DT (4.45%) 0.0027 (NH 3) X ... conversion factor) 4.0 lbs K/ DT X 1.2 = 4.8 lbs K 2 O/ DT . We'll need to know how much . Phosphate and Potash will be applied when ...
A ton of condensed soil is typically about 0.750 cubic yards (3/4 cu yd), or 20 cubic feet. Also, how do you convert tons of soil to cubic yards? 100 lb/ft 3 = 100 lb/ft 3 × 3 3 /1 ft 3 /yd 3 = 2700 lb/yd 3. Since there are 2000 pounds in a ton this is 2700.2000 = 1.35 tons per cubic yard and thus 15 cubic yards weighs 1.35 × 15 = 20.25 tons.
Is a cubic yard the same as a ton? A cubic yard is a measure of volume while a ton is a measure of weight. For example, a cubic yard of crushed rock is lighter than a cubic yard of topsoil. The reason Washington Rock sells topsoil and sand by cubic yard rather than by ton is that their weight varies with the seasons.
Answer: Bank Cubic Yards (BCY) can be converted to Loose Cubic Yards (LCY) by applying a Load Factor (L.F.) to the LCY depending on the type of material being exported. For example, Decomposed Rock in various states can range from 0.70 - 0.80, while Sand can range from 0.79 - 0.91. Page 2313 or ...
Convert cubic feet to pounds by multiplying by the bulk density of topsoil, and then converting from cubic feet to tons. This is 83 pounds per cubic foot by 108 cubic feet, for a mass of 8,964 pounds. There are 2,000 pounds per ton, so the conversion from yards to tons is 8,964 divided by 2,000, or 4.5 tons. Brian Baer
How many cubic yards in a ton depends on what your material is. For instance, topsoil has a 1:1 ratio. 1 cubic yard of topsoil would be 1 ton, so if you have topsoil, 17 cubic yards would be 17 tons. Gravel on the other hand has a 2:1 ratio. So, 17 cubic yards of gravel would be 34 tons.
Convert cubic feet to pounds by multiplying by the bulk density of topsoil, and then converting from cubic feet to tons. This is 83 pounds per cubic foot by 108 cubic feet, for a mass of 8,964 pounds. There are 2,000 pounds per ton, so the conversion from yards to tons is 8,964 divided by 2,000, or 4.5 tons.
VOLUME-TO-WEIGHT CONVERSION FACTORS APPLIANCES & FURNITURE ... Carpet 1 cubic yard 147.00 0.074 CA IWMB Carpet padding 1 cubic yard 62.00 0.031 CA IWMB ... Soil/sandy loam, loose 1 cubic yard 2,392.00 1.196 Tellus Institute Stone or gravel 1 cubic foot 98.00 0.049 FEECO
A cubic yard of topsoil, if compacted to get the air pockets out will weigh more than 1 tone. If the topsoil is loose, a cubic yard of it could weigh about 1 ton. A lot depends on the topsoil, and whether it has more stone dust or less in it. The more moist the topsoil is, the more likely it will weigh more than a ton.
Top Soil Unscreened Topsoil Yard Dirt Calculate Unscreened Topsoil Type in inches and feet of your project and calculate the estimated amount of Soil & Dirt in cubic yards, cubic feet and Tons, that your need for your project. The Density of Unscreened Topsoil: 2,410 lb/yd³ or 1.21 t/yd³ or 0.8 yd³/t
If you want an accurate answer, give your topsoil supplier a call to find out the density. For our example below, we'll use the estimate of 85lb per cubic foot: Convert your density to lb/yd 3. 85 lb/ft 3 = 2295 lb/yd 3 (1 pound per cubic foot equals 27 pounds per cubic yard) If you're in the US, divide 2295 by 2000 (there are 2000lb in a US ton).
Top Soil/Mushroom Soil Yardages 1 Yard of Top Soil/Mushroom Soil = 80 sq. ft (8′ x 10′ area) approximately 4 inches deep Landscape Stone: 1 scoop = Approximately 1 Ton 1 scoop covers approximately 80 sq. ft. – 4 inches deep. Product Weights: 1 Yard Top Soil = 2,000 lbs (1 ton) 1 Yard Mushroom Soil/Earthmate = 1,000 – 1,200 lbs
Converting Cubic Yards to Tons. Most gravel and crushed stone products have similar weights per ton. A general rule of thumb when converting cubic yards of gravel to tons is to multiply the cubic area by 1.4. For your reference, gravel …
The American Topsoil company says most half-ton pickup trucks can manage this safely. Heavier-duty one-ton and 3/4-ton pickups can often hold and handle up to 2 cubic yards, or about 4,000 pounds ...
Hi Terry, It depends on the density of the topsoil they are selling. I found a table that may help somewhat, but the density in pounds per cubic foot varies from 78 to 125 pounds per cubic foot.(Look in the table under earth.) If you know the density you can calculate the weight in tons of 15 cubic yards.
I need to convert 1,073 cy of soil (moist) to tons. This will vary a lot with soil composition and water content, anywhere from 1.05 - 1.75 tons/yd³, but try 1.35 ton/yd³ as a typical value, good quality topsoil at the light end, mixes …
• 1 ton per acre = 1 kg per 48 sq. ft. • lbs per sq. ft. x 21.768 = tons per acre • lbs per sq. ft. x 43,560 = lbs per acre • 1 acre = 0.405 hectares • 1 mile = 1.61 km • parts per million (ppm) x 0.00136 = tons per acre-foot To convert a soil test from ppm to lbs per acre. 1. Determine the depth of soil in inches that the soil ...
Calculate Unscreened Topsoil. Type in inches and feet of your project and calculate the estimated amount of Soil & Dirt in cubic yards, cubic feet and Tons, that your need for your project. The Density of Unscreened Topsoil: 2,410 lb/yd³ or 1.21 t/yd³ or 0.8 yd³/t.
Mulch, Dirt & Topsoil Calculator to Estimate Cubic Yards Required: Length in feet x Width in feet x Depth in feet (inches divided by 12). Take the total and divide by 27 (the amount of cubic feet in a yard). The final figure will be the estimated amount of cubic yards required.
It is a difficult conversion to calculate, because cubic yards are volumetric measurements and tons are weight measurements. The bulk density will determine the weight per cubic yard. Calculators can be found on the web to assist in completing this type of conversion, such as the one available at unitconversion.org.
For use in calculating quantities of Sand, Stone, Fill and Topsoil: Enter Data: V Enter Width of the Area in feet >>> Enter Length of the Area in feet >>> Results: Cubic Yards: Tons A thickness of: 2" A thickness of: 3" A thickness of: 4" A thickness of: 5" A thickness of: 6"
tons to cubic yards by Michael Berry on 04/18/05 at 20:15:15 I work at a rock pit and my boss came in today and said the he needed me to find out how to convert our materials from tons to cubic yards for a contractor that is buying …
Conversion Chart. The following is a guideline of conversion factors for quoted material. Lorusso Corporation does not guarantee quantities or yields. This conversion is based on material as loaded in truck bodies. The Lorusso Corporation sales policy for material is factored by the ton and is billed accordingly. Material. Conversion: Tons / C.Y.
Instant free online tool for cubic yard to ton register conversion or vice versa. The cubic yard [yd^3] to ton register [ton reg] conversion table and conversion steps are also listed. Also, explore tools to convert cubic yard or ton register to other volume units or learn more about volume conversions.


The 5th edition of the text book "Programming the Finite Element Method" has been completed. It is now with the Wiley production team and will be available to purchase at the beginning of the 2013/14 academic year. It is aimed at undergraduates, graduate students and practitioners in all areas that use the finite element method.
Smith, Griffiths and Margetts, "Programming the Finite Element Method", Wiley, 2013 can be preordered online.
"Programming the Finite Element Method" is the only engineering text book that introduces the reader to the basic concepts of the finite element method and then takes them on a journey where they learn how to write finite element programs to solve real world problems. Source code and libraries for around 70 example programs are provided. These are introduced step by step, building up the reader's expertise, from 1D and 2D problems that can be run on a desktop computer, to deceptively simple parallel programs that are capable of solving systems with up to a billion equations using tens of thousands of cores. These parallel programs are provided as ParaFEM.


More and Less Comparison - Worksheet One
This printable comparison math worksheet asks kids to count the number of shapes in each box and then follow the instruction to draw either more or less shapes in the empty box. This is worksheet one of two of this set and we have both color and black and white versions of this worksheet.. Make sure to check out the rest of our comparison and other math worksheets.
This more less comparison worksheet and the others on this site are all free to print and use.
Use as many copies as you like at home or in a class room, but don't reproduce them on another website
or other media. You are more than welcome to link to us from a website you have, but we have worked
hard to create these worksheets, so please don't take our content to use as your own.


I decided to create weekly homework sheets that address the CCSS. I also added a very important twist. Homework would be mostly done in the classroom. Basically, I was "flipping" homework. Each Monday my students receive their weekly math homework sheet which has problems for Monday, Tuesday, and Wednesday on it aligned to the CCSS. (Click here to see full size Google doc.)
Here is another example of one of my homework sheets that has new skills and review skills on it.
I have two math classes that I teach for 90 minutes each day. After I teach my lesson for the day, my students rotate through math stations. I use the word MATH to set up our stations. A and H are done every day by every student. M and T are done as needed or as time allows.
M - Manipulatives - Students work with hands-on materials or play games to reinforce skills.
A - At the Computer - Students complete work on websites such as IXL, LearnZillion, TenMarks
T - Teacher Time - This is where they meet with me for small group instruction.
H - Have a Go - This is where they work on their assignment and homework for the day.
By allowing my students to work on their math homework in class, I am there to offer support and correct misconceptions that arise. If for some reason a student doesn't finish their homework in class then it must be completed at home. I have my students show their homework to their parents each night and have the parents sign it. Each day we check the previous day's work via our interactive whiteboard. I pull up the Google document and we annotate right over it to show solutions.
Using this type of formative assessment is really allowing me to see each day how my students are doing in math. It has also eliminated so many of the stresses that traditional homework can cause. Each and every one of my students is having their needs met on a daily basis. Once a skill is taught and tested, my students know they will be held accountable to remember it.
Have you considered, or do you "flip" homework? What do you use for formative assessment? Please share in the comment section below.
(This post is part of the blogging challenge being hosted by Kelly Hines.)


Today, this particular piece was about numbers, but there is something very important nested within this piece that I want to highlight. For the sake of context, I'm presenting the full transcript of today's episode, and many more transcripts can be found here:
I will highlight the parts I wish to focus on (and the reason for this post).
What do the following words have in common: natural, imaginary, real, irrational, and transcendental. If you guessed “states of mind,” you’re probably not alone. But the better answer is they’re types of numbers. We take numbers for granted. One, two, three. These are the natural, or whole numbers. What could be simpler? Fractions are no trouble. Half a cup of sugar, a quarter teaspoon of salt. These are called rational numbers because they can be written as the ratio of two whole numbers. But many numbers aren’t rational. We call them irrational.
One of the most famous irrational numbers is the square root of two. The Pythagoreans’ of ancient Greece discovered this fact. They were a mystic cult, living according to strict rules established by their leader, Pythagoras. Numbers were divine to the Pythagoreans. So when one of their own, Hippasus of Metapontum, discovered the square root of two was irrational, it upset their entire understanding of the world. Legend has it that Hippasus was killed for his heresy. Ironically, we now call the rational and irrational numbers taken together, the real numbers. When we add a number called i, representing the square root of negative one, we get the imaginary numbers. They’re perfectly good numbers, though they’d probably have caused the Pythagoreans to drink hemlock-laced Kool-Aid.
And things only get stranger. We know that the rational and irrational numbers are both infinite. But there are infinitely more irrationals than rationals. That’s because there’s more than one type of infinity. This is the result of Georg Cantor’s pioneering work on transfinite numbers. Cantor’s contemporaries were extremely critical of his efforts. Henri Poincaré called Cantor’s transfinite numbers a “disease.” Leopold Kronecker, one of Cantor’s teachers, called Cantor a “scientific charlatan” and a “corrupter of youth.” Today, mathematics and engineering students can’t survive without knowing at least some of what Cantor unearthed.
Cantor’s work led him to study sets. The set of all red cars, the set of socks in the bottom drawer. Mathematicians believed sets were even more basic than numbers. So in the late nineteenth and early twentieth centuries they went about defining numbers using sets.
It seems crazy. Why fuss with sets? But it laid a foundation that helped us learn many surprising things about what we can and can’t do with mathematics. And … with computers. Today’s digital computers work with one thing, numbers. Peek inside and you’ll see everything expressed in numbers, from the icons on your desktop to the email waiting in your inbox. Numbers make our copiers copy, our phones phone, and our word processors process. We couldn’t do without them. Wonderful, practical, even divine numbers.
Now let's focus back on the highlighted part of this transcript. Throughout history revolutionary ideas have been scoffed at, ridiculed and rudely (if not violently) challenged. This is but one example, and many can be researched beyond just the sciences.
My point is that when people attack, ridicule, scoff and degrade "radical" ideas like the Venus Project, the Electric Universe, or people like Nassim Haramein, or conduct any other such action, remember that history is full of people who do this. They are the ones challenged, fearful, or simply too egotistical to accept something different.
In time, they are typically proved to be wrong at least to some degree, but I'm certain at the time they wielded great swords of superiority...at least in their own minds. :)
So remember that time based validation is the true test, and so is social and technical evolution.
Onwards and upwards, let not the baggage wielders of outdated thinking hold back the progress of mankind.


Operation Research Case Study With Solution
Business case studies take a lot of time to formulate. APPENDIX 1. SUPRIYA KUMAR DE ASSIGNMENT XLRI-PGCBM-18 NAME: GH. 2017/2018. 10. Problem: 1 2. 24. · Download Operation Research pdf, notes, books, syllabus for MBA, B Tech, BBA, B.COM 2020. Please sign in or register to post comments. operation research case study with solution helpful 18 0.
Adding Special Course Work To Resume
PROBLEM FORMATION & CALCULATION 4.1.OPTION 1 4.2.OPTION 2 4.3.OPTION 3 5. While reading case study examples operation research case study with solution students get to understand the mechanics of organizing and writing, the important aspect that otherwise be obscured from clear view. INTRODUCTION The …. RASOOL WANI SMS ID: 2217429 Table of Contents 1. By using mathematical methods, analysts can model business decisions and solve optimization problems (such as profit maximization or cost minimization problems) using linear and nonlinear programming and statistical analysis Assignment Problems:SOLUTION OF AN ASSIGNMENT PROBLEM Operations Research Formal sciences Mathematics Formal Sciences Statistics. ManagementParadise.com - India’s largest online mba management project download for Students and Professionals. Cutting Cafeteria Cost. Method of Transportation Transportation method is a method used to set the distribution of sources that provide the same product or kind of to the destination optimally. Operation Management. A flexible budget is created by inserting each line item in the monthly budget.
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- Operations Research and Simulation in Master Degrees: A case study regarding different universities in Spain Conference Paper (PDF operation research case study with solution Available) · December 2013 with 4,433 Reads How we measure 'reads'.
Aboriginal Health Worker Course
3. INTRODUCTION 2. PROBLEM RESULT & CONCLUSION 6. Sample Business Case …. 99013366442 - 9902787224 WE PROVIDE CASE STUDY ANSWERS, ASSIGNMENT SOLUTIONS, PROJECT REPORTS AND THESIS a r a v i n d .b a n a k a r @ g m a operation research case study with solution i l . c o m. Chandrashekar Muramalla. Operations research, or management science, is the application of advanced analytical methods in mathematics to complex business decision-making problems. 6 2.3.1 Excel Solution Embedded: 6 3. 2013. Related documents.
Linear Programming. This textbook is comprised operation research case study with solution of detailed case studies covering challenging real world applications of OR techniques.


P. Ablin, A. Gramfort, J.F. Cardoso and F. Bach. EM algorithms for ICA. Preprint. https://arxiv.org/abs/1805.10054
P. Ablin, J.F. Cardoso and A. Gramfort. Accelerating Likelihood Optimization for ICA on Real Signals. LVA-ICA ’18. https://arxiv.org/abs/1806.09390
Best student paper award
P. Ablin, J.F. Cardoso and A. Gramfort. Faster ICA under orthogonal constraint. ICASSP’18. https://hal.inria.fr/hal-01651842/document
P. Ablin, J.F. Cardoso and A. Gramfort. Faster independent component analysis by preconditioning with Hessian approximations. Accepted for publication in IEEE-Transactions on Signal Processing (2017). https://arxiv.org/abs/1706.08171
P. Ablin and K. Siddiqi. Detecting Myocardial Infarction Using Medial Surfaces. International Workshop on Statistical Atlases and Computational Models of the Heart (2015).


Intelligence is problem solving
Problem solving matters in both arts and science. And yes, you can cultivate intelligence
Is there such a thing as intelligence? Is there a quantifiable measure for the capability of the human brain? I think so.
From a mathematical perspective, here’s how I would define intelligence: the ability to solve NP problems. NP is a mathematical classification of a problem that roughly means it requires creativity. And by “problem,” I mean a broad range of tasks—from solving standard math problems, to writing, drawing, composing a piece of poetry, playing chess, flirting, finding the best way to tell uncomfortable truths, managing a company, or even physical tasks like rock climbing.
NP is a rigorously defined problem-class, but we are using it a bit loosely here, for simplicity. An NP task is essentially a problem that we cannot solve by mechanically following an algorithm step by step.
The problem may appear easy to solve in hindsight, after we’ve solved it. But the process of discovering the solution to an NP problem is hard—there’s no recipe for finding the solution. A mechanical robot cannot solve it. It requires intelligence. It requires creativity.
Chess is an NP problem. There are about 770000000…[32 zeros]...00000 legal chess board configurations. No algorithm can solve chess—it would require trying out all possible moves to determine the winning solution (this involves going through a large portion of those 7.7 * 10^45 possible configurations, which would take a modern computer 10^30 years to run). Chess requires intelligence/creativity. Each move requires smart decision-making that rely on strategic thinking, pattern-matched intuition, and calculating your opponent’s intent. It requires us to find a move that “works” without robotically trying out all possible move sequences. This is the essence of intelligence and creativity: the ability to discern the one solution that works from a near-infinite sea of possible solutions.
Solving math problems, unsurprisingly, is also a task that demands intelligence. Grade school math problems are unintelligent—we have prescribed recipes for solving them. Divide 2153692 by 235. You don’t even need to think. You just apply the algorithm of long division to solve it. Division is not an NP problem. But challenging math puzzles are. For example, can you come up with a proof for the Pythagorean Theorem? If you think of a math proof as a sequence of English sentences, then it is clear there are a near-infinite number of possible “math proofs” you can write down. Most of them are just garbles of words, like “Proof: I am hungry. Therefore a^2 + b^2 = c^2.” Only a small portions of these proofs are logically consistent. For example: “Proof: a^2 is an apple, b^2 is a pen, and c^2 is an apple-pen. Therefore, a^2 + b^2 = c^2.” Among these logically consistent proofs, only a tiny portion actually proves the Pythagorean Theorem. So, the problem of proving the Pythagorean Theorem is NP and requires intelligence, because a mathematician needs to discover the handful of proofs that work, from a mountain of proofs that don’t.
Creating art is also an NP problem. Take graphic design. In a canvas with 5 million pixels, there are 256^5000000 possible graphics you could create. Most of them are messy collages of colors, like this:
A tiny tiny portion of these graphics are considered artsy. The problem of the arts is to discover these rare configurations of pixels that appeal to the human eye, from an ocean of nonsensical noise. In this sense, art is quite similar to solving chess or a math puzzle (although our culture distinguishes them). This makes sense. You often hear chess masters or mathematicians describe their work as “an art.” From a certain point of view, math, chess, and art are the same—they are a treasure hunt in a near-infinite sea of possibilities for the one proof/chess move/painting that works. They are intellectual tasks. And the ability to solve them is the hallmark of intelligence.
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How to solve NP Problems fast
How to solve an NP problem? This is a bogus question. Because, by definition, there are no definite recipes for solving NP problems. The only systematic way to solve NP problems is by going through every possible solution in the near-infinite solution space, and checking if each works. This is dumb and slow. Luckily, there is a bag of tricks humans use so that we can solve NP faster than dumb robots. This “bag of tricks” is what makes us “intelligent.”
Pruning your search space: spend less time trying solutions that don’t work
Minesweeper is an NP problem (roughly). It’s played on a grid, where a number is written on every square to show the number of mines surrounding it. In each step of the game, the player clicks on a square—if it’s a mine she loses and the game starts over, if not, the game continues. A dumb algorithm for solving minesweeper involves trying out all possible squares. And if it hits a mine, start over, and try a different square. This is very slow.
Human players do better by logically deducing whether a square contains a mine by looking at the numbers of its adjacent squares. We then prune these squares-that-definitely-contain-a-mine from our search space. We reduce the number of squares / potential solutions that we need to try our luck on, using logic. This is intelligence.
Heuristic strategy: try the most-likely-to-work solutions first
Chess players rely on heuristic strategies to beat dumb machines. Yes, decision-tree based chessbots can beat humans. But those chessbots are actually less strategic than humans. They only win because a computer can execute 1 billion serial computations in 1 second, but we cannot.
Heuristic strategies for chess are called “chess theory.” It tells you general winning strategies like: 1. Use your pawns to control the center of the chessboard. 2. Don’t block up your bishops. 3. Don’t stack up your pawns. 4. Try not to blunder your queen… A human player does not simulate every possible chess moves to determine the best one, which is what most chessbots do. We apply these general strategies to select a few movies that are most likely to work, and then simulate those moves in our brain to determine the best one. That’s why we can play chess well, using far less compute resources than bots—a.k.a. intelligence.
Pattern matching from memory: if you memorized the solution to a problem, you don’t have to solve it again
A common strategy for solving hard math problems is to map it to a problem you already solved before. You don’t have to search for a solution anymore. You just take the solution you already have, modify it a bit to fit the new problem, and submit it.
In arts, it’s the same game. Art is the problem of finding configurations of color patches that appeal to the eye. Most artists don’t expend the mental effort to discover an original solution. They take existing solutions/paintings from other artists, pretty elements from nature, or a fancy advertisement they saw. They morph these solutions together, add in a touch of original modifications—and a new piece of art is born. Each painting is interpolated from a consortium of pre-existing paintings, natural landscape, or other aesthetic features the artist saw in her life. Every solution to the art problem is interpolated from pre-existing solutions, with some amount of original modifications by the artist.
Writing is an NP problem—its objective is essentially to find a sequence of words that work to convey a particular idea—and it’s also solved through pattern matching. I can formulate this sentence (and the thought behind it) in a matter of seconds because 1. I can pattern match from thousands of sentences and phrases I’ve written or read; 2. my conscious mind processes thoughts linearly, so I can chunk up my idea serially and map them into words relatively quickly. However, if you ask me to explain an idea I’ve never verbalized, such as the concept of “karma”, I would be groping for words. I have no past experience to map from.
Increase processing speed: if you can check the correctness of a solution faster, you will find a correct solution faster
Prime factoring a number is an NP problem, and a well-studied one. Pattern matching hardly works for prime factoring. There are some complicated logical pruning and heuristic strategies for the problem—but at the end of the day, you have to try dividing 981254632 by a bunch of prime numbers to figure out which primes are factors of 981254632, and which are not. In this case, a person who can execute the long division algorithm faster will solve the problem quicker. She will be considered more intelligent. So, intelligence also depends on how fast and accurately our brain can process logic, retrieve memory, pattern match, e.t.c.
Can intelligence be learned
Can intelligence be learned? I think yes, at least a large part of it. If you can train an artificial neural network to be better at problem solving, you can also train your biological network to improve your ability to solve NP problems.
You can learn heuristic strategies to solve different types of NP problems faster: a chess player can study chess theory, a mathematician can learn general proof strategies (induction, contradiction, e.t.c.), and a computer scientist develops classifications of coding problems (greedy, dynamic programming, recursion, e.t.c.) such that there is a general heuristic strategy for approaching each type of problem. Field-agnostic problem solving heuristics can also be learned. One such heuristic that I find useful is: To solve a problem with multiple constraints, ignore some of those constraints, and focus on the simpler version of the problem first. This is a nice heuristic that points you in the direction towards the right solution.
Pattern matching is, of course, also learnable. You can increase your repertoire of patterns to match from by reading more words, seeing more arts, solving more math problems, or analyzing more chess positions. You can improve your ability to recall patterns by building associative connections. If you developed good associative memory for words, you can find the right words for your sentence faster. You can also improve your efficiency at logical deduction by familiarizing yourself with various logical patterns. A=B, B=C, therefore...A=C. It’s a logical deduction you blurt out without thinking because our brains are so familiarized with the logic of the transitive property. 快乐 means happy, happy means 행복한, so 快乐 means 행복한. Your brain made the quick logical deduction by pattern matching from the logic of the transitive property. If Jane is reading, she feels happy. If Jane is not exactly feeling happy at the moment, then Jane...cannot possibly be reading. This is another logical pattern: if A then B, so if not A, then not B. You are probably less familiar with it, so your brain took more time to make the deduction.
You can up your brain’s processing speed as well. If you practice more long division, you get faster at it. If you practice logical deduction, you become more accurate and faster at it. If you practice recalling certain facts (say, you are a biologist and you use Anki to practice recalling various facts), your neuronal web responsible for storing those biological facts become better connected, and you can recall facts at higher speeds.
Maybe don’t worship intelligence
Why did I write this post? I wrote it because I got annoyed by....a cult of people who worship intelligence like Catholics worshiping virginity.
I have an IQ of 120, so I can’t think of any good way to destroy the world. But if we create an Artificial General Intelligence (AGI) with an IQ of 200, then it will think of things I can never possibly think of! It can think of crazy ways to destroy the world that we can never anticipate or forestall!
No bro. You and that AGI are both searching for a solution for destroying the world in an infinitely large solution space. IQ does not put a limit to what idea/solution you can come up with.
Some people have a very spiritual conception of IQ that reminds me of DC’s Justice League: there’s this thing called the Anti-Life Equation. Only people above a certain IQ can understand it. Stupid people who try to understand it will die from it. Somehow, society has internalized this idea, and mystified intelligence as some sort of unbreakable glass ceiling. People who self-classify as “smart” use this myth to pump their ego. People who self-classify as “stupid” cope with failings by externalizing the blame to “low IQ”. They deny themselves agency in the process.
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Theme of the week is: Managing your mood
Maths department curriculum intent statement
In the Maths department we strive to create an environment that will help students to develop their confidence in the subject, enjoy using Maths and thrive, whatever their prior attainment; providing students at all levels and abilities the chance to develop their mathematical thinking. We provide all students the opportunity to build on their key numeracy skills as they enter key stage 3. We work closely with our primary colleagues to ensure a smooth transition and to share resources. We are also able to offer enrichment activities/qualifications at all key stages; entering our most gifted students, from all key stages, into the UK mathematics trust challenges, we also have students who attend weekend masterclasses at Oxford University.
While we proudly teach using a variety of different methods, we are fully stocked with Pearson (Edexcel) textbooks targeting the latest qualifications at all levels.
Key stage 3
Our key stage 3 curriculum has been adapted from the Pearson 3-year scheme of work and covers units from across the 4 main curriculum areas: Number; Algebra; Geometry and Measure; Statistics and Probability. A heavy emphasis is placed on developing problem-solving skills, across all topics, and promoting the application of mathematics. We place the students in sets, based on their ability, from the start of key stage 3 allowing us to focus more closely on the topics that will help them develop as mathematicians; we monitor students closely, amending sets regularly.
Key stage 4
In key stage 4 we build on, and extend, the work done in key stage 3 using a curriculum based on the Pearson GCSE schemes of work. Students are placed in sets according to their ability and can be entered into the Higher or Foundation tier based on their ability. The problem-solving skills developed in key stage 3 are built upon and developed as students prepare for the “using and applying mathematics” elements that have become more frequent in the latest GCSE.
Our most able students are also offered the chance to study towards a statistics GCSE in Year 10 and the AQA Further Mathematics qualification in year 11; this offers excellent preparation to those wishing to go on to study A level Mathematics and Further Mathematics.
Key stage 5
We are fortunate enough to have 2 classes studying towards the Pearson AS/A level in mathematics in both year 12 and year 13. The AS/A level is split into 2 main areas; Pure mathematics includes material that may previously have been referred to as calculus, applied mathematics is divided into Mechanics and Statistics. Students are given the opportunity to practice exam questions regularly, reflect on their progress and are supported as they look to improve moving forwards.
We have separate classes in both years 12 and 13 studying towards the Pearson AS/A level further mathematics qualification. This prepares students for future degree qualifications which contain a substantial amount of mathematics; in addition to studying pure mathematics to a higher level, students can also choose to study modules from further mechanics, further statistics and decision mathematics.
In addition to our A and AS level classes we also have 2 classes of year 12 students studying towards the core mathematics qualification; this is an AS standard qualification that builds on the Higher level GCSE content and offers the opportunity to apply their learning in real life style contexts.


CAD: 3D solid modeling, dimensioning and tolerances, rendering, animation.
FEA: Finite Element (FEA) Analysis and simulation of stress, pressure, temperature, flow velocity distribution is space and time.
Failure Mode Effect and Analysis (FMEA): Extensive failure modes and effects analysis, and design iteration.
FEA (Finite Element Analysis)
Finite element analysis (FEA) software tools implements the physics based mathematical equations and numerical solutions in the background. All general purpose FEA software tools (ANSYS, Abacus etc.) provide a graphical user interface (GUI) to define the problem and desired simulation conditions: that it to define the 3D geometry, material properties (i.e. a rectangular plate made of cast aluminum), simulated conditions (externa load conditions and boundary conditions). Then the FEA software tool provides tools to automatically or customizer finite element mesh generation, constructs the back physics based equations and solves them using a selected numerical solution method. The result are then presented in the form of field variable distribution over space (for static simulations) and time (for dynamic simulations). For instance, the simulated results can be stress, strain, temperature, pressure, fluid speed as function of location in space (x,y,z) and time (t).
The FEA analysis process is generally described in three stages: 1. pre-processing stage where, geometry, material, simulation conditions (external inputs, boundary conditions, initial conditions) are defined and mesh is generated using the GUI tool. 2. Solver phase where the set of FEA equations are solved to simulate the conditions and predict the results. This phase can be done also interactive mode or in batch mode. Batch mode is more appropriate when a given product is to be simulated for many different parameters and external input conditions. A set of simulations can be run in batch mode 3. Post-processing stage is evaluating the results, i.e. displaying the stress distribution over the product for the simulated case. If the simulated case is dynamic, than the results can be animated over time for realistic presentation of the results. The engineer must have a solid understanding of the physics of the problem and how FEA software works. Using different FEA software packages is a simple matter of learning the GUI they provide. We must also select FEA software package that implements the appropriate physics based mathematical equations in the background, i.e. stress-strain relations, heat, energy and temperature, fluid flow and pressure relations.
- Identify different failure modes
- Analyze consequences of failures at different levels
- Estimate probability, severity and detection of failures
- Quantify risks involved in each failure mode
- Early identification and mitigation of potential failures
- Minimize late changes and warranty costs
- Helps with design choices with trade-off analysis
- Involves root cause and 5-why analysis


Using the Psion desk and scientific calculator.
The Psion calculator can be viewed as a simple desk calculator, or as a scientific calculator. You can use the keyboard or the stylus to operate it. You can flip the layout to suit right on left handed users. Operations in one view do not alter the other view, so you can swap between them without disturbing results. In the Series 7, you can use the embedded numeric keypad as well as the regular keyboard numerals.
A simple four function plus percentage key calculator with a single memory and memory add and memory subtract buttons. It provides a visual scrolling tape roll of past calculations.
A 26 memory scientific calculator with normal notation, fixed number of digits after the decimal point, and scientific notation. You can edit and reuse the last ten expressions entered, and insert the last answer at any point in the calculation. Trig functions include sine, cosign, tangent, hyperbolic trig functions sinh, cosh, tanh, and the inverse arcSine, arcCosine, and arcTangent. Powers, roots, reciprocals, common logorithms and natural logs, factorials, about 24 functions keys including the inverse function.
Base conversions. Explain use.
Shift+Ctrl+I lists keyboard shortcuts, which are different for each model of the calculator.
Ip and down arrows scroll through the till roll, or the last ten calculations in scientific view. M changes the sign of a number.
Steven Pemberton notes a hint about calculator for the Revo: typing just y, u, i, o, p is all that is necessary for the arithmetical functions (i.e. you don't have to press fn+i to get +, just i is enough).
You do need to note that different models of the Psion appear to have different keyboard shortcuts. Check your own model carefully.


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Starting Arithmetic now £ 6
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For only £1 (down from £3.60) you can buy the Tables Tables chapters from Starting Arithmetic.
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Category Archives: Science
Much of science and economics is about the rate of change, often with time. This rate of change is the slope of a graph, spreadsheets make this easy to find. Children are taught the equation of a line at primary … Continue reading
Primary school arithmetic and maths is necessary to pass many GCSEs so it makes sense to master it otherwise it will be harder to learn new stuff for GCSEs Here are some of them Accounting Biology Business and Economics Business … Continue reading


I had a request for a good math app, so this week I’m reviewing Park Math. We have the HD version for iPad.
I really like this one, although it’s very simple. There is a blue bear who walks you through the park, doing different math activities at each stop.
- On the swings, the bear counts the number of times a rabbit swings. (This one is kind of boring, but good for learners who need to hear counting out loud.)
- On the slide, the bear asks for simple addition. Since the ducks are all lined up, it’s easy for the player to count them all and get the correct answer. Or, if they want to actually have the ducks climb up, the can touch the ducks and the numbers at the top actually change so they can see the right answer. This made it easier for Ayub, since he could count, but not recognize the numbers to get the correct answer.
- On the seesaw, the learner has to put the same number of mice on each end to balance. I thought this would be too easy for Ayub, but he actually struggles with it occasionally, mainly because he just starts moving the mice around before he thinks about it.
- The apple tree asks for basic subtraction by asking how many apples will remain if a certain number fall. Again, the child can knock off the fallen apples and count the remaining ones. It even changes the apples so they can tell which ones they’ve already counted.
- There is sorting on a park bench where kids have to put the dogs in order from small to large.
- In the sand box, there is a pattern which the learner has to complete.
- And finally, there is a picnic blanket where the kid has to feed the hippo the correct number of healthy foods.
There are three levels of difficulty, so it can grow with a child. The description says the three levels correspond to preschool, Kindergarten, and first grade, but we’re still on level one, and it is the same level of addition he’s doing in school. The graphics are bright and cute. The game is pretty easy to navigate – even Lucy has played this before. The instrumental music is tolerable, although anything repeated for more than a few minutes tends to grate on my nerves. I will admit, this game doesn’t hold Ayub’s attention for as long as some others, but I think that may be because he really has to think on this one. He has only just recently started playing this, so I’m not sure if he will outgrow it quickly. It seems like some of the games could get a little repetitive. For $1.99, I’d say go ahead and give it a try.


An Overview Of Sawmill Operations Woodweb
Order of Operations Millionaire Game. In this millionaire style game, students will use order of operations to solve math problems involving addition, subtraction, multiplication, and division including exponents and parentheses. This is a single player game that can be.A typical layout of a mill using the kraft chemical pulping process is shown in figure 2 1. Mechanical, semichemical, and sulfite pulp mills differ in detail, particularly in wood preparation, fiber separation, and bleaching, but many of the downstream refining, bleaching, and papermaking processes are similar.


Kristin Holmbeck-Cannell joined Tempest Technologies as a Junior Analyst in 2012 after graduating from Loyola Marymount University (LMU) with a bachelor of science in applied mathematics. During her undergraduate career, Kristin worked on various research projects, including a project in Australia working with a GPS and inertial measurement unit to track the locations of marsupial moles, as well as an Air Force-funded research project in agent-based modeling of insurgency and civil violence. Kristin was the recipient of the LMU Program Scholar Award, the James M. and Dorothy E. Deveny Scholarship, and the Hannon Science and Engineering Endowment. She recently earned her MS in Applied Mathematics at CSU Long Beach in 2018.
She currently holds memberships at the Society for Industry and Applied Mathematics (SIAM), the Mathematical Association of America (MAA) and the National Mathematics Honorary Society, Pi Mu Epsilon.


Let the Games Begin
Rummy is a group of matching-card games notable for similar gameplay based on matching cards of the same rank or sequence and same suit. The basic goal in any form of rummy is to build melds which consist of sets, three or four of a kind of the same rank; or runs, three or more cards in sequence, of the same suit.
3 Different ways to Adjust Rummy Game into a Number related Game
The rummy game has endless varieties, and making it into a numerical game will give it instructive worth. Playing rummy, your kid may never realize they are doing extra numerical schoolwork!
Rummy Game Guidelines
Utilize an ordinary deck of cards for rummy. Arrangement thirteen cards to every kid and stack the rest of a heap on the table. Flip the top card above. The target in the online rummy game is to get a merge of either three or four cards of similar worth, or at least three cards in mathematical succession. Pros can be considered one or one over the Lord. Alternate getting cards from the shut deck or the one looking up. Set up cards in your grasp in potential sets/groupings. In a rummy game, when a player is finished with their turn, the other player gets their opportunity and picks a card from the dispose of the area or from the shut deck.
Math Variety 1: When they place the merge down in a rummy game, they should accomplish something with the numbers. From the outset, it will include or tallying them. As they get more seasoned, it may be increasing. For a lot of three fives, a youngster under ten can pick to include and could say, "Five in addition to five in addition to five is fifteen."
Math Variety 2: You can give them increase families or components to deal with to kids over 10. Include the three cards all things considered and express all the duplication realities that have that equivalent answer. A, J, Q, and K makes 36. So the player needs to concoct 6×6, 9×4, 12×3, and 2×18.
Math Variety 3: Play the rummy game and include focuses of course. Spread every one of their cards on the table and perceive the number of various numerical family groupings that can be made. Give extra focuses on every assortment. For this, Jack is 11, Sovereign 12, and the Lord is 13. A gathering with a 3, 5, 8 is an assortment 4, 9, K is an assortment. They should bring up the gathering and all the data that can be made with them, 9+4=13; 4+9=13; 13-4=9; 13-9=4, and so on.
Taking the rummy game and changing it into a mathematical game makes math more diversion for your youngster. Kids in a single-family at particular evaluations could play similar games with various desires; the more youthful ones check, the more seasoned ones include or increase or even gauge likelihood.


Year 3 Maths
Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole (ACMNA058)
Students use fractions for many different things.
– Prepare to use fractions by revising previously learnt fractions. Bring up different fractions on the IWB and ask students to name this faction. Click on the picture to show the fraction.
– Link: Fractions
– Discuss with students that fractions are equal parts of a whole. Show through pictures.
– Listen to the podcast from ‘What are fractions the Basics’
– Students look at a range of fractions, and how they are represented. They are ask to draw pictures to represent the fractions on the IWB. Link: Fractions
– Students are set the challenge to cut the paper plate into fifths. They will need to mark it out before cutting and show a teacher. They are then able to glue this into their book and colour a selected amount of fifths and write the fraction next to it. (eg: colour in 2 fifths and write 2/5)
– Cooking is a great way to teach fractions. If possible get the class together and cook some pizzas. Ask the students to prepare before they cook, by collecting the amount of people in the class, asking each student how many pieces and then tallying it all up in order to have enough pizza.
– Explain to students that a pizza normal comes in 8 slices and ask students to record the fraction for
each student in the class.
– Recording template have been linked: Pizza Day Recording Fractions.
There is also a great fractions game linked for students to play individually or it can be completed as a class.
It looks at larger fractions represented by smaller ones (eg: 4/8 = 2/4 = 1/2)
– Link: Fraction Monkeys
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The HUG is a damless system that uses kinetic power of moving water. Rapids can add 70 MW power without impacting on the environment. Africa could benefit from its kinetic power of water from rapids. This would provide a return on investment within just a few years.
Now let’s explain the real reason for the HUG: POWER
The formula for Kinetic Energy is KE= ½ x A x V 3 x (.35) efficiency (A = area swept; Velocity). The area of the throat of the HUG is 3.26 m2
Kinetic Energy = ½ x 3.26 m2 x (7.7 m/s*)3 x .35 = 260kW/turbine x 6 = 1.56 MW
Acceleration = a = g (acceleration of gravity) = 9.8 m/sec
(Final Velocity)2 = 2 x a x s (2 x 9.8 m/sec x 3.05 m)= 7.7 m/sec


Just about a few in five mothers and fathers found maths the hardest topic to assistance their small children with for the duration of lockdown, a study indicates.
The very same proportion (59 for every cent) reported that homeschooling highlighted their possess deficiency of confidence in maths and anything involving quantities, in accordance to the poll commissioned by charity Nationwide Numeracy.
But the study, of much more than 600 mom and dad, indicates that 65 for every cent believe their personal maths abilities have enhanced as a final result of homeschooling.
Research: Covid ‘puts pupils an added month at the rear of in maths’
Studying reduction: Five vital findings from new report
Viewpoint: ‘I’m hopeless at homeschooling – is that so mistaken?’
There is substantially a lot more function to do to support older people who wrestle with daily maths, the charity claims.
Lockdown: Dad and mom struggled with maths for the duration of homeschooling
Total, 39 per cent said owning to do maths can make them experience anxious, in accordance to the survey of 2,000 British adults.
Just about just one in 3 grown ups (31 for each cent) claimed they struggle with everyday maths – and 29 for each cent avoid circumstances involving numbers, the report indicates.
Serving to little ones with their homework or homeschooling is a single of the means that folks say they are battling with each day maths, the charity discovered.
Of the mom and dad surveyed, 59 per cent said maths was the most tough lesson to teach all through lockdown.
Nationwide Numeracy chief executive Sam Sims mentioned: “Range self confidence and techniques are wanted in each individual factor of lifestyle – at function, home and supporting children at college.
“This study reveals there is a enormous quantity of anxiety about numeracy and substantially more do the job to do to guidance the a single in a few British older people who say they struggle with day to day maths.
“Everyone warrants to truly feel assured with figures and this Nationwide Numeracy Day [today, 19 May 2021], we are going all out to clearly show how, with the correct help, everybody can make improvements to their each day maths.”
1 Poll questioned 2,000 United kingdom grownups – including 632 mom and dad of schoolchildren – between 4 May possibly and 6 Could.


March 14 was Pi Day. Pi is a symbol used in math to calculate circumference and area of circles.
Mrs. Gloria Simon challenged WSS to donate 314 cans of food to the Cannon County Food Bank by 3/14. For every can a student brought in, s/he got to vote for a WSS employee to be “pi-d” in the face (with a pie).
In addition, the upper grades (6-8) had a competition to see who could memorize the most digits of pi. Prizes were awarded and the winner was the student who got to throw the pie at a WSS employee.
WSS donated 930+ cans to the food bank (1001 pounds of food)
Tristan Morten was the winner of the digit recitation (64+ digits)
Elva Magana was the runner-up.


|Statement||By C.A. Van Velzer and Chas. S. Slichter ...|
|Contributions||Slichter, Charles Sumner, 1864-1946, joint author.|
|LC Classifications||QA152 .V278|
|The Physical Object|
|Pagination||ix, 371 p.|
|Number of Pages||371|
|LC Control Number||03001093|
Algebra: Structure and Method, Book 1. by Richard G. Brown. "Far better than most others" - by Derek Owens (Atlanta, GA United States) This is a well thought out Algebra textbook. I started teaching from it earlier this year and have grown to appreciate it very much. I am especially pleased the more I compare this to other books. Most math. Pre-Algebra - Fractions Objective: Reduce, add, subtract, multiply, and divide with fractions. Working with fractions is a very important foundation to algebra. Here we will brieﬂy review reducing, multiplying, dividing, adding, and subtracting fractions. As this is a review, concepts will not be explained in detail as other lessons are. This series (if you can get hold of it): PDF High School Algebra I Unlocked: Your Key to Mastering Algebra I (High School Subject Review) By Princeton Review.
Advice. Thisbook’semphasisonmotivationanddevelopment,anditsavailability, makeitwidelyusedforself-study. Ifyouareanindependentstudentthengood. high school math. social sciences. literature and english. foreign languages. High School Algebra Curriculum. Below are the skills needed, with links to resources to help with that skill. We also enourage plenty of exercises and book work. Curriculum Home. Important: this is a guide only. Check with your local education authority to find out their requirements. how one can do algebra by taking xto be just a number, and school algebra then becomes generalized arithmetic, literally. Formal algebra in the sense of R[x] can be left to a later date, e.g., a second course in school algebra. Section 1 is thus entirely elementary, and is nothing more than a direct extension of arithmetic.
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 . Access the free Student Edition of your textbook by selecting your program from the drop-down menu. No Registration Required. No Password Required. Supported By Advertisements. Choose Your Program. A Focal Points Curriculum. Bridge to Success - HS. Bridge to Success - HS Bridge to Success - MS. Common Core Common Core Algebra tutorials, lessons, calculators, games, word problems & books. This is an annotated and hand-picked list of algebra tutorials, lessons, worksheets, games, word problems, and algebra books. It is a very long list, and includes a great variety of resources. I have personally chosen each website to make sure it is truly useful for my visitors! Life of Fred teaches algebra in two books covering high school algebra, Beginning Algebra and Advanced Algebra. Each lesson in the books teaches concepts through story and examples. The book is largely self-taught. Dr. Schmidt will answer questions and .


Have you ever struggled with math homework or test preparation? Kuta Software is the solution you need. Kuta Software is a math education software company that creates interactive, customizable math solutions for students and educators.
Kuta Software has become famous for math teachers and students looking to enhance their performance and streamline their workflow.
Moreover, its user-friendly interface makes it easy for anyone to navigate, regardless of their math experience level. In short, Kuta Software is a game-changer in tackling complex math problems with ease and efficiency.
Keep reading to learn more about Kuta Software, its features, its available products, and how it can benefit educators and students. We will also discuss the benefits Kuta Software provides educators and students and look at reviews and user feedback.
Whether you are a math teacher or a student, this post will help you understand everything there is to know about Kuta Software.
Table of Contents
What is Kuta Software
Kuta Software is an incredible tool for mathematics and is the perfect solution for students and teachers alike who want to take their math skills to the next level. It has multiple customizable features, including multiple-choice and short-answer options and helpful step-by-step solutions to even the most challenging equations and problems.
Kuta Software offers a suite of math education software products to help students of all levels understand and learn math concepts. The software includes tools like equation editors, graphing calculators, and worksheet generators to help students improve their math skills.
Kuta Software was launched in 2002 by Jason Shattuck, a mathematics software who wanted to create software that would help students learn math in a fun, attractive way. Since then, the company has grown and now serves over 50,000 teachers in 90 countries.
Must-Have Features of Kuta Software
Kuta Software offers a range of features that make it easy for students and educators to use and learn from its products.
1. Customization Options
One of the unique features of Kuta Software is its customization options. Teachers can make personalized worksheets and assignments tailored to their students’ requirements. Customization options include selecting various difficulty levels, choosing specific problem types, and adding custom questions.
2. Multiple Platforms and Devices
It is software for math teachers and is available on numerous platforms and devices, including Windows, Mac, iOS, and Android. This means that students and teachers can access the software on various devices, making it easy to use both in and out of the classroom.
3. Interactive Math Solutions
Kuta Software offers interactive math solutions that help students understand math concepts through visual representation. Tools such as graphing calculators and equation editors make it easy for students to visualize equations and graphs, helping them better understand the material.
4. Unlimited Questions
Did you know that with Kuta software infinite algebra 1, you can make new questions for your assignments with just one click? Yes, it is accurate, and the best part is that the further questions will differ from the original ones but still follow the same rules. You can select the type of questions you want, and the software makes them for you. You can even create new questions for just one part of your assignment or the whole thing.
5. Presentation Mode
Kuta Software is helpful for teachers when they use it with a modern screen that shows pictures and stuff. It offers one to four questions at a time on the net. When you are teaching, you can use this tool to make your examples and then show the questions on the giant board. This saves time when planning and teaching, making it easy to show tough questions with pictures and charts.
You can display one question at a time, and you can do the following:
- Change the zoom level so that students can read it easily
- Draw lines beside the question to help you organize your work if you want to solve the question
- You can move to another question. It is helpful while reviewing homework
- Reveal the answer
- Show/hide the question number and the directions.
What is the Different Type of Kuta Software Products
Kuta Software offers a range of products designed to satisfy the requirements of different types of users.
1. Kuta Works
It is an online platform that lets teachers create and assign personalized worksheets and assignments to their students. It also provides real-time grading and analytics to help teachers track their students’ progress.
2. Kuta Software for Math Teachers
Kuta software – infinite calculus evaluating limits worksheet answers is a suite of fantastic software products designed specifically for math teachers. It includes tools like a worksheet generator, graphing calculator, and test generator, making it easy for teachers to create and assign work to their students.
3. Kuta Software for Test Prep
It is a suite of products designed to help students prepare for standardized tests such as the SAT and ACT. The software includes practice tests, quizzes, detailed feedback, and analytics to help students recognize areas they must enhance.
How Kuta Software Can Benefit Educators and Students
Kuta Software can benefit both educators and students in various ways.
1. Enhancing Student Performance
Kuta software Infinite Algebra 1 interactive math solutions can help students better understand math concepts and boost their math skills. Personalized worksheets and assignments help students work on areas where they require the most help, while real-time grading and analytics help teachers monitor their students’ progress.
2. Streamlining Teacher Workflow
Kuta Software’s suite of products for math teachers streamlines the process of creating and assigning work to students. The software makes it easy for teachers to make personalized worksheets and assignments, track students’ progress, and provide detailed feedback.
3. Accommodating Different Learning Needs
Kuta Software’s customization options and attractive math solutions accommodate various learning needs and styles. Teachers can create personalized worksheets and assignments, and students can interact with the material in a way that best suits them, whether through visual representation or practice tests and quizzes.
Math Learning Software Kuta Software Games
Kuta Software Games is a math learning software that is designed to help students learn math in a fun and exciting way.
1. Math Learning Environment
The software consists of games tailored to help students learn math concepts like algebra, geometry, statistics, and trigonometry. The games are designed to be engaging and challenging, allowing students to develop essential math skills useful for their future studies and careers.
2. Unlimited Words Game
The Unlimited Words Game in Kuta Software is a versatile and advanced tool for students to sharpen their skills. It is the best software tool for those not good at writing. It also has a custom mode, where users can add words and definitions. The game presents words in different forms like synonyms, antonyms, homophones, and multiple meanings, ensuring a comprehensive understanding of word choice in other contexts.
3. Unlimited Math Calculations
The Kuta software infinite geometry supports different mathematical disciplines like algebra, calculus, trigonometry, and geometry. It also features customizable templates to suit the specific requirements of various users. The platform’s ability to handle numerous computations helps save time and boost productivity. Another notable feature is its integration capabilities with tools like Microsoft Excel and Google Sheets.
4. Word Search
Kuta Software is a complete educational software that allows teachers and students to access and work on different math-related assignments. One of Kuta Software’s many features is Word Search, an activity that improves vocabulary retention while enhancing spelling skills. With Kuta Software’s Word Search feature, teachers can create custom worksheets for their students or choose from a library of pre-made word searches.
5. Divide and Conquer game
The Divide and Conquer game is a problem-solving tool in the Kuta Software that breaks down complex problems into smaller, manageable parts. This strategy helps individuals tackle complex tasks by allowing them to focus on specific subsets of the problem. The Divide and Conquer game works systematically, where every subproblem is solved independently before being integrated with other parts of the problem. This approach offers an organized and structured method to solve challenging mathematical equations or other specialized tasks for professionals in engineering or finance.
Using Kuta Software Login to Simplify Online Classroom Use
We are all aware online learning has become a prevalent method of education worldwide. In this context, Kuta software login has emerged as a practical approach to simplify online classroom use.
- Kuta software login is a simple and user-friendly platform that allows students to access online resources and study materials. With Kuta software login, students can access a range of subjects like mathematics, science, and social studies.
- The platform allows teachers to create and share assessments with students, monitor progress, and provide personalized feedback. Moreover, it offers a comprehensive database with expansive problem-solving questions, making it an ideal choice for distance learning.
- One of the significant benefits of using Kuta software login is its ability to personalize learning experiences. With Kuta software login, teachers can create customized assessments and track the progress of individual students. By personalizing learning experiences, Kuta software login helps students enhance their academic performance and achieve their learning goals.
- Another significant benefit of using Kuta software login is the ease of use. The platform is user-friendly and can be easily accessed on multiple devices. Students can access their assignments and course materials from any location at any time, thus providing them with flexibility and convenience. Moreover, Kuta software login is customizable, enabling teachers to streamline their online classrooms efficiently.
- In addition to providing personalized experiences and ease of use, Kuta software login also improves the accuracy and efficiency of grading. The platform’s automated grading system saves teachers’ time and effort by grading assessments quickly and accurately. This allows teachers to focus on providing feedback and addressing the individual needs of their students.
- Kuta software login is a powerful tool that has revolutionized online learning. Its user-friendly interface, personalized learning experiences, ease of use, and automated grading system make it an ideal choice for teachers and students. With Kuta software login, teachers can enhance their teaching methods and facilitate student learning, making it an essential tool for distance education.
Kuta Software Pricing and Availability
Kuta Software is a powerful suite of math software programs designed for educators and students. It is available on the Kuta Software website, and the pricing is based on the number of licenses purchased.
The more rights purchased, the lower the cost per license. Kuta Software is available for both Windows and Mac operating systems.
- Subscription Options: For those interested in subscribing to Kuta Software, flexible subscription options are available. You can also cancel a subscription at any time, and it is charged monthly or yearly, depending on the user’s preference.
- Free Trial Availability: Kuta Software offers a free 14-day trial for users who want to test the software before purchasing. This trial version has all the features of the full version, allowing users to fully consider the software before purchasing.
Customer Support and Resources for Kuta Software Users
Kuta Software offers comprehensive customer support and resources to guide educators and students to get the most out of their software.
- Support Options: Kuta Software provides a dedicated support team that can answer any questions or issues that users may have. Support can be reached through email or phone, and a response is usually received within 24 hours.
- FAQs and Knowledge Base: An extensive knowledge base includes FAQs, user guides, and other helpful resources. Users can search this knowledge base to find answers to their questions.
- Community Forum: Kuta Software also has an active group forum where users can ask questions and find help from other educators and students. This community is an excellent resource for those who want to connect with others using Kuta Software.
Reviews and Feedback on Kuta Software
Kuta Software have obtained positive reviews from educators and students around the world.
- Testimonials from Educators and Students: Many educators have reported that Kuta Software has helped them to create engaging and effective lesson plans. Students have also provided positive feedback, stating that the software has made math more fun and accessible.
- Online Ratings and Reviews: Kuta Software has received high ratings on popular review sites like Trustpilot and Capterra. Users report that the software is easy to use, effective, and provides excellent value for money.
List Of Top Competitors of Kuta Software
Kuta Software is a leading educational software provider for math teachers and students. However, it operates in a highly competitive landscape with several other prominent players.
Have a quick look at top companies, including.
Kuta Software is an excellent math software that offers educators and students powerful tools to help them succeed. The software is affordable, easy to use, and has a range of helpful resources to support users. As Kuta Software continues to grow and develop, it becomes a more valuable tool for math educators and students.
With its customizable options, innovative features, and various subscription plans, Kuta Software makes learning math easy, efficient, and enjoyable.
Kuta Software is worth considering if you are looking for math software to help you improve your math skills and streamline your workflow.
FAQ: Know Everything About Kuta Software
1. Can I try Kuta Software before purchasing it?
Yes, Kuta Software provides a free trial of its products that you can use before deciding to purchase a subscription.
2. What types of math does Kuta Software cover?
Kuta Software covers various math topics, from essential addition and subtraction to advanced calculus and trigonometry.
3. Is Kuta Software suitable for both individual and classroom use?
Yes, Kuta Software is suitable for both individual and classroom use. It provides options for single-user licenses as well as classroom licenses.
4. What kind of support does Kuta Software offer?
Kuta Software offers various support options, including email support, community forums, and a knowledge base with frequently asked questions and tutorials.


Lisbon, 5-6 June 2017
This two-day short course will be on Spatial and Spatio-temporal Bayesian Models with R, lecturing by Prof. Virgilio Gómez-Rubio, University of Castilla-La Mancha, Spain.
- This short course is aimed to statisticians and other researchers who are interested in learning about spatial statistics, how to fit spatial and spatio-temporal Bayesian models to geostatistical, lattice and point pattern data with R and R-INLA.
CEAUL - Center of Statistics and Applications, University of Lisbon, Portugal. FCT Project: UID/MAT/00006/2013


The 4th problem has strictly combinatorial nature. You're given two numbers and , where . You have to answer two following questions:
- What is the number of permutations which can be created after performing exactly swaps of adjacent elements from the sequence
- What is the number of permutations which can be created after performing at most swaps of any two elements from the sequence
I omit in that editorial the fact that you have to return these results modulo , but remember to do that.
Let's solve the first question first. The idea that came to my mind is to use the dynamic programming concept here. Let's define
number of permutations achievable from using exactly adjacent swaps, but with the restriction that we don't swap the same elements more than once.
In other words, is the number of permutations of elements with exactly inversions. That observation helps us to define a recursive relation. If we have already computed for all , we can get by inserting the -th element at some place and we know that if after that insertion, there are elements after the -th element, we just created exactly new inversions. It follows that the complete recursive relations is:
which can be computed faster as:
The last term of the above equation is define only for , otherwise it's 0.
The base cases are:
So far, we computed the number of permutations with exactly inversions. The last observation is that if you're allowed to do exactly swaps, you can achieve any permutation with inversions (the last element of that sequence is either 0 or 1 depending on the parity of ), because you can erase any inversion by swapping back these elements immediately after the inversion was made with exactly one additional swap. In other words, you can use exactly 2 swaps to make no swaps.
To compute the exact result, you have to sum up the values of for .
I suspected that the answer is somehow connected to the Stirling numbers, but didn't know how exactly. I thought that I can write a brute force solutions to provide answers for small and then use the OEIS (the On-Line Encyclopedia of Integer Sequences) to figure out the exact solution. Let be the answer to our question. It turned out that a brute force can be written as a simple DFS on the graph, where permutations are nodes, and there is an edge between two permutations if and only if you can transform one to the other using exactly one exchange of elements. I managed to do that quickly and it gave me the following table:
|n / k||0||1||2||3||4|
You can observe that the value for is the same as when because if you can exchange elements, you can create all permutations.
If you want to identify in OEIS an sequence depending on two variables ( and here), you have to put its values in the row major form i.e. print values row by row. In that case, it's 1,1,2,1,4,6,1,7,18,24,1,11,46,96,120 and it gives the sequence A109822 and the recursive relation for that is:
where is the absolute value of the Stirling number of the first kind for and . These numbers can be computed using the recurence relation and a dynamic programming concept.
The time complexity for both questions is .
You can find my solution from the contest here:


In this post, I take a closer look at the global average. What is it and what does it actually mean for us?
From my regular posts, one might have noticed that average scores are always higher for top 10K FPL teams than for random selections. Top teams have better, more diligent managers and, therefore, regularly outscore casuals. Now let’s look at the bigger picture.
Average Points Distribution
I ran a script for the overall league table after the last three match days and took snapshots of all the scores for all the 3.06 million managers in the game and here are the results.
Each graph contains two lines:
- a grey one depicts interval average scores for each 5% of FPL teams (roughly 150K teams), i.e. for the following ranges: 1-150K, 150K-300K, 300K-450K, and so on;
- a blue one depicts cumulative averages, i.e. average scores for the following ranges: 1-150k, 1-300K, 1-450K, and so on; the last one for 100% is the overall average.
Please note, that these are overall ranks on the horizontal axes, and not GW ranks. Click on a graph to make it larger.
GW12 – final results
- Official average score: 55
- Actual average score: 55.02
GW13 – intermediate results after the matches on Saturday
- Official average score: 26
- Actual average score: 26.76
GW13 – final results
- Official average score: 50
- Actual average score: 50.82
What conclusions can we derive from these data?
- Rounding. First thing that strikes my eye is that FPL doesn’t actually use the standard mathematical rounding to calculate the average. They rather use the floor function, i.e. they round average points scored down to an integer number. Therefore, actual average score is always slighly higher than the one that appears on our monitors.
- Negative slope. Both lines slope down in all the graphs. There is always a hike at the end of the grey lines which reflects good results of recently created teams.
- Overall average normally corresponds to the average points scored by the teams in the middle of the overall table, i.e. to the average score of the 50%-55% interval. Average points scored for the top 1.5M teams are higher, for the other 1.5M teams they are lower.
I’ve analysed overall league tables after the league updates. It means that such a downward slope also reflects rank changes. Indeed, teams with good scores go up in rankings increasing average scores for intervals of higher ranked teams. Teams with bad scores go down in rankings decreasing average scores for lower intervals. But what are average scores for each interval before such movements in rankings?
Well, it’s harder to create such a graph as we can’t sort the overall league table by rank as of the start of the week. But to get an idea, here is such a graph for my sample of 20K randomly selected teams for GW13:
Both lines still have a negative slope, but it is not as steep. Average score for the top 5% of FPL teams as of the end of the GW is 63.3, while average score for the top 5% of teams as the they were at the start of the week is approximately 58.2 points.
Depending on your overall rank, average points scored by FPL managers around you will be different. The higher rank one achieves, the tougher competition he gets as there are better managers around who score more points on average. It leads to the situation that every experienced FPL manager is already familiar with: over the season, gaps in the overall league table get bigger, and, with every gameweek played, it will be tougher and tougher to catch up with those who are at the top now.
In this post, I’ve only taken a look at 3 match days. Can things change from week to week? I believe this situation is typical for most weeks. Theoretically though, there might be some exceptional weeks when casuals outscore top managers. As I’ve pointed out in my latest post on the results of GW13, 60% of the average points were scored by just 10 players with high ownership. Such players usually have even higher ownership among top fantasy managers and are often referred to as ‘template’ players. If most such players fail in one single week and the likes of RvP, Sturridge, and Baines recover from injuries and bring point hauls, I guess we could see a different picture.


We know how much you love a new coin design so earlier this month we asked you to vote for your favourite 2017 release.
This turned into a hotly contested 3 horse race between the Jane Austen £2, the Sir Isaac Newton 50p and the WWI Aviation £2 coin. But there could only be one winner and the coin you chose was…
THE SIR ISAAC NEWTON 50p!
Sir Isaac Newton is widely recognised as one of the most influential scientists of all time and a key figure in the scientific revolution. He changed our understanding of mathematics and physics, redefined the way we see the world and shaped the security of our currency in his role as Master of the Mint. Designed by Aaron West, this 50p coin has been issued to commemorate the achievements of Sir Isaac Newton and remembers the legacy he left.
In total there were over 900 votes with only 29 votes separating the top 3:
The Sir Isaac Newton 50p coin is due for individual release later this year, so make sure you sign up to receive updates on its availability.


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Percentilez-score. 15.87 0.0. 17.11 0.05 What cholesterol level corresponds to the 90th percentile, the level at. g) How tall must a man be to be in the 90th percentile and 99th percentile of height for American men. Solution: In this case, you know the percent and you want b = SAT − mGP A = 550 − (53.3)(2.6) = 411. The student with a GPA in the 90% percentile has a z-score of 1.28 which corresponds. GPA = (z-score)(sGP A) + Publicerad i: Nutrition Metabolism and Cardiovascular Diseases, 26 (6), 510-516 metabolic profile, corresponding to cMetS score >= 90th percentile.
Z-scores measure how outstanding an individual is relative to the mean of a population using the standard deviation for that population to define the scale. Note that percentiles use the median as the average (50th percentile), while z-scores use the mean as average (z-score of 0). From our normal distribution table, an inverse lookup for 99%, we get a z-value of 2.326 In Microsoft Excel or Google Sheets, you write this function as =NORMINV(0.99,1000,50) Plugging in our numbers, we get x = 1000 + 2.326(50) x = 1000 + 116.3 x = 1116.3 In the Z-table you can find in the row of 2,2 and the column of 0,08 the percentile 98,87. This means that 98,87% of the population is smaller. In a kitchen of 90 cm high the lowest point of the wash-up bowl is 75 cm high.
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The average, in this case, could either be lower than 5 seconds or somewhere in between. A percentile gives a much better sense of real-world performance because it shows a slice of response time curve. The question doesn't state whether she wants at least the top 30% or at max the top 30%, but the former seems reasonable. Choosing 0.53 as the z-value, would mean we 'only' test 29.81% of the students.
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C. 90th percentile. D. 95th percentile E. None of the above.
For example, if you know that the people whose golf scores …
Finding the z-score that corresponds to a given Percentile (area shaded to the left of the z-score). 2010-09-11
A particular test-taker scored 125.6. What is the PERCENTILE rank of this test-taker's score? A. 50th percentile. B. 10th percentile. C. 90th percentile.
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GPA = (z-score)(sGP A) + Publicerad i: Nutrition Metabolism and Cardiovascular Diseases, 26 (6), 510-516 metabolic profile, corresponding to cMetS score >= 90th percentile.
This means that 90% (18 out of 20) of the scores are lower or equal to 61.7. 3. Use the QUARTILE function shown below to calculate the 1st quartile.
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p. Find a z-score Given a Percentile Using the TI-84. Watch later. Share. Copy link. Info. Shopping.


Brain Teasers/Split 100 coins with 10 heads up evenly
You have a 100 coins laying flat on a table, each with a head side and a tail side. 10 of them are heads up, 90 are tails up. You can't feel, see or in any other way find out which side is up. Split the coins into two piles such that there are the same number of heads in each pile.
- Divide the coins randomly into two piles, one with 90 coins and the other with 10 coins.
- Let's say the pile with 90 coins has n (0 to 10) coins with head up. Then the other pile has 10 - n coins with head up.
- Flip all the coins in the 10 coin pile. Now the pile has n coins with head up.