When it comes to playing dice based games of chance, knowing how to take advantage of the roll of the dice, can give you that extra edge when you need it most. There are other advantages to understanding dice probabilities.
For one, understanding dice probabilities will open up a world of calculating probabilities, which can be applied across a wide variety of applications and disciplines, especially when it comes to casino games. However, this guide focuses on dice-based games such as craps and other traditional games that require dice totals to determine winners and losers.
Calculating Dice Probabilities – It’s Easier Than You Think
While it may sound rather complex and complicated (if one were to go by the name of this guide – calculating dice probabilities), the truth is that it is considerably more accessible than you may believe. Like most skills that we learn in life, calculating dice probabilities begins with the basics and, once you’ve got those down, you can move up to more complex calculations.
The root of calculating dice probabilities begins with understanding a basic formula:
Dice probability is simply:
the number of possible results ÷ The number of desired results
In other words: If you were to desire a result of 6 (using just a single six-sided die), your probability would be:
1÷6 = 0.167
Which can also be expressed as a percentage, in this case: 16.7%
If one were to attempt to calculate the dice probability when employing two dice, the formula would be slightly different. Now we are dealing with a formula known as an Independent Probability Calculation.
So, your formula for calculating the independent results of each dice would be thus:
Probability of Both = Probability of result one (first dice) x Probability of result two (second dice)
In other words:
Let’s use our previous desired outcome of 6, only this time we want that result for both dice. Our calculation would then be:
1/6 x 1/6 = 1/36 = 1 ÷36 = 0.0278
Again, this can also be expressed as a probability percentage:
Starting with Just One Die Probabilities
If you are completely new to the concept of calculating the probabilities or outcomes of dice rolls in games, your best bet is to start with just a single die. This will make working out various calculations using the provided formula a lot easier to digest and to understand. It will also help to get you used to the art of calculating probability by looking at the number of possible outcomes compared to the results (the numbers you’re looking for) that are possible.
When we look at a single die, we see that there are six sides or six faces, numbered 1, 2, 3, 4, 5, and 6. This means that, at any given moment when the die is cast (thrown), there are six possible number results.
When applied practically, that is to say, when used in a game of chance, there will always be a specific number that you are after, over all other number facets on the die.
So, whichever number you decide is the one you are after, simply apply the formula previously covered to calculate your odds percentage:
Probability = the number of possible results against the number of desired results. So to summarise our example: Probability = 1 ÷6 = 0.167 (if 6 is your desired result. Otherwise simply replace this number with whatever number is the number that will give you the winning result).
In betting with dice, the probability is always defined between 0, which is no chance at all, and 1, which is the certainty of chance. The easiest way to express this is by multiplying your desired number by 100 to give you your probability as a percentage. In the case of our example (6) that would yield a probability percentage of 16.7 percent (chance).
Advancing to Two Dice Probabilities
Of course, most games that we all love to play usually use more than one die, the average being two. So it then becomes more useful to be able to calculate the probability percentages based on two dice, each with its own independent probability.
Now, it is important at this stage not to become flustered by the addition of another die. The formula is still simple enough to understand and to use on a practical level. In our example, we’ve used 6, the highest possible result on a standard six-sided gaming dice. When it comes to calculating the results of two (or more) dice, you then begin to move into the realm of independent probabilities. The reason for this is quite simple. The results of one die do not depend on the results of the other, which essentially means that you will need to calculate for each die separately.
Whenever you employ more than one die, you will have to deal with the separate chances or odds of each die in the roll producing the desired result that you are after. Unlike single die probability calculations, the golden rule for calculating independent probabilities is that you need to multiply the individual probabilities (each die in the roll) together to get your outcome.
With multiple dies in the roll, your formula for calculation is then modified slightly to accommodate for these changes.
While our single die formula contained only a single calculation string, your new calculation will be as follows: Probability of both die = probability of the outcome (result) of your first die times (x) the probability of the outcome of your second die.
To simplify this even further, we use fractions. Let’s say that, in our example, we’ve decided that the number 6 is optimal. Since there is a one in six chance of actually rolling a 6, your fractional representation will be 1/6. If we want both die to yield the optimal result of 6, our formula would look like this:
Probability = 1/6 X 1/6 = 1/36
To make this more useful to you, a final calculation is needed:
1/36 = 1 ÷ 36 or 0.0278
Again, this is easier to use in practical calculations when expressed as a percentage. So, if you’re looking for the probability percentage of rolling two6’s, that would be 2.78%.
What About Rolling Two Different Numbers from Two Dice?
Naturally, most games will not require prefect sixes for a win. You’ll often find that a variety of results are needed, depending on the game and what the win requirement is. Let’s say that your winning result requires a 5 and a 4. You can still apply the formula that we’ve looked at for rolling two dice with the same number result desired. However, since it doesn’t really matter which of the two dice produces the 4 and which produces the 5, you can apply the maximum 36 possible result matrix.
So, out of a total of 36 possible results, you’re looking for two specific numbers. By applying the following, slightly modified formula:
Probability = Number of possible results over the number of desired results = 2/36 or 0.0556
Again, we move this into a percentage value which helps to calculate probability more accurately:
You may have also noticed that this result actually gives you double probability over rolling two 6’s.
What About Calculating Total Score Resulting from Two (or more) Dice?
In some cases you may need to calculate the probability of getting a total score based on two or more dice. In this instance, we can still use our original formula:
Probability = The number of desired results ÷ the number of probable outcomes
However, for the purposes of determining totals, we’ll need to look a bit more into calculations based on different sides. While the same rules apply in terms of determining the total outcome based on multiplying the number of sides on your first die by the number of sides on your second die, counting the number of desired outcomes becomes slightly more tricky.
For example, if you were looking for a total of 4 from two dice, you’d have three possibilities to achieve this:
Die One = 3 + Die Two = 1 Total = 4
2. Die One = 2 + Die Two = 2 Total = 4
3. Die One = 1 + Die Two = 3 Total = 4
So, to roll a pair of dice with the resulting total of 4, we now know that there are three possible paths to the desired result. We can thus apply the same 36 possible result matrix, giving us the following formula:
Probability= Number of desired results over the number of possible results giving you 3/36 or 0.0833
Again, we can express this as a percentage = 8.33%
Interestingly, the most common number to come up as a total when rolling two dice is 7. This is because there are six different ways to achieve this total result, with a probability of:
6 ÷ 36 = 0.167 or 16.7%
Dice Probabilities in Summary
When we talk of probabilities, we really mean the chance of something happening. Within the context of a standard six-sided die, your chances of rolling a 1 are just as good as your chances of rolling a 6. This is simply because each number represented has a 1 in 6 chance of coming up.
However, when you add a second die to the game, the odds of the dice yielding a result of 2snake eyes) are far less than the dice yielding a result of 7. The reason for this is also simple since the individual die can each only produce one possible result to create a total of two, that is 1 on each die (1+1). On the other end of the scale, producing a total of 7 from two die yields far more possibilities, including:
2 + 5
4 + 3
3 + 4
5 + 2
6 + 1
Ultimately, since there are always thirty-six possible results when rolling a pair of dice, it is always best to determine the total number of possible results based on your scenario. Another example, if you require a total result of 8 to win, you would need to determine how many ways this could be achieved. In the case of a total of 8, you’d have five possible combinations:
4 + 4
2 + 6
5 + 3
6 + 2
3 + 5
Finally, to determine the probability, divide the number of ways one could achieve the desired total result by the total number of possible outcomes, which will then give you your weighted probability. Dividing 5 by 36 would then give you your probability percentage of 13.89% (0.1389).
Ethan Miller is an online casino expert with a tremendous knowledge of all casino games, games strategy, online casino bonuses and reviews. Ethan is the casino content chief editor at Casinofy
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Linear perspective revolutionized the way artists perceived and incorporated spatial depth in their work. Devised in solid, mathematical terms in the 15th century, linear perspective creates the illusion of three-dimensional space on a tow –dimensional surface.
To create effective linear perspective, artists establish a horizon line, a vanishing point on that line, and multiple orthogonal, or vanishing lines. The horizon line is a horizontal line that runs across the paper or canvas to represent the viewer’s eye level and delineates the sky meeting the ground. The orthogonal lines, which distort objects by foreshortening them, create the optical illusion that objects grow smaller and closer together as they grow farther away. These imaginary lines grow smaller and closer together as they get farther away. These imaginary lines recede on the paper to meet at one point on the horizon called the vanishing point.
The difference between one point perspective and two-point perspective is how many vanishing points there are and where they are placed on the horizon line. For more basics consider coming into Ogden Blue and take a class with one of our very fine instructor’s.


1234 Dinosaur colouring book is a fun counting colouring book with dinosaurs, flying reptiles, and swimming reptiles and footprints to count.
A fun and educational colouring book, perfect for 3 years and up. This colouring book will help make time stuck at home fun. The main pages feature a large dinosaur, flying reptile or swimming reptile illustration, its name, a numeral and number word. Main pages also feature footprints with numbers to count. There is also a double spread counting each dinosaur and a double spread collage of all the dinosaurs.
Cover printed on 300gsm Uncoated paper
Inside pages printed on 120gsm Uncoated paper
210 x 210 mm
Designed by Charlotte Filshie
If this item is sold out just get in touch to see if we have any in store and we can post out to you


Nobel Prize-winning mathematician John Nash Jr. was born in Bluefield on June 13, 1928. The math prodigy excelled at Carnegie Tech (now Carnegie Mellon University) and Princeton University.
One of his mentors was professor John von Neumann, who helped develop the computer and the hydrogen bomb. Nash focused his studies on game theory, which examines rivalries in the context of theoretical math. His 1950 doctoral thesis transformed the field of economics by applying game theory to business competition.


Saturday after 11AM
Sunday after 1PM
Friday in the afternoon
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EducationClemson University, B.A. French & International Trade (August 2007)
Clemson University, B.A. German (August 2007
College of Charleston, M.A.T. Elementary Education (May 2013)
ExperienceI love working with children of all ages! During my graduate studies, I was a substitute teacher at various schools in the Charleston area. I completed my student teaching assignment as a fourth grade teacher at Jennie Moore Elementary School. Upon my graduation, I worked as a second grade teacher at Christ Our King-Stella Maris School until 2014, when my daughter was born. I am now looking to tutor students in grades K-8 in any subject and all levels of French (I am a native French speaker).
HobbiesIn my free time, I enjoy playing trivia, running, arts & crafts, needlework, traveling, and chasing after my 1-year-old daughter. I work part time as an after school teacher at Christ Our King-Stella Maris School.
SAT Subject Test in French with Listening, 8th Grade math, 7th Grade Writing, 7th Grade Science, 7th Grade Reading, 7th Grade math, 6th Grade Writing, 6th Grade Science, 6th Grade Reading, 6th Grade math, 5th Grade Writing, 5th Grade Science, 8th Grade Reading, 8th Grade Science, SAT Subject Test in French, French 4, French 3, French 2, French 1, French 1, CLEP French, AP French Language and Culture, AP French, Kindergarten - 8th Grade, 8th Grade Writing, 5th Grade Reading, 5th Grade math, 1st Grade math, 8th Grade, 7th Grade, 1st Grade, 2nd Grade, 2nd Grade, 3rd Grade, 4th Grade, 5th Grade, 6th Grade, French, 1st Grade Reading, 1st Grade Writing, 4th Grade Writing, 4th Grade Science, 4th Grade Reading, 4th Grade math, 3rd Grade Writing, 3rd Grade Science, 3rd Grade Reading, 3rd Grade math, 2nd Grade Writing, 2nd Grade Reading, 2nd Grade math, Elementary Math
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- The way I show composing â€“ This post stops working in more detail the way I show composing making use of a workshop model.
- Kinds of Writing Lessons â€“ If you’ve got ever been uncertain of precisely what classes to instruct in writing or you merely want newer and more effective tips for composing classes, always check down this post for concept a few ideas and a few ideas for producing classes according to your studentsâ€™ needs.
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- COMPLIMENTARY Toolkit that is writing Printables Grab some free printables and strategy cards to simply help your students work separately and thrive during composing workshop.
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- Totally free Persuasive Writing encourages â€“ Grab a list and collection of task cards of my personal favorite persuasive writing prompts for 4th/5th graders.
fifth Grade Math Some Ideas
We show mathematics through a combination of entire group instruction and mathematics facilities. Below you’ll find plenty of links on how to utilize directed mathematics facilities in an upper classroom that is elementary.
- How we Teach mathematics in fifth Grade â€“ This post provides an in depth breakdown of the way I train math to my 5th graders.
- Getting to grips with Math Centers â€“ mathematics centers are a huge section of my mathematics instruction. This post will make suggestions through some relevant concerns and points to consider when you’re beginning mathematics facilities.
- Launching Guided Math Centers â€“ This post stops working the guidelines and actions to effectively introducing led mathematics facilities.
- Led mathematics Procedures to Teach â€“ On this post, we share most of the procedures to teach for directed mathematics, including the things I do within my class room.
- Arranging Your Math Block â€“ For this post, we share a few other ways you can schedule your mathematics block.
- Organizing Math Centers â€“ On this post, I share methods for arranging mathematics centers and show the containers i personally use to arrange mine.
- Managing Math Centers â€“ In order for mathematics facilities to work, they should appropriately be managed. Check this out post for all guidelines and some ideas for managing mathematics facilities.
- Led mathematics when you look at the Upper Grades â€“ This post stocks a look that is visual description of each and every of my mathematics facilities.
- COMPLIMENTARY Guided Math Binder â€“ Get and stay arranged with one of these free guided math types and printables.
- Mathematics Manipulatives for fifth Grade â€“ On this post, we share my favorite manipulatives with plenty of free printables and tasks.
- My Top Tip for Making Math Centers Work for me personally â€“ This post shares my top tip to make mathematics centers work with me personally with some freebies.
- 7 How to help Students with Math Centers â€“ All pupils may be effective with mathematics centers. Study guidelines and methods to aid pupils with this post.
- Training mathematics with Small Groups â€“ In addition to mathematics facilities, we additionally show entire team instruction with little groups. Find out more with this post.
- COMPLIMENTARY Take Home Multiplication and Division Math Facts Toolkits â€“ grab plenty of free printables and resources which will make your own personal mathematics facts get hold of toolkits about this post.
- Math Bulletin Board Ideas â€“ Want some some ideas for mathematics bulletin panels? Positively always check away this post!
fifth Level Math Skill-Specific Posts and Freebies
Click the links below to see my archive of posts and resources for every fifth grade mathematics ability.
Technology and Social Studies
- How exactly to Implement Close studying in Science â€“ This post helps guide you to make use of close reading with science texts and passages. This tactic additionally works together social studies texts.
- Quick and Easy Social Studies Ideas â€“ with this post, we describe two of the best (and simple that is super social studies tips.
- Making Textbook studying Engaging and Comprehensible for All Learners â€“ You certainly will definitely wish to check always this post out in the event that you anticipate making use https://fdating.reviews/ of a social studies or technology textbook. This post stocks a strategies that are few engaging pupils when reading a textbook.
Listed below are a blog that is few about class administration which are especially beneficial to fifth grade instructors.
- Classroom Management guidelines: This post shares my classroom management tips that are best whenever using fifth graders.
- How to approach chatting right back â€“ a strategy is shared by this post for coping with pupils who argue or talk right back.
- A method for Excessive Talking â€“ On this post, we share a proven way that we manage excessive talking with my fifth graders.
- Just how to Keep Procedures in position All Year â€“ everybody knows just how essential training procedures are. This post stocks just how to keep those procedures all 12 months.
Assessments and Grading
- Data Tracking Forms for Benchmark or Quarterly Assessments â€“ you track your data if you give quarterly assessments, grab the free forms on this post to help.
- The main one information Tracking Form to make use of with Any Assessment â€“ This COMPLIMENTARY data form that is tracking with any evaluation and it is my go-to tracking kind.
- Practical guidelines for Standards Based Grading â€“ in the event that you have to utilize standards based grading, check always away this post for many practical guidelines.
Aside from the above linked websites, i’ve some favorite products which are an absolute must have if you’re teaching 5th grade when it comes to time that is first


Oh dear, he’s going to try to teach us again…
Using Probability to Cheat the Lottery
The number that has come up the fewest number of times in the National Lottery in the UK is the number 20 (175 times). The number that has come up the most frequently is the number 44 (244 times). This is despite the fact we have every reason to believe each ball is equally likely to occur.
From this, can you guess which numbers you should pick next time you play? Should you pick the most frequently occurring numbers: 44, 38, 40, 23, 33, 39 on the grounds that they come up the most frequently? Do you really believe these balls are inherently more likely to be pulled out of the machine, in a repeatable way?
Or should you pick the numbers that have occurred the fewest number of times: 20, 13, 41, 16, 21, 15? If all the balls are equally likely to come out we expect the statistics to tend towards equal numbers, so are these numbers due?
What about the numbers that have gone the longest without being picked: 46, 12, 1, 27, 45, 35. Surely, every week they don’t get picked increases the likelihood of it being picked next time.
Have you decided which of these three options you’d side with?
If you selected option 1, no points. If you selected option 3, no points. But if you selected option 2, still no points. The fact is that historical trends have no impact on future consequences in a system like this. Each time all the balls are put back in and the probability doesn’t change. Some readers may be familiar non-experts with “Probability Theory”. Probability Theory is a method of determining how likely things are based on their historical trend; common things occur commonly, to over-simplify it.
Probability Theory Vs. The Principles of Probability
If historical patterns tell us nothing, what is Probability Theory about? See, historical patterns do tell us something. Historical patterns tell us the likelihood of a things happening, within certain confidence intervals.* But historical patterns don’t affect the probability, they are simply a method of understanding the chances. In fact, Probability Theory tells us that the chance of each ball coming out of the lottery machine is about equal, but not exactly equal. The principles of probability you learned in school tell us that Probability Theory came out as “about” equal because of the imperfections of statistics in action (i.e. the practical results).
*If Probability Theory tells us the probability of a thing happening 36/100, the truth could be anywhere between 30-42/100. The confidence interval is 6.
Join me in a small experiment: take any die you believe to be unbiased. Now, roll it 36 times and record each time each number comes up. Doing it? Okay. We’re going to analyse the data twice: once according to the principles of probability (that you learned in school) and once according to Probability Theory.
Did you get each number 6 times? No. Does that lead you to believe that your die is biased? No. You accept that there is a difference between the theory and the practice, and that in theory the probability is still 1 in 6 for each six numbers. You wouldn’t believe your die was biased unless one number came out sixteen times or more. This is you doing something called “significance testing”. There is an accurate way to do it, but you can kind of guess. Yes the numbers came out different numbers of times, but you don’t feel that difference is significant. So you continue guessing around 1/6 probability.
Now analyse your data backwards. Forget that each face of a die has a 1 in 6 chance of coming up, and look at your data. Using Probability Theory, now tell me whether your die is biased or not? Probability Theory takes the practical results, and builds the principle out of them, which is the reverse of what we just did. The method for doing this is pretty simple, write the following fraction:
(the number of times a number came up)/(the number of events)
I told you to do this 36 times, so it is:
(the number of times a number came up)/36
I know you didn’t do the experiment, so here are my results:
1: 4/36 =1/9
2: 6/36 =1/6
4: 8/36 =2/9
6: 6/36 =1/6
According to Probability Theory my die is biased against the number 1 coming up and for the number 4.


I get this strange result by substracting earlier time stamp for later one:
pd.to_datetime('2021-05-21 06:00:00') - pd.to_datetime('2021-05-21 06:02:00')
Timedelta('-1 days +23:58:00')
Timedelta('-0 days 00:02:00')
What is the correct way to calculate a negative time difference? Thank you!
Timedelta('-1 days +23:58:00') is the proper representation of a negative time difference in pandas (and also in pure python)
# using pure python from datetime import datetime datetime(2021,5,21,6,0,0) - datetime(2021,5,21,6,2,0) datetime.timedelta(days=-1, seconds=86280)
this is because the difference is properly calculated as
-120 seconds, but individual time elements cannot exceed their moduli. the timedelta components are normalized. To represent negative 2 minutes, a negative day & positive time component are used.
and days, seconds and microseconds are then normalized so that the representation is unique, with
- 0 <= microseconds < 1000000
- 0 <= seconds < 3600*24 (the number of seconds in one day)
- -999999999 <= days <= 999999999
Note that normalization of negative values may be surprising at first. For example:
from datetime import timedelta d = timedelta(microseconds=-1) (d.days, d.seconds, d.microseconds) (-1, 86399, 999999)
it is possible to retrieve the total seconds as a negative integer using the method


LED displays are mostly driven by pulse width modulation, and gray levels are represented by different pulse widths. Therefore, the LED emission state is always the same, and the gray level is represented by the length of the luminescence.
Formula (1) is the color coordinate calculation formula of LED, X, Y, Z is three stimulus value, t is the luminous time, LED through the pulse width modulation gray level, the luminous time t determines the gray scale size, from the formula (1), no matter how gray level change, its color coordinates remain unchanged.
There is a linear relationship between the gray level and the XYZ three stimulus value and the time t. When the total gray scale series of LED display is N, the XYZ three stimulus value corresponding to each gray level step "1" is as follows:
The gray value of LED, N and M is three, XYZ, K, respectively:


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IGN is Ducal
not sure if this is a bug or a misunderstood “feature”.
The expected difficulty (for attacker) or bonus (for defenders) is thought to be:
1 skull = Nil
2 skull = 25%
3 skull = 50%
4 skull = 75%
5 skull = 90%
however through observation this appears to not be the case.
2 skull @ 20%
3 skull @ 30% or so
4 skull @ 60%
5 skull @ 65%
the in game graphics bar is grossly incorrect, they imply what is expected as above but the maths seems very different.
The pictures below are for a 5 skull battle. They show that with nearly a 3rd of points the alliance on the left is still behind.
Could this be looked into please?


Elementary school children who need a little extra help with their homework have a new resource at the library. Brittini Trytek, a teacher at Holy Name, will be available at the library from 5-8 on Monday, Wednesday and Thursday and all day on Saturday to assist children who need help in getting their homework done.
The children should bring their books and their homework assignment with them to the library. Brittini will help them understand how to do the assignment. She will not do the assignment for the children. With Learning Express, an online database, and other library resources, Brittini and the children can do extra practice in math and reading.
Brittini can help children research material for projects using the books in the library and trusted Internet sources. She will teach the children how to find accurate online information using the Student Research Center, Learning Express, Ebsco Digital Books and Kids.gov.


Created by W.Langdon from gp-bibliography.bib Revision:1.7615
The proposed genetic programming approach for nonstationary data analytics (GPANDA) provides a piecewise nonlinear regression model for nonstationary data. The GPANDA consists of three components: dynamic differential evolution-based clustering algorithm to split the parameter space into subspaces that resemble different data generating processes present in the dataset; the dynamic particle swarm optimization-based model induction technique to induce nonlinear models that describe each generated cluster; and dynamic genetic programming that evolves model trees that define the boundaries of nonlinear models which are expressed as terminal nodes.
If an environmental change is detected in a nonstationary dataset, a dynamic differential evolution-based clustering algorithm clusters the data. For the clusters that change, the dynamic particle swarm optimization-based model induction adapts nonlinear models or induces new models to create an updated genetic programming terminal set and then, the genetic programming evolves a piece wise predictive model that models the dataset.
To evaluate the effectiveness of GPANDA, experimental evaluations were conducted on both artificial and real-world datasets. Two stock market datasets, GDP and CPI were selected to benchmark the performance of the proposed model to the leading studies. The GPANDA outperformed the dynamic genetic programming benchmarks and was competitive to the state-of-art-models.",
Supervisor: Nelishia Pillay",
Genetic Programming entries for Cry Kuranga


Ep. 19. How To Make Numbers Sticky: Chip Heath on Making Data Count
GUEST: Bestselling author Chip Heath, Making Numbers Count
When we look at the world through numbers, our brains can’t always compute the full picture, says Chip Heath, co-author of Making Numbers Count. On this episode, this New York Times bestselling author (Made to Stick, Switch) shares how the right numbers told the right way can be absolutely illuminating. The trick is translating ...
February 6, 2022


|DNA source||Cosine (BTSF)|
|Powers and Abilities|
Enhanced Mathematical solving skills
Extendable ruler claws
|Users||Ben Tennyson (BTSF)|
|Series||Ben 10: Stupidity Force|
Ben 10: Stupidity Force: End Of Omnivangelion: Future
|First Appearance||Stupidity Force: REBORN|
Math is a Complexian alien from the planet Complexia. His name is a pun on the word "math" which means "boredom" or "evil". He appears in Ben 10: Stupidity Force and Ben 10: Stupidity Force: End Of Omnivangelion: Future.
Math is at least (9+7*68)/68 (solve that and you will find out) feet tall, and resembles a bipedal math teacher, with one ruler coming out of each wrist, and no tail. Despite the fact that Complexians are supposed to know nothing but boredom and mathematics, Math is shown to be friendly towards nerds (though not at first).
Math has super-human math powers and agility, enabling him to jump great distances and calculating how far he flew and lift objects many times his weight and discovering the objects size.
He also possesses a large, retractable, ruler on each wrist. This ruler can be used to hit or measure opponents or to create a shockwave. He is also extremely durable, being shown to be able to survive in history class and eat a anchovies pizza with no apparent effect. Math can also release a sonic bore from his mouth, although this seems to be more of an intimidation tactic rather than an offensive feature. Even though he is not the coolest of Len's aliens, he can perform mathematical moves with expert execution.
Complexians brains are hardwired for nerdiness, and, as such, Math's only weaknesses are his lack of coolness, and highly boring temperament. This causes Math to become easily distracted and difficult to stop once he starts solving math problems.
- Con of Math


AI Hub Tampere workshop for engineers interested in educational and practical application of numerical optimization and control on August 25th, 2023.
About the Event:
The workshop will start with a short introduction of AI Hub and our research group. Then, we provide some motivating examples on numerical optimization. In the next part, we will have a demo on implementation of the optimal control on a real robot.
Further, the workshop will continue with some fundamental concepts in numerical optimization, such as quadratic and nonlinear programing, single/multiple shooting, etc. Then, we introduce CasADi, an optimization framework suitable for many largescale problems. Set of simple educational examples with increasing complexity have been prepared, so you can try and play with during the workshop. This will help you to get a grasp on how some abstract concepts can be programmed and solved, even if you do not have much prior experience about the topic.
We will also show some examples derived from real life applications, where you can use these techniques, including trajectory optimization and a model predictive control. We will also brief how optimal control can be used in the context of shared control.
Attending the workshops requires the installation of CasADi toolbox and other software.
Ilmoit. päättyy: 25.08.2023 00:00


Method of factors is a mathematical approach used to solve problems by breaking them down into smaller, more manageable pieces. The method is also known as the factorization method or the factor analysis method. The method of factors is used in a variety of fields, including physics, engineering, and economics. It has also been used in studies of human behavior, such as psychological experiments. The advantage of the method of factors is that it allows for a more systematic and efficient way to solve problems.
What Are The Main Types Of Factors?
There are four main types of factors:
1. Common Factors
2. Unique Factors
3. Environmental Factors
4. Situational Factors
How Do You Teach Factors?
There are a few different ways that you can teach factors, depending on the age and ability level of your students. For younger students, you can use games and activities to help them understand what a factor is. For older students, you can introduce more abstract concepts such as algebraic expressions one of the branches of mathematics.
One way to teach factors is to have students find all the factors of a number. This can be done with a game or activity in which students have to identify all the factors of a given number. For example, if you are finding factors of 24, the student would identify 1, 2, 3, 4, 6, 8, 12, and 24 as its factors. To make this more challenging, you can give larger numbers or ask for specific types of factors (such as prime numbers).
Another way to approach this concept is to have students find the greatest common factor (GCF) of two or more numbers. This can be done by listing out the factors of each number and finding the largest number that appears on both lists. For example, if we were finding the GCF of 12 and 18, we would list out their factors:
12: 1, 2, 3, 4, 6, 12
18: 1, 2, 3, 6, 9
What Are Factors For Beginners?
If you’re new to the method of factors, there are a few things you should keep in mind. First, it’s important to have a good understanding of basic algebra. Second, the method of factors is best used for solving quadratic equations. Third, be sure to check your work carefully when using this method, as mistakes can easily be made.
How Do You Explain Factors To A Child In Math?
There are a few different ways to explain factors to a child in math. One way is to use a number line. Start with the number 1 and draw a line. Then, count up by 2’s until you get to the number 10. Next, count up by 3’s until you get to the number 15. Finally, count up by 4’s until you get to the number 20. By the end of this exercise, the child should be able to identify the factors of any number on the number line.
Another way to explain factors is through multiplication. For example, if you’re trying to find the factors of 12, you can start by breaking it down into two smaller numbers: 3 x 4. This shows that 3 and 4 are both factors of 12. You can also use multiplication to show that 1, 2, 6, and 12 are all factors of 12 by multiplying 1 x 12, 2 x 6, and so on.
Finally, another way to help a child understand factors is by using objects or pictures. For example, if you’re trying to find the factors of 16, you could start by drawing a square with 16 dots inside it. Then, ask the child to draw lines connecting any two dots along the edge of the square – this will create 4 equal sections within the square. This shows that 1, 2, 4, and 8 are all factors of 16 because they can divide the square evenly into four sections.
What Is Difference Between Factors And Multiples?
Factors are the numbers you multiply together to get another number. Multiples are the numbers you get after multiplying a number by an integer (whole number). Factors are always smaller than the number they produce; multiples are always larger. For example, factors of 12 are 1, 2, 3, 4, 6, and 12; multiples of 12 are 12, 24, 36, 48, 60. You can find out if a number is a factor of another number by division: if the remainder is zero, then the first number is a factor of the second. Find out if a number is a multiple of another number by multiplication: if the result is equal to the second number, then the first one is a multiple of the second. You are getting this knowledge only on infospreee.com.


2016 CAP = $185,100
2015 CAP = $183,300
NOTE: There may be an additional federal cap applicable to the effort report due to federal legislation raising the cap maximum from $183,300 and it will affect effort reporting beginning on the 1/16 report.
The salary cap amount for each half year is calculated as follows using the 2015 Salary Cap:
January – June = 181 days (182 if leap year)
July – December = 184 days
$183,300/365 days = $502.19/day
$502.19/day x 184 = $92,402.96 (salary cap amt. for 6 month period July – Dec.)
$502.19/day x 181 = $90,896.39 (salary cap amt. for 6 month period January – June)
Individuals with 1 FTE, which is the majority, will have the difference between the cap paid amount, and what should have paid calculated as follows:
$142,695.48 = ~ ½ of total base of $285,391 (4 cent difference due to HCM systemic rounding). This is the amount used to calculate the cost share portion in the system.
$142,695.48 x 3.49% adjusted pay = $498,007.23/$100,670.08 (salary cap maximum amount of pay)
= 4.946% (4.95% rounded).
4.95% - 3.49% = 1.46%
1.46% is, then, the minimum effort adjustment needed. Obviously, this can be more depending on amount of effort actually committed. (E.g., 5% was actual vs. 4.95%)
Should there be an occurrence of an individual less than 1.0 FTE, the system calculates what their salary would be at 1.0 in order to be able to ascertain this adjustment. For example:
Annual Base Salary = $200,000
FTE = 0.75
Salary Cap = $183,300
Amount of actual pay against salary cap in system = 10%
$200,000/.75 = $266,667 (Adjusted amount salary would be if 1.0 FTE)
$266,667*.10 (% paid in system) = 26,667/$183,300 (salary cap) = .1455 or 14.55%
14.55%-10% = 4.55%
4.55% is, then, the minimum effort adjustment needed. Again, this can be more depending on amount of effort actually committed.


I am new to Java Programming and have no clue what I'm doing. I have an assignment that involves base converting. I really need help getting started because I don't even understand the instructions. Here is the assignment:.
The simple math behind decimal-binary conversion algorithms
One algorithm for converting a base 10 number to another base b involves repeatedly dividing by b. Each time a division is. At each step, the dividend is the quotient from the preceding step; the. The algorithm stops when the quotient is 0. The number in the new base is the sequence of remainders in.
In this exercise you will use this algorithm to write a program that converts a base 10 number to a 4-digit number in another. The base 10 number and the new base. The start of the program is in the file BaseConvert.
The simple math behind decimal-binary conversion algorithms
Save this file to your. The program will only work correctly for base 10 numbers that fit in 4 digits in the new base. We know that in base 2 the. In base 8, the maximum. In general, the maximum base 10 number that fits in 4 base b.
Add an assignment statement to the program to compute this value for the base that is input and assign it. Add a statement that prints out the result appropriately labeled. Compile and run the. Now add the code to do the conversion. The comments below guide you through the calculations—replace them with the. So far the program does not print out the answer. Recall that the answer is the sequence of remainders written in reverse.
Since they are each integers, if we. So, we will use a variable of type String.This site offers several examples where representing a number in a base different from the customary 10 may have a great advantage.
For example, binary representation is instrumental in solving NimScoringTurning Turtles and other puzzles. As every one knows nowadays, this is also the system underlying the modern computer technology. Along with the binary, the science of computers employs bases 8 and 16 for it's very easy to convert between the three while using bases 8 and 16 shortens considerably number representations.
To represent 8 first digits in the binary system we need 3 bits. In order to obtain its binary representation, replace each of the four digits with the corresponding triple of bits: For the hexadecimal system conversion is quite similar, except that now one should use 4-bit representation of numbers below Thus it appears that the shortest way to convert numbers into the binary system is to first convert them into either octal or hexadecimal representation.
Now let see how to implement the general algorithm programmatically. For the sake of reference, representation of a number in a system with base radix N may only consist of digits that are less than N. Let's represent the algorithm mnemonically: result is a string or character variable where I shall accumulate the digits of the result one at a time.
I would like to have a function say called Conversion that takes two arguments M and N and returns representation of the number M in base N. The function might look like this.
As you see, at some point the function calls itself with a different first argument. One may say that the function is defined in terms of itself.Jave walk through: Number Base Conversion
Such functions are called recursive. The best known recursive function is factorial : n! The function calls applies itself to its arguments, and then naturally applies itself to its new arguments, and then We can be sure that the process will eventually stop because the sequence of arguments the first ones is decreasing. Thus sooner or later the first argument will be less than the second and the process will start emerging from the recursion, still a step at a time.
Not all programming languages Basic is one example allow functions to call themselves recursively. Recursive functions may also be undesirable if process interruption might be expected for whatever reason. For example, in the Tower of Hanoi puzzle, the user may want to interrupt the demonstration being eager to test his or her understanding of the solution. There are complications due to the manner in which computers execute programs when one wishes to jump out of several levels of recursive calls.
Note however that the string produced by the conversion algorithm is obtained in the wrong order : all digits are computed first and then written into the string the last digit first. Recursive implementation easily got around this difficulty. With each invocation of the Conversion function, computer creates a new environment in which passed values of M, N, and the newly computed S are stored.
Completing the function call, i. Recursive functions store a sequence of computations implicitly. Eliminating recursive calls implies that we must manage to store the computed digits explicitly and then retrieve them in the reversed order. It's best implemented with a stack data structure. Stack admits only two operations: push and pop.
Intuitively stack can be visualized as indeed a stack of objects. Objects are stacked on top of each other so that to retrieve an object one has to remove all the objects above the needed one. Obviously the only object available for immediate removal is the top one, i.
The function is by far longer than its recursive counterpart; but, as I said, sometimes it's the one you want to use, and sometimes it's the only one you may actually use. Contact Front page Contents Algebra. What is what?If you search the web for "How to convert from decimal to binary" you will find four simple algorithms: two for the integer and two for fractions. They are presented with examples below in the first part of the article.
In the second part this article explains the very basic math behind each of them. Knowing it may help you remember any of the algorithms if you suddenly forget them.
I strongly suggest you take a notepad and a pen and perform the operations along with me to better remember the math.
Here are the four algorithms with examples that you can find on the web. To convert integer to binary, start with the integer in question and divide it by 2 keeping notice of the quotient and the remainder.
Continue dividing the quotient by 2 until you get a quotient of zero. Then just write out the remainders in the reverse order. Here is an example of such conversion using the integer Now, we simply need to write out the remainder in the reverse order — So, 12 in decimal system is represented as in binary.
To convert fraction to binary, start with the fraction in question and multiply it by 2 keeping notice of the resulting integer and fractional part. Continue multiplying by 2 until you get a resulting fractional part equal to zero. Then just write out the integer parts from the results of each multiplication. Here is an example of such conversion using the fraction 0.
So, 0. To convert binary integer to decimal, start from the left. Take your current total, multiply it by two and add the current digit. Continue until there are no more digits left. Here is an example of such conversion using the fraction To convert binary fraction to decimal, start from the right with the total of 0.To get back the original number we count all the integers in the binary number we have 5.
We write from right to left the first 5 powers of two, starting with the power zero:. Now we multiply each of these numbers with their respective from the original binary number: Then we add each pair. We get:. Java code for converting from decimal to hex.
Clicking on a short link user will be automatically redirected to the original URL. There are many URL shortening services available online, like tiny. Implementing a URL shortening service is not a complex task, and it is often part of system design interviews. In this post, I will try to explain the process of implementing the service. Before implementation, it is always a good idea to write down what it is needed to be done in the form of functional and non-functional requirements.
Users need to be able to enter a long URL. Our service should save that URL and generate a short link. Users should have the option to enter the expiration date. After that date passed, the short link should be invalid. Let's say that we want to have a short link with a maximum length of 7. The most important thing in a URL shortener is the conversion algorithm. URL conversion can be implemented in several different ways, and each way has its pros and cons.
When using a hash function, it is sure that different inputs will result in different outputs. The result of the hash is longer than seven characters, so we would need to take the first seven characters. But, in this case, there could be a collision because the first seven characters could already be in use as a short link. Then, we take the next seven characters, until we find a short link that is not used.
The second way of generating a short link is by using UUIDs. The probability that a UUID will be duplicated is not zero, but it is close enough to zero to be negligible.
Since a UUID has 36 characters, that means that we have the same problem as above. We should take the first seven characters and check if that combination is already in use. The third way would be converting numbers from base 10 to base A base is a number of digits or characters that can be used to represent a particular number. Base 10 are digits , which we use in everyday life and base 62 are [a-z][A-Z]. This means that, for example, a number in base 10 with four digits would be the same number in base 62 but with two characters.
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Java Programming - Base Conversion...PLEASE HELP!?
I've been looking into the math behind converting from any base to any base. This is more about confirming my results than anything. I found what seems to be my answer on mathforum. I have the converting from a larger base to a smaller base down okay because it is simply take first digit multiply by base you want add next digit repeat. My problem comes when converting from a smaller base to a larger base. When doing this they talk about how you need to convert the larger base you want into the smaller base you have.
An example would be going from base 4 to base 6 you need to convert the number 6 into base 4 getting You then just do the same thing as you did when you were converting from large to small.
The difficulty I have with this is it seems you need to know what one number is in the other base. So I would of needed to know what 6 is in base 4. This creates a big problem in my mind because then I would need a table. Does anyone know a way of doing this in a better fashion. I thought a base conversion would help but I can't find any that work.
Shortening Strings (URLs) using Base 62 Encoding
And from the site I found it seems to allow you to convert from base to base without going through base 10 but you first need to know how to convert the first number from base to base. That makes it kinda pointless. Commenters are saying I need to be able to convert a letter into a number.
If so I already know that. That isn't my problem however. My problem is in order to convert a big base to a small base I need to first convert the base number I have into the base number I want.
In doing this I defeat the purpose because if I have the ability to convert these bases to other bases I've already solved my problem. Edit: I have figured out how to convert from bases less than or equal to 10 into other bases less than or equal to I can also go from a base greater than 10 to any base that is 10 or less. The problem starts when converting from a base greater than 10 to another base greater than Or going from a base smaller than 10 to a base greater than I don't need code I just need the basic math behind it that can be applied to code.
This seems a very basic question to me, so excuse me if I lecture you a bit. The most important point for you to learn here is that a number is not its digit representation.We want to convert a decimal number to binary with the arithmetic calculations done in binary. We can use nested multiplication as in Horner's Algorithm to represent a number:. As binary arithmetic is very tedious for us we would prefer to utilize the division algorithm and perform repeated division by the base recording the remainder each time.
Divide both sides of this equation by bthe remainder is then a 0repeat and the remainder is a 1then a 2etc. Converting a fraction to base b is as simple, just use repeated multiplication and recover the integer part each time until the desired accuracy is achieved.
Now the computer saves a lot of calculation time by using a table lookup. We can do the same thing in our math. Most of us have the binary numbers through 8 memorized. Converting from base 8 to base 2 is just a 3 digit lookup converting from hexadecimal to binary is just a 4 digit lookup.
Example Covert We will treat the integer and fraction parts separately for now. Complements in Radix r. Euclid's Division Algorithm.


STEAM & SEAL DAY
SATURDAY, MAY 12TH
9:00 AM – 12:00 PM
With the introduction of a new STEAM lab at Samuels, we aim to create a better future for our students by instilling an understanding and desire to learn about STEM concepts from an early age. By providing applicable skills in science, technology, engineering and math, Samuels students will also be prepared for the next level of their education. Samuels will become a STEAM pipeline school, allowing interested students to continue their STEM-focused education at Hamilton Middle School and Thomas Jefferson High School after they graduate from Samuels.
Check out the STEM website today!
3rd-5th grade students document their STEM learning in Seesaw.
You can connect to your child’s STEM journal by following the directions below:


The Shine Academy is excited to announce that it will offer Shine 7+ and 8+ programmes from Summer term (April 2022). These will comprise 1.5 hour sessions every weekend during term time. These sessions will aim to reinforce a strong maths foundation and to stretch the children to the right level for their upcoming 7+ and 8+ exams.
The following time slots for Y1 and Y2 groups next term are currently available:
- Shine 7+ Programme, for Y1 children:
- 9:00 – 10:30AM on Saturdays
- 10:45AM – 12:15PM on Sundays
- Shine 8+ Programme, for Y2 children:
- 11:15 – 12:45 on Saturdays
- 11:15 – 12:45 on Sundays
A Brief Introduction to The Shine Academy:
The Shine Academy is an accelerated learning programme focused on improving our children’s intellectual and cognitive skills in maths. The Shine programme is highly structured and systematic based on Shanghai maths teaching methodologies adapted for the UK curriculum.
The Shine programme is based on weekly weekend sessions during term time, delivered in small groups of c. 6 children. For KS1 students, our sessions are 1.5 hours long and for our KS2 students it is 2 hours long.
There are groups across all year groups for primary schools: Y1 and Y2 are mainly for those who are going to sit 7+ and 8+, and Year 3-5 programme is focused on building the children’s mathematical mindset, stretch and challenge their maths abilities and prepare them for 11+ exams and secondary schools.
The Shine Academy offers one free trial session for new students. If you’re interested in trying the Shine programme for your child, please contact them via the ‘contact us’ link on The Shine Academy website.


WASHINGTON D.C. – The Biden Administration’s Department of Education revealed in a report published on Thursday that mandatory COVID-19 school lockdowns and remote learning had a seriously negative impact upon American students, with one of the steepest declines in grades in decades in a wide variety of subjects, including reading, mathematics, and others.
The Education Department noted that grades dropped across the board throughout – and after – the pandemic to degrees not seen in education in over 30 years.
“In 2022, the National Center for Education Statistics (NCES) conducted a special administration of the NAEP long-term trend (LTT) reading and mathematics assessments for age 9 students to examine student achievement during the COVID-19 pandemic,” the report said. “Average scores for age 9 students in 2022 declined 5 points in reading and 7 points in mathematics compared to 2020,” the DOE claimed. “This is the largest average score decline in reading since 1990, and the first ever score decline in mathematics.”
According to records kept by NCES – part of the Department of Education that collects, analyzes, and publishes statistics on education – math scores went down for the first time ever, whereas reading experienced its most major decline in three decades; these statistics affected students almost uniformly, students with histories of lower academic performance showed an even greater drop in scores than their higher-achieving classmates.
“In 2022, reading and mathematics scores for students at all five selected percentile levels declined compared to 2020,” the report said. “In both subjects, scores for lower-performing age 9 students declined more than scores for higher-performing students compared to 2020.”
NCES Acting Associate Commissioner Daniel McGrath stated that the damage done to education in the United States during the pandemic was significant.
“These are some of the largest declines we have observed in a single assessment cycle in 50 years of the NAEP program,” he said. “Students in 2022 are performing at a level last seen two decades ago.”


On page 3:
The number associated with a point is the coordinate of the point. As long as the context is clear, we will follow the standard convention of using the real number for both the name of the point and its coordinate
This presupposes several things. First, that real numbers are parasitic, and that the first class citizens of this ontology are the points. Second, that the number is only ever the index of the point, or some property (coordinate) of the point. Disgusting.


2 edition of Metric and comparison geometry found in the catalog.
|Statement||edited by Jeffrey Cheeger and Karsten Grove|
|Series||Surveys in differential geometry -- v. 11|
|The Physical Object|
|Pagination||ix, 347 p. :|
|Number of Pages||347|
Geometry Math Exercises: Worksheets,Games & Quizzes Geometry - Free Math Worksheets, Games, Tests etc - Preschool to 7th Grade - MathFox. Geometry Games. I'm having trouble understanding a proof of the Bishop's volume comparison theorem and any help would be really appreciated. It's a simple part of the proof but I'm not quite getting what they want to say. The proof is the one in Gallot, Hulin and Lafontaine's Riemannian Geometry book. So it .
The book is divided into four parts. Part I: Tensor geometry, consisting of chapters 1, 2, 3, and 4. Part II: Geodesic and distance geometry, consisting of chapters 5, 6 and 7. Part III: Geometry à la Bochner and Cartan, consisting of chapters 8, 9 and Part IV: Comparison . 6. Comparison theorems 44 Chapter 4. Space-times 47 Chapter 5. Multilinear Algebra 49 1. Tensors 49 2. Tensors of inner product spaces 51 3. Coordinate expressions 52 Chapter 6. Non-euclidean geometry 55 1. The hyperbolic plane 55 Bibliography 59 3File Size: KB.
Define metric. metric synonyms, metric pronunciation, metric translation, English dictionary definition of metric. adj. Of or relating to the meter or the metric system: US . In mathematics, the differential geometry of surfaces deals with the differential geometry of smooth surfaces with various additional structures, most often, a Riemannian es have been extensively studied from various perspectives: extrinsically, relating to their embedding in Euclidean space and intrinsically, reflecting their properties determined solely by the distance within.
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Metric and comparison geometry. [Jeff Cheeger; Karsten Grove;] Print book: EnglishView all editions and formats: Publication: Surveys in differential geometry, Summary: Contains works which treat developments in metric geometry and comparison geometry. Rating: (not yet rated) 0 with reviews - Be the first.
Subjects: Distance geometry. ISBN: OCLC Number: Description: ix, pages: illustrations ; 26 cm. Contents: Collapsed manifolds with bounded sectional curvature and applications / Xiaochun Rong --Nonnegativity and positively curved manifolds / Burkhard Wilking --Examples of manifolds with non-negative sectional curvature / Wolfgang Ziller --Perelman's stability theorem / Vitali.
The book’s four chapters are based on lectures given by leading researchers in the field of geometric analysis and low-dimensional geometry/topology, respectively offering an introduction to: the differentiable sphere theorem (G.
Besson), the geometrization of 3-manifolds (M. Boileau), the singularities of 3-dimensional Ricci flows (C. Metric geometry is a branch of geometry with metric spaces as the main object of study.
It is applied mostly to Riemannian geometry and group theory. Subcategories. This category has the following 11 subcategories, out of 11 total. Comparison Geometry for Ricci Curvature Xianzhe Dai Guofang Wei 1 1Partially supported by NSF grant DMS 2 A Ricci curvature bound is weaker than a sectional curvature bound but stronger than a scalar curvature bound.
Ricci curvature is also special that it Metric Space and Optimal Transportation. File Size: KB. A Course in Metric Geometry. Selected Titles in This Series 33 Dmitri Burago, Yuri Burago, and Sergei Ivanov, Acourseinmetricgeometry, ∞ The paper used in this book is acid-free and falls within the guidelines [CE] J.
Cheeger and D. Ebin, Comparison Theorems in Riemannian Geometry,NorthCited by: In mathematics, a metric or distance function is a function that defines a distance between each pair of elements of a set.A set with a metric is called a metric space.
A metric induces a topology on a set, but not all topologies can be generated by a metric. A topological space whose topology can be described by a metric is called metrizable. One important source of metrics in differential. This book documents the recent focus on a branch of Riemannian geometry called Comparison Geometry.
The simple idea of comparing the geometry of an arbitrary Riemannian manifold with the geometries of constant curvature spaces has seen a tremendous evolution recently.
This volume is an up-to-date reflection of the recent development regarding spaces with lower (or two-sided) curvature 5/5(1).
Viewing Finsler spaces as regular metric spaces, the author discusses the problems from the modern metric geometry point of view.
The book begins with the basics on Finsler spaces, including the notions of geodesics and curvatures, then deals with basic comparison theorems on metrics and measures and their applications to the Levy concentration. Preface In this book we study complete Riemannian manifolds by developing techniques for comparing the geometry of a general manifold M with that of a simply connected model space of constant curvature M al conclusion is that M retains particular geometrical properties of the model space under the assumption that its sectional curvature K M, is bounded.
Volumes I and II of the Spivak 5-volume DG book are mostly about Riemannian geometry. Cheeger/Ebin, Comparison theorems in Riemannian geometry (). An introduction to research-oriented pure mathematical Riemannian geometry.
Lovelock/Rund, Tensors, differential forms, and variational principles () pages – Metric conversion charts and calculators for metric conversions Temperature Weight Length Area Volume Speed Time Angle Pressure Energy and Power Health and Wellbeing The metric system originated in France in following the French Revolution although decimal units had been used in many other countries and cultures previously.
interactions between geodesics and metric properties such as completeness. It then introduction to comparison theory by Jeff Cheeger and David Ebin [CE08] (which attempt to provide a comprehensive introduction to pseudo-Riemannian geometry, throughout the book I do point out which of the constructions and theorems of.
Lectures on Geodesics Riemannian Geometry. Aim of this book is to give a fairly complete treatment of the foundations of Riemannian geometry through the tangent bundle and the geodesic flow on it. Topics covered includes: Sprays, Linear connections, Riemannian manifolds, Geodesics, Canonical connection, Sectional Curvature and metric structure.
Metric thread type is most common in Europe. It has a cylindrical inner and outer diameter precise in millimeters.
The fine taper of metric tapered thread allows for the best possible force transmission. In writing, you can identify metric threads by a capital “M” plus an indication of their nominal outside diameter (ex. M22 x ). The central theme of this book is the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry.
The first five chapters are preparatory in nature. They begin with a very concise introduction to Riemannian geometry, followed by an exposition of Toponogov's theorem--the first such treatment in a.
Metric Measure Geometry Comparison theorem for observable diameter 31 Spectrum of Laplacian and separation distance 34 Chapter 3. Gromov-Hausdorﬀ distance and distance matrix 37 In this book, we study Gromov’s metric geometric theory [19, §31 2] on the space of metric measure spaces, based on the idea of concentra-File Size: 1MB.
The book begins with the basics on Finsler spaces, including the notions of geodesics and curvatures, then deals with basic comparison theorems on metrics and measures and their applications to the Levy concentration theory of regular metric measure spaces and Gromov's Hausdorff convergence theory.
Analysis and Geometry in Metric Spaces is an open access electronic journal that publishes cutting-edge research on analytical and geometrical problems in metric spaces and applications. We strive to present a forum where all aspects of these problems can be discussed.
Request PDF | On Jan 1,Jeff Cheeger and others published Comparison theorems in Riemannian geometry. Reprint of the original | Find, read and cite all the research you need on ResearchGate. An excellent reference for the classical treatment of diﬀerential geometry is the book by Struik .
The more descriptive guide by Hilbert and Cohn-Vossen is also highly recommended. This book covers both geometry and diﬀerential geome-try essentially without the use of calculus. It contains many interesting results and.A Course in Metric Geometry.
For example the Toponogov Triangle Comparison Theorem and This introductory book on hyperbolic geometry is based on lecture notes for a Master course entitled.a deeper study there is a ﬁne book: O’Neill, Semi-Riemannian geometry, Academic Press, I recommend this book also for its concise summary of the theory of manifolds, tensors, and Riemannian geometry itself.
The ﬁrst substantial question we take up is the existence of Riemannian metrics.


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- And would lose other 840 times – losing -$840.00 with them.
Mathematically speaking, it is a negative expected value bet, because you would have an expected final loss of 💰-$360.00.
Is betting on Hrvace worth it?
🔴 Hrvace: the model predicted that the probability of this event happening is 10.18% and we know that avarage odds offered by the bookies are 6.25. That is, when you make 1000 bets of $1 like this one, you:
- Would have hit 100 times – having a profit of $525.00;
- And would have lost other 900 times – with a loss of -$900.00 because of them.
That is why this bet does not have value. In the end, you would have had a final loss of 💰-$375.00.
Handicaps analysis for the match Mladost Zdralovi x Hrvace
The handicap market is also very searched for by bettors in professional bookmakers and our model can help you with that. If you have no idea what a handicap is, do not worry! We have a complete article about the Asian handicap on sporting betting that will answer all your questions. You can click on it and leave it open on another tab so you can read later.
This is what our nice robot has to tell us about these markets:
⚖ Handicap 1×2: -0.75 Mladost Zdralovi
⚽ Expected goals: 3.00 goals
Tips for the Handicap 1×2 market for Mladost Zdralovi x Hrvace
⚖ Handicap 1×2: our model believes that the ideal handicap is -0.75 Mladost Zdralovi and the available handicap to bet at the moment is -1.25 Mladost Zdralovi.
Since the difference between the handicap we calculated and the offered by the bookie is 0.50, this means that the best bet for the Handicap 1×2 is on: 1.25 Hrvace.
Tips for the Goals Handicap market for Mladost Zdralovi x Hrvace
⚽ Goals Handicap: our model believes that the ideal handicap is 3.00 goals and the available handicap to bet at the moment is 2.75 goals.
We can notice that the difference between the handicap predicted by the model and the one available to bet at the bookmaker is 0.25. Therefore, the recommended bet for the Goals Handicap is on: + 2.75 goals.


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In this paper, a comparison in the performance of metaheuristic algorithms was performed for solving the inverse kinematics problem of redundant robot manipulators.
First, a review of several popular metaheuristic techniques and their variants was made. Then, the forward kinematics for the 6-DOF UR5 universal robot and the 7-DOF Motoman SIA20D were obtained using the DH convention. Two optimization problems were defined to evaluate the performance of the different heuristic approaches in order to identify their weaknesses and strengths.
The first one consists in solving the inverse kinematics only for the position of the defined Tool Center Point (TCP) of the manipulators; the second one, which is the major contribution of this work, extends the analysis of the studied algorithms to solve the inverse kinematics for a desired pose of the end-effector of the robot. To validate the robustness of each metaheuristic, 30 trials were performed for each optimization problem. Each trial consisted of finding the joint values for 50 random positions within the robot’s workspace and validating how many optimal solutions were obtained during that trial. The results present the best and worst performing metaheuristics based on the optimal solutions obtained, standard deviation of the optimal solution and the execution time.
Full article (pdf):


GCSE 9-1 Exam Question Practice (Cumulative Frequency) 4.9 34 customer reviews. 17. 1. direct-inverse-proportion-corbett-ans. Contents. The first revolves around drawing the graphs given the data, the second revolves around interpreting. The cumulative frequency table gives some information about the amounts of money spent by the 120 men. You can & download or print using the browser document reader options. Attempt every question 4. (d) The data in L2 and L3 are similar to the data in L1 but they are in a frequency format. Videos. Previous Invariant Points Video. Created: Oct 17, 2017 | Updated: Jan 17, 2019. Previous Inequalities Practice Questions. To create a cumulative frequency table all we need to do is add the frequencies together as we progress down the column. The same data is presented in the following table. Maths revision video and notes on the topic of Cumulative Frequency. for the 60 mathematics graduates. 5-a-day Workbooks. Cumulative frequency 30 150 160 170 Height (cm) … Proportion (direct & inverse) 1. direct-inverse-proportion-pdf-corbett. 1. cumulative-frequency-answers.pdf-corb. GCSE Revision Cards. Give your answer correct to 1 Switch off the cumulative frequency graph (Plot1). (a) Draw a cumulative frequency graph (b) Using the curve, estimate the median. (b) Find the percentage of mice that weigh 70 grams or less. The spinner is spun and the frequency the letter A is recorded every 10 spins. Create your website today. September 2, 2019 September 2, 2019 corbettmaths. Dont spend too long on one question. The first value is the first frequency value, we then add this to the second value to get the second cumulative frequency value. Name: _____ Cumulative frequency Age 40 < t < 50 Frequency 12 20 34 11 . Search for: Contact us. 1 The cumulative frequency table shows the height, Height 140 < h < 150 140 < h < 160 140 < h < 170 140 < h < 180 140 < h < 190 140 < h < 200 in cm, of some tomato plants. Practice Questions; Post navigation. GCSE Revision Cards. come with answers. www.justmaths.co.uk Cumulative Frequency (H) - Version 2 January 2016 Cumulative Frequency (H) A collection of 9-1 Maths GCSE Sample and Specimen questions from AQA, OCR, Pearson-Edexcel and WJEC Eduqas. O 50 100 150 200 250 300 350 400 10 20 30 40 50 60 70 80 90 100 110 120 Amount spent (£) Cumulative frequency b) Use your cumulative frequency diagram to estimate the median. Choose the settings shown here. Some of the worksheets displayed are Mathswatch clip 186 cumulative frequency, Gcse exam questions on cumulative frequency grade b 1, Mathswatch work foundation questions, The higher work ebook, Wjec ebook questions, , Mathematics linear 1ma0 cumulative frequency box plots, 1 minute maths too fast for a first time use but. Question 2: The cumulative frequency graph below shows the salaries of 80 teachers. Corbettmaths - A video that demonstrates how to draw cumulative frequency graphs. Check your answers seem right. Whether you want a homework, some cover work, or a lovely bit of extra practise, this is the place for you. A second batch of mice are normally distributed with the same mean and standard deviation as those of the first group mentioned above. Reading Cumulative Frequency Graphs Video . This carefully selected compilation of exam questions has fully-worked solutions designed for students to go through at home, saving valuable time in class. The table below shows this information. The weights in grams of 98 mice are shown in the cumulative frequency diagram. Click here to enter your comments. These are the Corbettmaths Textbook Exercise answers to Cumulative Frequency Graphs Find the probability that at most three mice weigh 70 grams or less. Quiz & Worksheet Goals Powered by https://www.numerise.com/GCSE Revision Video 25 - Cumulative Frequency Do you have any comments about these exam-style questions? Set up Plot 3 to display a boxplot of the frequency data in L2 and L3 on the same graphing screen. (a) Write down the median weight of the mice. It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. The Corbettmaths Practice Questions on Cumulative Frequency Graphs. Search for exam-style questions containing a particular word or phrase: To search the entire Transum website use the search box in the grey area below. Give your answer correct to 1 decimal place. This Cumulative Frequency graph shows the heights of 58 Scouts. gcse questions. (f) Find the percentage of the second batch of mice that weigh 70 grams or less. Whether you want a homework, some cover work, or a lovely bit of extra practise, this is the place for you. Video questions. The times taken by customer service operators to answer 120 telephone calls are illustrated in the cumulative frequency diagram shown below. 2. When you have done all you can, look at the answers and mark your work Then try the Diagnostic Questions Quiz on the topic, trying to explain each answer When you have finished the Quiz, click Review Answers and read through other students' explanations for any questions you got wrong until you find one that makes sense to you The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper. (2) (b) Use your cumulative frequency diagram to estimate the median. (e) Use the values from the table to estimate the mean and standard deviation of the weights. 5. (a) Complete the cumulative frequency table. The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The lowest salary is £4,000 and the highest salary is £39,000. 30 21 40 26 Spins Frequency of 10 10 20 12 (a) Complete plot the relative frequencies on the graph below. The solutions to the questions on this website are only available to those who have a Transum Subscription. Check your answers if you have time at the end mathsgenie.co.uk. Cumulative Frequency Graphs Textbook Answers. advanced charts and graphs > revision > gcse questions. Once you find your worksheet, click on pop-out icon or print icon to worksheet to print or download. (a) Write down the median weight of the mice. 1. cumulative-frequency-pdf1.pdf-corbett. Primary Study Cards. frequency tables Mathster; Corbett Maths Amount (£ A) spent Cumulative frequency. Cumulative frequency is especially useful when trying to answer a "more than" or "less than" question about a population, or for checking if some of your calculations are correct. With some ordering of values and addition, you can quickly calculate cumulative frequency for any data set you have. Histograms: Worksheets with Answers. Cumulative frequency and box plots RAG. My Tweets. Weights w grams: 0 < w ≤ 40: Contents. Some of the worksheets displayed are Mathswatch clip 186 cumulative frequency, Gcse exam questions on cumulative frequency grade b 1, Mathswatch work foundation questions, The higher work ebook, Wjec ebook questions, , Mathematics linear 1ma0 cumulative frequency box plots, 1 minute maths too fast … (Total for question 1 is 3 marks) Height Cumulative Frequency 140 < h 150 7 140 < h 160 17 140 < h 170 32 140 < h 180 51 140 < h 190 57 140 < h 200 60 (a) On the grid, plot a cumulative frequency graph for this information. The same data is presented in the following table. Two worksheets, each with four questions. Name: Exam Style Questions Cumulative Frequency Corbettmctths Box Plots Ensure you have: Penctl, pen, ruler, protractor, pair of compasses and eraser You may use tracing paper if needed Guidance Read each question carefully before you begin answering it. Calculating the cumulative frequency is just adding up the frequencies as you go along. This quiz/worksheet combo can be used to check your understanding of displaying data in cumulative frequency tables. 5-a-day Workbooks. 0 - A < 100 13 0 - A < 150 25 0 - A < 200 42 0 - A < 250 64 0 - A < 300 93 0 - A < 350 110 0 - A < 400 120 (a) On the grid, draw a cumulative frequency diagram. Cumulative Frequency Videos. April 4, 2018 August 12, 2019 corbettmaths. Cumulative Frequency Author: John Corbett Created Date: 3. This is the Corbettmaths video tutorial on Drawing Cumulative Frequency Graphs (a) Find the probability that the teacher selected is paid less that £15,000. The table shows the test marks for 31 students. Cumulative Frequency Videos Drawing Cumulative Frequency Graphs Video . the cumulative frequency graph in Activity 5. website builder. And best of all they all (well, most!) (2) (c) Use your cumulative frequency graph to find an estimate for the median age. (g) A sample of five mice is chosen at random from the second batch. The heaviest mouse weighted 160g. Work out an estimate for the number of these Scouts with a height greater than 160cm. Preview. The weights in grams of 98 mice are shown in the cumulative frequency diagram. Make three criticisms of Marcoâs graph. Cumulative Frequency and Box Plot Practice Questions. Videos; Post navigation. Author: Created by Maths4Everyone. Corbett maths Mass 40 < m 45 Frequency Mass 50 < m, 55 70 70 75 Frequency Midpoint Length 10 < L' 20 30 < L £ 40 40 < L 50 Frequency Midpoint Length 10, t, 15 15 < t, 20 Frequency 43 Midpoint Cost 8 < C' 12 12 < C' 16 20 Frequency Midpoint Duration (years) 10 'd < 20 30 £ d < 40 Frequency 16 Height 130 140 140 150 160 160 h 170 Frequency 120 Mathster; Corbett Maths a) On the grid, draw a cumulative frequency diagram. This site was designed with the .com. 1. Click here for Answers . And best of all they all (well, most!) Worksheet will open in a new window. Cumulative Frequency and Box Plot Practice Questions Click here for Questions . Cumulative Frequency 17 32 51 57 60 (a) (b) On the grid, plot a cumulative frequency graph for this information. The table goes like this: Score 69 Frequency 3 Cumulative frequency - - I get the first part with the score and the frequency (3 people got a score of 69), but I don't have any idea how to work out the cumulative frequency or what it means. Marco drew this cumulative frequency graph using the data. 0.8 Relative frequency of an A 0.6 0.4 10 20 40 50 30 Number of spins (3) The cumulative frequency table gives some information about the amounts of money spent by the 120 men. Age (A) in years Cumulative f requency 20 < A 30 20 < A 40 20 < A 50 20 < A 60 20 < A 70 (1) (b) On the grid opposite, draw a cumulative frequency graph for this information. Corbettmaths - A video that shows you how to interpret cumulative frequency graphs. 13 + 33 = 46 How accurate was the estimate? Step 1: Construct a cumulative frequency table for this data. A teacher is picked at random to answer a survey. The heaviest mouse weighted 160g. arrow_back Back to Cumulative Frequency Diagrams Cumulative Frequency Diagrams: Worksheets with Answers. Name: 1 st September Factorise 4y2 — 9w2 5-a-aay Higner Corbettmaths Calculate the distance between the coordinates (1 , 3) and (3, 8). Videos, worksheets, 5-a-day and much more Showing top 8 worksheets in the category - Maths Watch Answers Cumulative Frequency. Cumulative Frequency and Box Plots. (b) Find the percentage of mice that weigh 70 grams or less. I've got a homework question about averages and there's this one part about cumulative frequency and I've not got the slightest idea what this means. February 12, 2019 August 10, 2019 corbettmaths. Next Increasing/Decreasing by a Fraction Practice Questions. 1 The cumulative frequency table shows the height, in cm, of some tomato plants. Fully differentiated lesson on cumulative frequency graphs and box plots. Next Trigonometric Graphs Videos. You will be quizzed on terms, such as frequency tables. come with answers. (b) Find the median height. Always show your workings Revision for this topic ... Use this information and the cumulative frequency curve to draw a box plot! Showing top 8 worksheets in the category - Maths Watch Answers Cumulative Frequency. Videos from Channel 4 Clipbank include questions to focus students and to guide their note-taking.
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Welcome to National Institute of Education
New initiative of the NIE to Modernize the Classroom
The Faculty of Science and Technology has introduced ICT animations in the teaching learning process. (Presently for Science and Mathematics - Grade 6 to 11). NIE has mapped the resource with competency of each grade and subject in the curriculum.
These animations have been developed by the University of Colarado- USA, and NIE has negotiated the copyrights and permission to translate to Sinhala and Tamil. Students and teachers use these valuable international resources for their learning and teaching which is available in a DVD and also accessible directly in the web. NIE is to publish a booklet with an accompanying DVD containing exercises and explanations which will help classroom teaching and self directed learning. Presently the e_copy can be obtained by sending an email to firstname.lastname@example.org with the subject heading science and maths animations.


Total tuition fee (local)
Total tuition fee (foreign)
- Prospective participants will normally have a good honours degree in a social or physical science. This may include any engineering or science subject. For social sciences, a BSc if preferred, although the BA Accountancy and Finance is acceptable.
- Plus a grade C from A Level or equivalent in a maths based subject, for example maths, pure/applied, further maths, statistics and physics. Students who have not performed well in Finance, Maths or numeracy modules in their first degree are unlikely to be offered a place.
- Alternatively prior work experience in a related field will be considered in place of a degree at the discretion of the teaching team.
- Bond Pricing And Fund Management
- Corporate Finance 1
- Corporate Finance 2
- Dissertation (MSc Finance)
- Financial Reporting
- International Finance
- Portfolio Analysis
- Quantitative Methods for Finance I
- Quantitative Methods for Finance II


Box Hill School is proud to rank amongst the top ten schools in Surrey for pupil rankings in post 16 education.
DfE statistics state that the percentage of our GCSE students gaining five or more GCSEs at A* to C, including English and Mathematics, is 53%. It is NOT. The figure for our mainstream Year 11s is 84% from the summer 2013 examinations. We remain well above the national average.
2013: Box Hill School's Best GCSE Results Ever
- 86.4% A*- C pass rate overall in Year 11
- 18.3% higher than national average across all subjects
- 22.1% A* and A grades
- Outstanding pass rate of 98% in Maths and 93% in English. All attaining A*-C grades.
For more information on individual subject pass rates please click here.
IB results – the rewards of amazing effort!
Box Hill students once again raised the bar as they achieved a record pass rate with an average of 30 points in the International Baccalaureate – beating the worldwide average for the first time!
- 12 subjects achieve 100% pass rate at level 4 or above
- 94% of 6th formers got into first or second choice universities
- Overall Box Hill Diploma pass rate of 89.4% smashes world average by 11% points
- Bilingual diplomas awarded up by ten on last year
For more information on individual subject pass rates and unviversity destinations please click here.


Say we start with one cell, put it in minimal medium, where it and its daughter cells will grow and divide once every hour:
In minimal medium , E. coli divides typically in 60 min., or 1 generation= 60 min.
We can calculate how long it will take to get a billion cells from just one:
Let g = number of generations. 2 gens. --> 4 cells, 3 gens. --> 8 cells, or
N (no. of cells) =1 x 2g (starting with one cell).
If we started with 100 cells, after 1 gen. we would have 200 and after 2 gens. 400, 3 gens., 800 etc.
More generally, starting with No cells: N = No x 2g
Since we want to know how much time it will take: express generations in terms
If we let tD = the generation time, or doubling time, then the number of generations that have passed during the time interval t is just t/tD: So g = t/tD.
So now N = No x 2t/tD. One can thus see that growth is exponential with respect to time.
Now we could solve this equation for t, since we know we want N to be 1 billion, No is 1, and tD is 1 hr. Taking the logarithm base 2 of both sides:
log2 (N/No) = t/tD, or t = tDlog2(N/No) = 1 X log2 (1,000,000,000/1) = log2(109)
But suppose your calculator doesn't do log base 2. No problem, convert to log base 10 ("log") or natural log base e ("ln").
log2X = logX/log2 = logX/0.3 and log2X = lneX/lne2 = lnX/0.69 (Also: 2x = 10xlog2 and 2x = exln2)
So log2(N/No) = log(N/No)/log2 = t/tD or log(N/No) = (log2/tD)t = Kt, where K=log2/tD or K=0.3/tD.
Or back to the exponential form: N/No =10Kt or: N =No10Kt
Or, since most scientific calculators have natural log functions:
N = NoeKt, where K = ln2/tD = 0.69/tD, another common form of the exponential growth equation.
We could also have approached this question of rates of change of N with time more naturally using calculus (Note: familiarity with calculus is not necessary for this course.) If you have a million cells, then after one generation time youll have gained 1 million. If you had 100, you wouldve gained 100. In general, the rate of increase of N with time is just proportional to the number of cells you have at any moment in time, or: dN/dt = KN
Separating variables: dN/N = Kdt.
Integrating between time zero when N = No and time t, when N = N:
lnN - ln No = Kt - 0, or ln(N/No) = Kt, or N = NoeKt
We can calculate the constant K by considering the time interval over which No
has doubled. This time is the doubling time, tD. For that condition:
N/No = 2 = eKtD. Taking the natural logarithm of both sides: ln2=KtD, or K=ln2/tD, exactly as above.
|Base 2||Base 10||Base e|
|Exponential form||N = No2K2t||N = No10K10t||N = NoeKet|
log2(N/No) = K2t
|log(N/No) = K10t||ln(N/No) = Ket|
Definition of constant
K2 = 1/tD
K10 = log102/tD = 0.3/tD
|Ke = ln2/tD = 0.69/tD|
All this looks worse than it is. Exponential growth using a base of 2 is intuitively obvious. And once you see the derivation, the exponential growth equation using log or ln can be simply applied to problems using a calculator. You just have to keep track of what you know and what you are after.
|Graphically, the depiction of exponential growth looks
|Or, with the ordinate (Y-axis) plotted on a logarithmic scale,
a semi-log plot:
In reality, there's a lag before cells get going, and there's a limit (thankfully) to cell density, as nutrients become exhausted and/or toxic excretions accumulate. The final plateau is called stationary phase:
© Copyright 2000 Lawrence Chasin and Deborah Mowshowitz Department of Biological Sciences Columbia University New York, NY