I did statistical tests to determine the significance of my Meal Tolerance Test (MTT) results.
I started with one-tailed tests of products that I had reason to suspect would raise my blood glucose more than the others. One-tailed tests are appropriate for cases where there is a priori knowledge. The suspect products were Smart Carb #1 bread from Julian Bakery, The Crisp Bar from eat-rite, and Glucerna Shakes. I expected Smart Carb #1 and The Crisp Bar to raise my blood glucose a lot based on my previous tests and from evaluating their ingredients. Glucerna Shakes were suspect because of their high carb count and because corn maltodextrin is their top nutrient.
The test statistic is the difference between the mean change in blood glucose (Δ BG) for the product being tested and the mean ΔBG for all the other products in the category (excluding the one being tested). The significance level is the probability that a difference this large could have arisen by chance if, in fact, the products have no differential effect on blood glucose.
One-tailed tests confirm or disprove an a priori hypothesis – e.g. in the case of Smart Carb #1, that all other breads would have lower ΔBG. Two-tailed tests make no a priori assumptions; they are for post hoc hypothesizing. Think of two-tailed tests as fishing expeditions to find significant differences between products. There is little difference in how one- and two-tailed tests are calculated: one-tailed tests are based on the actual difference of the mean ΔBGs, two-tailed tests on the absolute value of the difference of the mean ΔBGs.
I did two types of statistical test: homoscedastic t-tests, which assume all observations are drawn from the same normal population, and randomization tests (also called permutation tests), which make no assumptions about the underlying distribution.
The null hypothesis is that the ΔBGs are independent of the products. By random shuffling, we assure that the ΔBGs are indeed independent of the products. The randomization test compares the difference of the measured mean ΔBG of a product and the measured mean ΔBGs of all other products to a large number of variations created through random shuffles to determine the likelihood that the actual difference between measured means could have occurred randomly.
Randomization test process – All the ΔBGs for all the products in a category are put into a single data set. This data set is randomly shuffled. The mean of the first Nt shuffled ΔBGs in the data set is calculated, where Nt is the number of ΔBGs observed for the product being examined. The mean of the rest of the ΔBGs in the data set is also calculated. If the difference between these two means is greater than or equal to the original difference between the mean ΔBGs, a counter (nge=number greater than or equal to) is increased by 1. This process is repeated 999 times for each statistical randomization test. The significance level is then (nge+1)/(NS+1), where NS is the number of shuffles (999). This is essentially the percentage of times after shuffling that the test statistic is at least as large as it was when it was not shuffled. A more complex explanation follows the example.
“Fishing Expedition” Significance Level
When searching for the best product without a priori knowledge, the significance level produced by randomization tests or t-tests is misleading. It needs to be corrected based on the number of products tested. The more products tested, the more likely it is that products will be found to be better than others purely by chance. For example, if I test 10 products and significance levels are are valid, on average I should find one product whose significance level is 10% or better even if there is no differential ΔBG between the products. In fact, the probability of finding a product whose apparent significance level is 10% or better is in excess of 65% (1-0.90^10). Therefore, a significance level of 10% for one or more products when testing 10 or more products is not at all unusual even if there is no differential ΔBG between the products. To correct for this, I calculate a “Fishing Expedition” significance level. This is the probability of obtaining a significance level better than or equal to the actual significance level obtained when there are multiple products. The “Fishing Expedition” significance level is 1-(1-significance level)^number of products.
I used one-tailed tests for Smart Carb #1 because I had a priori knowledge that it would probably spike my blood glucose more than the other breads. The significance level of the one-tailed randomization test of the difference in the means between Smart Carb #1 bread and all of the other breads is 0.1%. This means that if there was really no difference at all between Smart Carb #1 and all of the other breads and all of the observations (regardless of distribution), the probability that Smart Carb #1 would have shown such poor blood gluclose results in my experiment just by chance is less than 0.1%. This is a very low probability, so I have a high degree of confidence that Smart Carb #1 really does spike my blood glucose.
I could not use one-tailed tests for Chompie’s Carbs…Not! Sesame Bread because I had no a priori knowledge of what the results would be. The “Fishing Expedition” significance level of the two-tailed t-test for Chompie’s Carbs…Not! Sesame Bread is 15%. This means that if there was really no difference at all between Chompie’s Carbs…Not! Sesame Bread and all of the other breads and all of the observations were drawn from the same normal population, the probability that at least one of the products would have shown such good blood gluclose results in my experiment just by chance is 15%.
Similarly, the “Fishing Expedition” significance level of the two-tailed randomization test for Chompie’s Carbs…Not! Sesame Bread is 12%, meaning that if there was really no difference at all between Chompie’s Carbs…Not! Sesame Bread and all of the other breads (regardless of the distribution), the probability that at least one of the products would have shown such good blood gluclose results in my experiment just by chance is 12%.
The 15% and 12% “Fishing Expedition” significance levels are low enough that I am reasonably confident that Chompie’s Carbs…Not! Sesame Bread has less effect on my blood sugar than the other breads.
Further Explanation of Randomization Tests
Suppose the data consist of 10 ΔBG scores for Product X and 40 ΔBG scores for other products. Compute the mean ΔBG score for Product X and the mean ΔBG score for all the other products. Suppose we expected, based on the ingredients in Product X, that it would have a more unfavorable effect on blood glucose levels than would other products. In other words, our hypothesis is that the mean ΔBG score for Product X will be larger than the mean ΔBG score for other products. Suppose it turns out this way and the difference in the means is 18 mg/dl. But is this significant, or could it have occurred due to chance? It is possible that due to naturally occurring variations in blood glucose levels having nothing to do with ingestion of the products, one could get a difference in the mean ΔBG scores as large as 18 mg/dl. Indeed, because of naturally occurring variations in blood glucose levels and glucometer inaccuracies, in an experiment involving a small number of readings, one would seldom find that the mean ΔBGscores of two products would be the same. So how does one determine whether a difference in mean ΔBG scores as large as 18 mg/dl could be due to chance or is more likely due to a real difference between the products?
One way to do this is a randomization test. I used a computer, but the mechanics of the test are best visualized with a deck of 3″ by 5″ note cards. Recall that in our experiment Product X has 10 ΔBG observations and the other products have 40 observations and the mean ΔBG score for Product X is 18 mg/dl higher than the mean ΔBG score for the other products. This difference in the means is our test statistic and the “actual value” of the test statistic is 18 mg/dl.
Now write down each of the 50 ΔBG scores on a separate note card. The null hypothesis is that the ΔBG scores are independent of the products – in other words, the products have no effect on the ΔBG scores. The alternative hypothesis is that the products do have an effect on the ΔBG scores and indeed, the mean ΔBG score is higher (worse) for Product X than for the other products. We test the null hypothesis (which we hope to reject in favor of the alternative hypothesis) using the following procedure:
If the null hypothesis is true, the observed ΔBG scores are independent of the products. We can ensure this is true by shuffling the note cards into two piles – one containing 10 cards and the other containing 40 cards. We then compute the mean ΔBG score for each pile. The difference in these means we call the “pseudo statistic”. If the alternative hypothesis is correct and Product X really is worse than the other products, then ordinarily when we shuffle the data the value of the pseudo statistic should be less than the value of the statistic for the unshuffled data, which in this case was 18 mg/dl. However, by chance the pseudo statistic could be greater than or equal to 18 mg/dl – we know it could be at least 18 mg/dl by chance because even after shuffling, the note cards in the Product X pile could be the actual ΔBGs for Product X. It is unlikely, but it could happen.
If it turns out that the difference in the mean ΔBG score for the shuffled data is greater than or equal to 18 mg/dl, we will add 1 to a counter we call “nge”, which stands for number greater than or equal. Shuffle the note cards again into two piles of 10 cards and 40 cards. Recompute the difference in the mean ΔBG scores. Compare this to 18 mg/dl. If it is greater than or equal to 18 mg/dl, add 1 to the nge counter. Repeat NS (Number of Shuffle) times, where NS is a large number like 999.
After completing NS shuffles, the significance of the score 18 mg/dl is determined by computing (nge+1)/(NS+1). Let’s suppose that (nge+1)/(NS+1) is 0.003 after conducting 999 shuffles. This means that in 999 shuffles, there were only two instances where the difference in the mean (nge+1)/(NS+1) scores was greater than or equal to 18 mg/dl. We can conclude that if the products have no effect on (nge+1)/(NS+1) scores (which we ensure by shuffling the ΔBG scores relative to the products), it is extremely unlikely that the difference in the mean ΔBG scores between Product X and the other products would have been as large as 18 mg/dl by chance. Therefore, we reject the null hypothesis of no product-specific effect on blood glucose levels in favor of the alternative hypothesis that Product X is worse than the other products.
Dr. Eric Noreen wrote most of this Statistical Analysis page and wrote the computer macros used in all our statistical analyses. Gary Noreen bears sole responsibility for everything on this web site, however.


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Using Slots to increase Your Likelihood of Winning
There are numerous ways to enjoy playing casino games. The type of casino game you choose depends on your own private preference and budget. There is a casino game for everyone in order to play any casino sport that you find fun and exciting. You need to choose games carefully so you maximize your likelihood of winning. To be able to learn about different casino games then read the sections below.
Probably the most popular casino game types may be the standard casino game. This internet casino game is named following the popular William Benton McDonald who created the standard deviation. Standard deviation is really a mathematical concept that determines the likelihood of a specific event to occur. There are three main types of standard deviation game titles: binomial lottery games, online games, and standard slot game titles. Binomial lottery games deal with a finite group of numbers and include spins with equal chance components.
The next casino game type is the slot machine game. Slots are popular because there are always consistent winning combinations. Additionally it is one of the easiest games to learn. Slots are available in a wide variety of casino hotels all over the world.
Another popular type of casino game may be the house edge. A residence edge is the percentage of a casino’s investment, which is continuously made by an investor. House edges vary widely according to the gaming casinos. For instance, in a progressive gambling house where jackpots are won often, a house edge using one single combination is likely. The home edge on multi-layaway machines is even lower, because the possibility of hitting more jackpots concurrently is slender.
All types of gambling are characterized by some form of betting in terms of the total amount wagered and the amount of combinations possible. You will find a relationship between these two variables, known as the Blackjack Breakdown. The essential concept behind the Blackjack breakdown can be a casino will decrease the probability of winning a combination if more people are at that casino, or the casino decreases the odds of hitting a particular sequence of numbers, for instance a specific number of cards 사설 카지노 dealt.
One of the most popular casino games is poker. There are numerous variations of the card game. One of the most popular variations is holdem. Although the rules for each variation of poker may differ slightly, they all follow exactly the same pattern of betting, raising the amount wagered, and taking the money from the player prior to the match begins. In older game titles, the house advantage is the players’ advantage, or the amount of money they might potentially win without spending any of their own funds.
Among the simplest forms of casino games is the sport of blackjack. Blackjack makes use of the “house” advantages to calculate the expected reduction and the amount of chips you can possibly lose. The typical deviation is used to measure the random variables, or variables which are away from control. Blackjack, like holdem, also has an assumption of what the modern casino will do, namely what the typical deviation would be if the game were to continue on its study course. This assumes that the gambling establishment will remain in the same hands most of the time, which it often will.
Slot machines are popular game titles in casinos since they allow players to bet on smaller amounts, but have the largest jackpot payouts. To calculate the best times to place these wagers, developers use statistical analysis. They consider the random variables of a slot machine game and use them to the types of reels that will be used, and also the odds of a specific outcome. They then determine the very best times to place bets, and where to place them to maximize your chances of hitting more tickets. Although you might not personally have the ability to determine the very best times to play slots, the slots that pay the most are the most popular places to play, so that is where you need to put your wagers.


A rate of growth
of an organism, a part of an organism
, or a population
of organisms which, when graphed, produces an exponential
curve. Such a rate occurs, for example, during the exponential growth phase, when a population of bacteria
l (or other) cells divide at a constant
rate so that the total number of cells doubles with each division
From the BioTech Dictionary at http://biotech.icmb.utexas.edu/. For further information see the BioTech homenode.


Mathematics and Statistics
- Quantitative Reasoning
- Critical Thinking
3 credit hours:
One course from the list below at the appropriate level, determined by placement.
I prove a theorem and the house expands:
The windows jerk free to hover near the ceiling,
The ceiling floats away with a sigh.
- Explore how math and data provide information about the world.
- Explain and present information in mathematical forms.
- Design problems, consider limitations, and calculate results.
- Identify mathematical approaches to address questions.
Yucca symbol = This course also meets the U.S. Global Diversity requirement.
|HNRS 2221||Mathematics in the World|
|MATH 1130||Survey of Mathematics|
|MATH 1220||College Algebra|
|MATH 1250||Trigonometry & Pre-Calculus|
|MATH 1300||Statistical Literacy|
|MATH 1350||Introduction to Statistics|
|MATH 1430||Applications of Calculus I|
|MATH 1440||Applications of Calculus II|
|MATH 1512||Calculus 1|
|MATH 1522||Calculus 2|
|MATH 2118||Mathematics for Elementary and Middle School Teachers III|


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To improve the math scores of our kids, this step is essential!
OECD is celebrating its 50th anniversary in 2011, and the Paris-based NGO released its international educational rankings, placing the US in a three-way tie for math, equaling Portugal and Ireland, just beneath No. 24 Luxembourg.
"That long-held empirical value of pi, I am not saying it should be necessarily viewed as wrong, but 3 is a lot better," said Roby, the 34-year old legislator representing Alabama's second congressional district, ushered into office in the historic 2010 Republican mid-term bonanza.
Pi has long been defined as the ratio of a circle's area to the square of its radius, a mathematical constant represented by the Greek letter "π," with a value of approximately 3.14159. HR 205 does not change the root definition, per se. The bill simply, and legally, declares pi to be exactly 3.
Roby, raised in Montgomery, Ala., is on the House Committee on Education and the Workforce, and the Subcommittee on Early Childhood, Elementary and Secondary Education.
"It's no panacea, but this legislation will point us in the right direction. Looking at hard data, we know our children are struggling with a heck of a lot of the math, including the geometry incorporating pi," Roby said. "I guarantee you American scores will go up once pi is 3. It will be so much easier."
[A big hat tip to Ian Squires, the brilliant creator of this spoof.]


The Promise of Fractal Progressions
Speaker: Ronald Tiggle
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Since the 1980s, Fractal theory has developed and is being used by some physicists to explain the nature of the universe and by some astrologers to explain the Hermetic Principle in more mathematically precise terms. Since a fractal is a precise mathematical function that maintains its proportionality when calculated on different scales, astrologers have embraced it to explain secondary progressions, solar arc directions, and other progressions rates such as quarterly progressions as well as an array of other progression and solar arc rates.
Although these astrologers have embraced the flexibility and the mathematical precision of fractal theory, they have failed to realize that the standard methods traditionally used by astrologers to calculate secondary progressions and solar arc directions have a small error built into them which makes them increasingly inaccurate the older the person becomes. These errors have serious implication for rectification and electional astrology.
Before the promise of fractal progressions and directions can be realized, these long-hidden errors in calculating progressions and directions must be identified, the default settings in astrological software must be corrected, and the curriculum in astrological schools must be revised.
During his presentation, He will show you how to calculate Secondary and Solar Arc Directions correctly and point out why the traditional method is incorrect and describe the magnitude of the error. The correct calculation options will be identified in popular astrological software such as Sirius, Solar Fire, Kepler 8, and Janus. A method will also be given to correct the error when your software only uses the traditional method.
In addition, methods for calculating other fractal progressions, for example quarterly progressions will be provided.


Since the beginning of last year, more than 100 million people have been infected by Covid19 (novel coronavirus disease, Covid19). British mathematicians have calculated the total number of novel coronavirus particles scattered around the world, which is more than enough to hold in a 330-milliliter can of Coke.
According to Reuters, October 10, Kit Yates, a mathematician at the University of Bath, used the global rate of new infections and estimated viral loads to calculate that there are about 2 quintillion, or 2 billion, 1 billion viral particles scattered around the world.
1quintillion is equal to 10 to the 18th power.
The average diameter of a Novel Coronavirus particle is about 100 nanometers, he says, and even taking into account the protruding protein on the surface of the virus and the voids that form when the particles come together because of their roundness, all the virions still wouldn’t fill a 330-milliliter can of Coke.
The calculated numbers underscore the destructive power of particles too small to be seen by the naked eye, Yates said. “It’s amazing when you think about all the trouble, the destruction, the hardship and the lives lost over the past year, just a few mouthfuls.”


Abacus is a simple tool or a hardware used for performing rapid arithmetic calculations. Calculations based on abacus was invented at ancient times and now widely used a brain development programme. It consists of a rectangular frame holding a number of vertically arranged rods, on which beads slides up and down.
- One of the most popular calculating method from ancient times.
- Children do fast calculations in mind by visualizing Abacus bead movements.
- Researches prove that Abacus learners uses both sides of the brain- left hemisphere & right hemisphere.
- Highly effective in improving the concentration level of children.
- Mental Arithmetic is a term used in Abacus for the calculations done in mind.
- Even large numbers can be calculated in mind, that too within seconds
- Mental arithmetic improves student’s imagination skills.
- Effective in cracking competitive time based tests.
- Mind calculation enhances the concentration level of child.


Recommended Online Slot Machines For You to Have fun with
Slot Machine. The only real guide to how online slot machine games operate may be the word: random. So let’s begin with the literal explanation: “A random number generator, which might be used to generate a number selection which has a possibility of being random”. How online slot machines really work
A random number generator (RNG) is really a mathematical formula that, when properly implemented in a gambling software application, helps generate the most likely winning numbers for just about any slot machine games. It takes the history of spins, accumulated statistics as time passes, and creates a new random number combination by taking the total expected number of wins, then 카지노 커뮤니티 adjusts the odds based on those numbers. In short, the very best online casinos are those that use RNG to look for the upshot of every hand that individuals play. That is why many players consider online slot machines the most “free” of all gambling games. With no initial investment necessary to start playing, it is possible to simply play the games normally as you want.
As it turns out, there are three basic types of slots that most online casinos offer you. Blackjack, baccarat, and video slots. Of course, the exact details of each kind of game may vary slightly from casino to internet casino, however they are all relatively exactly the same. When slots are re-cycled, the effect is new slots that even now have the same odds of earning.
Blackjack is probably the most widely played of all slots. It is simple to understand: blackjack is really a variation of roulette wherein the primary prize includes coins drawn from a hat. This means that one person in the game will win one coin for every time they strike a single jackpot. The basic strategy for winning with blackjack would be to wait for the modern casino to reveal its collection of symbols. Once these symbols have been revealed, the player must then simply decide whether to push the “roup” button on the machine or to try to win with a single crazy symbol drawn from the hat.
Baccarat is a closely guarded casino game. Just experts and customers of the casino employees know exactly how to play it. A new player who doesn’t know the overall game might want to consult with a dealer before playing, or else risk losing all of the money that they have won. Wild symbols drawn from the hat aren’t often found in baccarat, so it might be wise to consult a dealer before playing.
Video slot machines are the last option for individuals who want to win real cash. In order to determine how online slots work, you need to first understand how a video slot machine works. Like a regular video slot machine game, a video slot machine runs on the random quantity generator (RNG). The random range generator takes an unseen digital seed and produces numbers that are impossible to predict. These numbers are then written on a little piece of paper that the player must carefully scrutinize before deciding what number to place their bet on.
Unlike traditional slot machines, there is a greater potential for hitting a winning jackpot on video slots. There are also more chances of winning small prizes. Some on-line casino sites offer video slots that feature jackpots up to three thousand dollars; some web sites offer around seven thousand bucks. While a land-based casino’s utmost bet on a video slot machine game may be only one dollar, at an online modern casino, you’ll be able to win thousands.
Online slots games are no longer strictly for teenagers and young adults. Anyone can play online slots video games. Winning amounts in these video games do not vary based on someone’s age or gender. Additionally, there are no age restrictions on playing slots. There is no such thing as too outdated or too youthful to play these slot video games. In order to win the jackpot, all you need to do is choose the recommended online slot machines games for you to play.


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In collaboration with researchers from the University of Minnesota and the University of Pennsylvania and CueThink, an online application focused on improving math problem-solving and collaboration skills, they will help middle school students better understand numerical and mathematical concepts.
“The grant is important to me because I am passionate about helping students improve their abilities to engage in mathematical problem solving,” said Rhodes. “Collaborating with peers to tackle challenging problems is one of the most exciting parts of learning and doing mathematics. I want to work to bring these experiences to all students in ways that are engaging and that effectively support their learning of mathematics.”
The four-year grant is part of NSF’s Discovery Research preK-12 program.
Georgia Southern’s COE offers students multiple program opportunities, including undergraduate and more than 30 graduate program options that span campus locations in Savannah, Statesboro and Hinesville, and online. Programs offered by the COE prepare future teachers, school psychologists, counselors, school library media specialists, instructional technologists, researchers and leaders through intensive field experiences, cutting-edge technology and research-based instruction.


In my thesis I developed a novel method for Caricature Generation. This method was implemented in a program which takes images of faces as input and automatically produces caricatures as output.
The method relied on the notion of “anti-face” in conjunction with the use of unbiased distortion functions. These two concepts constituted the basis of a mathematical set of rules that can be used for caricature generation purposes.
Simply put, the anti-face is the exact opposite of a given face, as depicted below:
These are some sample results of a program that implemented the method:
By deploying a reverse variant of the method one can drive an input face towards the average face. Studies show that the average face is commonly considered to be attractive. Thus, in a sense, the method can also be utilized in order to attain beautification.
Example of the same program adjusted for beautification:


Do you understand how to estimate the percentages of successful the lottery, such as the Florida Lottery? You may estimate Just about every list of odds for every various lottery match you Enjoy. Along with the support of a little hand-held calculator or While using the no cost calculator with your Laptop, you just multiply the quantities with each other and insert one particular division procedure when “the buy” of one’s preferred figures just isn’t expected for a certain lottery match.
What you “will need to grasp” is the quantity of complete balls the profitable quantities are drawn from…..is it fifty nine, fifty six, 42, 49, or 39? If there is a secondary drawing for The only added ball, including the “crimson ball” with Powerball or even the Mega Hundreds of thousands’ “gold ball” you need to know the amount of balls are Within this team also. Are there forty nine or 39?
It won’t matter if it is the Florida, Ohio, Texas, PA or NJ Lottery. This tactic or formula provides you with the accurate odds. Florida Lottery is 6/53. Big apple Lottery is six/59. The Ohio Lottery, Massachusetts Lottery, Wisconsin Lottery, plus the Condition of Washington Lottery carry a six/forty nine lottery figures ratio. Illinois Lottery carries a 6/fifty two.
When you have this facts effectively before both you and your calculator in hand, you can start Doing work the formulas. You might want to select 5 frequent balls and one additional ball properly matched towards the successful drawn quantities to gain the multi-million dollar jackpot that most of us aspiration about winning sometime.
In the first case in point you can find 56 balls in the very first group and forty six balls from the secondary group. So that you can get the Jackpot you should match all these balls (5 + one) precisely, but not automatically to be able. The California Lottery’s Super Lotto Plus is 47/27. The large drum is spinning While using the First Element of the drawing. There is a one/fifty six opportunity to match your selection to this first ball.
With a single ball eradicated just after the first quantity continues to be drawn, you now have a one/fifty five potential for matching One more just one of the numbers to the second ball drawn. With Every single drawn number a ball is taken out lowering the volume of remaining balls by a total of 1.
The chances of you the right way matching the variety on the 3rd ball to be drawn has become one/fifty four from the total variety of balls remaining during the drum. Using the third ball faraway from the drum and sitting with the other two successful numbers, your odds of the right way matching the fourth ball is reduced to one/fifty three.
As it is possible to see each time a ball is unveiled through the drum the odds are reduced by one. You started using a 1/fifty six chance, then with Each and every new profitable quantity it is actually reduced to 1/55, 1/fifty four, one/53, and Using the fifth ball you may have the chances of 1/fifty two accurately matching this fifth profitable amount. This is the to start with part of the formula of how you can work out your odds of winning the lottery, including the Florida Lottery.
Now get these 5 odds symbolizing the 5 profitable figures (one/fifty six, one/55, one/54, one/53, and 1/52). The “1” along with the portion represents your a single and only possibility to correctly match the drawn range.
Now you take your calculator and multiply all prime numbers (1x1x1x1x1) equivalent a single (one). Subsequent you multiply all The underside numbers (56x55x54x53x52). Correctly entered and multiplied you find the overall is 458,377,920. The brand new fraction gets one/458,377,920. This is a 458 million to 1 opportunity to gain. In the event you had been needed to decide the figures so as much like They’re drawn, then these will be the odds towards you to definitely earn this Pick five/56 ball lottery match.
The good news is or regrettably, You aren’t required to decide on the quantities in the exact purchase They’re drawn. The second action in the components 토토사이트 will lessen the odds, which lets you match these 5 profitable numbers in almost any purchase. On this stage you’ll multiply the number of balls drawn — five (1x2x3x4x5). With calculator in hand you see that the entire equals 120.
To provde the ideal to settle on your five matching figures in almost any purchase, you build these odds by dividing one hundred twenty/417,451,320. You surely require a calculator for this one. 120/458,377,920 lessens your odds of winning this lottery to one/3,819,816. They are about three.5 million to 1 odds against you of winning this Decide 5/56 ball lottery game.
If this ended up the Mega Millions Lottery, you must include the “gold ball” to these five profitable drawn balls so as to acquire the Multi-Million Greenback Jackpot. The one gold ball is calculated being a 1/forty six chance of matching it properly, and since you are drawing only one range it must be an actual match. Again, you only have that “1” opportunity to do it proper. Now you should multiply three,819,816 by 46.
Get your calculator and do the multiplication. Your remaining odds towards you winning the Mega Thousands and thousands Jackpot are calculated to generally be 175,711,536 or Obviously mentioned 175 million, 711 thousand, 5 hundred 36 thirty-6 to 1 (175,711,536 to 1). Now you know how to determine the percentages of successful the Mega Hundreds of thousands Lottery.
The Powerball Lottery calculations are determined by a 1/fifty nine for the first 5 white balls and one/39 for the “crimson” electricity ball. The main set of multipliers is 59x58x57x56x55. This group totals 600,766,320. Now divide 600,766,360 by 120 (1x2x3x4x5). Your new overall is 5,006,386. There is a 1/39 chance to capture the “crimson” ball. 39 x five,006,386 provides the real odds of profitable the Powerball Jackpot, particularly 195,249,054 to 1.
A further 5 +one Lottery that is apparently just about everywhere in the United States is definitely the “Very hot Lotto” which has a 39/19 depend. It’s played in 15 distinctive States. DC Lottery, Delaware Lottery, Idaho Lottery, Iowa Lottery, Kansas Lottery, Maine Lottery, Minnesota Lottery, Montana Lottery, New Hampshire Lottery, New Mexico Lottery, North Dakota Lottery, Oklahoma Lottery, South Dakota Lottery, Vermont Lottery, along with the West Virginia Lottery. The final odds of winning the bare minimum $one Million Jackpot is ten,939,383 to one.
A Pick six/fifty two ball Lottery video game formulation appears like this: (one/fifty two, one/fifty one, one/50, one/forty nine, 1/48, 1/47) for a total of 14,658,134,four hundred divided by 720 (1x2x3x4x5x6) for the percentages of one/20,358,520. Your chance to win the 6/52 Lottery is in excess of 14.five million to at least one to win, including the Illinois Lotto.
The Hoosier Lottery that uses Indiana State’s nickname, carries a six/48. Michigan Lottery is 6/forty seven, Arizona Lottery and Missouri Lottery are 6/forty four, Maryland Lottery is six/forty three, and Colorado Lottery is 6/forty two. Review this to your Florida Lottery.


Math and Your Child
Why does it matter if your one, two, three or four year old knows math. Won’t they learn that in Kindergarten? Can they actually understand math concepts, add or subtract numbers, or do the math required of Kindergarten when they are such a younger child?
The answer is YES!
According to the National Council of Teachers of Mathematics:
“The National Council of Teachers of Mathematics affirms that a high-quality, challenging, and accessible mathematics education provides early childhood learners with a vital foundation for future understanding of mathematics. Young children in every setting should experience effective, research-based curricula and teaching practices. Such practices in turn require policies, organizational support, and resources that enable teachers to do this challenging and important work.”
Babies, toddlers and Pre-Schoolers know quite a bit about math. It’s in everything they do, see, touch and feel. Practices should be used to strengthen their problem-solving skills and reasoning abilities using both formal and informal techniques. Verbal commands and expressions are important to this group, so encouraging the child to communicate what they are thinking and learning will be key to their success in learning and understanding the different mathematical concepts.
Let's take a look at each age group so as parents and caregivers, you can begin to understand why math is important and why you need to seek out a school that teaches it. Every advantage your child receives in early education will only benefit them as they grow older. Their little minds are so thirsty for knowledge and they will soak it up and retain it. Further, if your child has a learning disability, it is beneficial to get them tested earlier in life to better understand their deficiency and to help them learn in the way that is best for them. At Seven Branches Academy, we test our children according to the State of Georgia’s recommendations.
Toddlers (One & Two Year Olds)
- Toddlers can help match objects that are alike or that are needed together. For example, pairing together a fork with a spoon, a pot with its lid, a pair of socks with shoes, a hat with mittens, etc… This pairing game allows them to understand and develop early reasoning skills.
- They enjoy filling and emptying containers to teach them volume.
- They can understand the meaning of numbers one and two – they know how to take “just one” or to give their friend two blocks while they keep two blocks. As the child reaches age two, they can imitate counting but cannot understand quantity beyond two. As they near 2 ½ years old, they will be able to add one plus one and subtract two minus one.
- They realize that when an object is hidden, that it still exists. They can build a structure with blocks, can put a puzzle together and can remove a part of a toy and replace it. These all teach them the beginnings of Geometry.
- Toddlers begin to understand time through daily routines such as when it’s time to eat, sleep and play. Further they begin to see measurement differently when things are in pieces verses whole (there’s more when it’s in pieces than in a whole version).
- They begin to understand patterns – groups of large and small objects, day and night and types of animals or sounds. Learning patterns is the beginning of reasoning and Algebra.
Three & Four Year Olds
- Three to four year olds are naturally inclined to use mathematics by saying “he has more than me” or “it’s too big to fit there”. They develop their curiosity, imagination and problem solving in this manner.
- Numbers are important to this group. Some three year olds are able to count to ten, although not in the correct order. By the time the child reaches four, they are able to count beyond 20. They also know that the larger the number is, the greater the value.
- They are able to create a necklace of beads and determine the pattern for the beads.
- They are able to understand “first” and “last”.
- Three and four year olds love to put 3 to 5 piece puzzles together. This helps also with Geometry and encourages the child to think logically about how the pieces fit together.
- When they create an object, it will normally be symmetrical in shape. This rudimentary thinking is the beginning of spatial relational thinking involved in Geometry, Physics, Algebra and math in general.
- As they begin learning to jump and run, they are actually learning deductive reasoning about how far they can run without hitting something and how long they can jump in relation to a fixed object.
As you can see, although the concepts are simple, math is very much involved in early education. Teach your child to love math and its concepts, and they will continue that love math as they go through the next 12 years of school! Seven Branches Academy is here to help. We are not a daycare, but an academy focused on teaching your children the necessary building blocks to their academic success.
National Council of Teachers of Mathematics: What Is Important in Early Childhood Mathematics?
National Association for the Education of Young Children: Early Childhood Mathematics: Promoting Good Beginnings
PBS Parents: Child Development


[SDL] How about an SDL_RenderFillQuad function?
meklu at meklu.org
Fri Sep 30 06:11:14 PDT 2016
If you're not too worried about performance, you could draw a
rectangle into an SDL_Texture
and then draw it rotated with SDL_RenderCopyEx. Of course you'd have
to do a bit more
additional arithmetic yourself as the function takes an angle in degrees.
On Fri, Sep 30, 2016 at 3:37 PM, SeanOConnor <sean at windowsgames.co.uk> wrote:
> I need to draw a graph in my game but it looks like the SDL_RenderDrawLine
> only draws lines 1 pixel wide. With a bit of maths I can work out the 4
> points needed to draw a line of any width but the only SDL function that
> draws a primitive seems to be:
> which only draws rectangles with no rotation.
> I'm guessing this SDL function just draws two triangles to make this
> rectangle based on the SDL_Rect it's sent, so surely it'd be trivial to
> create a new function SDL_RenderFillQuad that accepts four SDL_Points and
> draws two triangles based on that?
> And maybe an SDL_RenderFillTriangle too that takes three SDL_Points?
> SDL mailing list
> SDL at lists.libsdl.org
More information about the SDL


Some say..is that an abacus? Actually, it is the same idea just a much smaller scale. This tool is can be used as a whole group lessons, calendar time, interactive carpet time, and center renforcements. We created them at our school w/ card stock, a hole punch, pipe cleaners, and two different colored pony beads. Great parent volunteer activity.
The best example I've seen of the use of this tool is for the teacher to have one and all students to have one. Teacher asks "How can I make 4?". All students use their own think time and build "4" on their rekenrek. A student may have slide over four beads on the top OR bottom but they might have also slid over 3 on top and 1 on bottom OR two on top and two on bottom OR one on top and three on bottom. This leads to the conversation on how to decompose the number '4'.
For a DEEP explanation of how Rekenreks came around and more activities please visit the K-5 Math Teaching Resources.
Want to see something cool! Look:
A fellow coach of mine made a big one! This is my version on her genius work (that is also my adorable daughter playing with our kitten!) This will be great for demonstrations for whole group but also for centers time. From across the room, the teacher can see what the students are doing in that center. I also added the dimensions incase you wanted to make one yourself. All you need is a 10' pole, the joints listed above, a PVC cutter (totally worth having one on hand), and two different colored pool noodles. Cut, stick together, and go! We chose not to glue the pieces together because over time the pool noodles may need to be replaced. You can make that choice. Please, let me know how it goes if you dive in to Rekenreks!
Lastly, for more classroom examples and deeper understanding on the Rekenrek. I suggest getting your hands on the teacher book Number Talks. It comes with a DVD that shows a classroom at work with the Rekenrek.


This is a scenario made popular by the American game-show "Let's make a deal"; The host, the eponymous Monty shows the contestant three doors and tells them there is a car behind one of the doors and booby prizes (typically goats) behind the other two. The contestant gets to choose a door and then Monty opens one of the doors they didn't choose showing them a goat. He then offers them the chance to change their mind. Initially most people say something like "..it's fifty-fifty, so no, I won't change" - but it's not 50/50, changing your mind at this point doubles your chance of getting the car.
Possibly because I did a year of Game Theory on my degree the first thought I had when I initially heard this problem was "where are the odds invested?". When you pick your first door your odds are a third. However - two-thirds odds are invested behind the other two doors and when Monty shows you which of those doors has a goat you know that none of the odds are now behind the door he just showed you; the car can't be behind that door (Monty showed you the goat). Your original door still has a third of the odds and so now the final door MUST carry the two-thirds odds that you didn't choose initially. Changing your mind now doubles your odds.
It's not a straight fifty-fifty because Monty introduced some new information half-way through the game. He showed you which of the two-thirds doors don't have the car.
The Wikipedia article is very good - I nicked the picture from there.
The problem is interesting because it shows how little innate understanding of game theory (and statistics, and probability) most people have. You gotta trust the maths, not your instincts.


The following describes and calculates a number of useful properties of an object defined by a triangular surface mesh. Specifically, we consider:
, where is an infinitesimal area on the surface
The volume is given by If the density is uniform, mass is just density times volume.
Assuming its a uniformly dense solid (as opposed to a thin shell, e.g.) the centroid is defined as
In tensor notation we have
In general the above integral give the moment of inertia about axes passing through the origin of the coordinate system. To get the body centered moment of inertia we can use the parallel-axis theorem:
where is the mass of the object and is the centroid.
This is defined using tensor notation as
The trace of will be equal to the surface area of the mesh.
This only works if all the triangle facets have to be oriented consistently. That is, in the face data, for each face the vertices have to be listed in a counter-clockwise order, while looking at the face from outside the mesh. If the vertices are consistently clockwise, that would result in a negative value for volume. In such a case, switching any two columns in the face data will make it oriented properly. The surface integrals are evaluated exactly directly on the triangles. So, the total surface area and the area tensor can be calculated in each face and added up.
, where is the area of the face. The area of each triangle is calculated by taking cross product of two edges of a triangle. Half the magnitude of this vector is the area of the triangle. This step also gives us the normal to the triangle face, which will be needed later on.
The volume integrals can be done directly by decomposing the mesh into tetrahedrons and evaluating the integral for each tetrahedron. An elegant alternative is to use the Gauss Divergence Theorem. We can use it to recast the volume integrals as surface integrals.
The surface integral can then be written as a summation of the integral evaluated per face.
The integrand is calculated exactly on each triangular face. There are 10 functions whose volume integrals need to be evaluated-- 1 for volume, 3 for centroid and 6 for the moment of inertia.
For obtaining the integral that gives us the volume, the function has to be such that , so that the right hand side in the Divergence Theorem equation equals volume. For example, it can be taken to be . In the code I take where , whose divergence is also unity. This is done because this particular function is needed later in calculating the other integrals.
Plugging the latter into the equation of the divergence theorem, we get
where lies on the surface, and are the components of the outward facing normal at . As mentioned earlier, the surface integral can be written as sum of exact per-face integrals.
The others are calculated similarly. The
python code follows. The sample program calculates the the mass properties for triangulated unit cube of unit density.


1. At Maths Doctor our core aim is to make our students feel fully supported when it comes to their maths education, so often in places like LOCATION pupils are struggling at school and in need of extra tuition. Maths Doctor supplies that and a whole lot more. We assess your child and then personalise a tuition plan that’s perfect for them, with one-to-to teaching from our highly qualified tutors, it will no longer matter if Bracknell schools’s publish stats aren’t what you want your child to achieve because with Maths Doctor they’ll reach their potential. Contact us today by filling out the form to the right.
2. Contacting Maths Doctor today by filling out the form to the right could be the best decision you make when it comes to your child’s maths education. With many schools being oversubscribed and with Maidenhead not being exempt you’ll be right to worry if your child can reach their potential. With Maths Doctor’s help, tailored tuition plans and one-to-one support from our highly qualified tutors, your child will feel confident and be achieving the level they deserve.
3. Just like many cities in the UK, Newbury has issues with oversubscribed schools and pass rates that could be improved. Does this make you worry about your child’s performance in maths? Do you feel like they need extra help? Calling upon Maths Doctor could see your child going from mediocre grades to grades that will benefit them later in life. Simply fill out the form to the right of this page for your free, no obligation assessment and to hear more about the personalised tuition our highly qualified tutors will give.
4. With one in five schools being oversubscribed and many parents in places like Windsor being concerned over the quality of teaching their child receives when it comes to their maths education, you won’t be the only parent in the area looking for private tuition. At Maths Doctor we know your concerns and we do everything to provide the solution that allows your child to flourish and go on to achieve everything you believe they can in maths and much more. All you need to do is fill in the form to the right of this page and one of our advisers will be in touch for a no obligation assessment.
5. When it comes to important subjects in your child’s education, maths is one of the most vital, which means if they don’t succeed at school it could be a detriment to their whole future. In Amersham, like many other cities in the UK, there are parents just like you looking for more support for their child. At Maths Doctor we understand your child’s needs and tailor lesson plans personally to them, this not only allows their grades to improve but their confidence too. Just fill out the form to the right or call us today for your registration free assessment.
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7. Maths is a key subject for getting on in the world, without a good grade in maths your child could find many doors are closed to them. If by living in Buckingham you’re feeling like they aren’t being given the support they require, there’s no need to move, just contact Maths Doctor today by filling out the form to the right for your no obligation assessment. To hear more about our personalise tutoring and tailored lesson plans, our highly qualified tutors and experience in supporting pupils of all abilities, call us today or fill out the form to the right.
8. Maths Doctor has a wealth of experience when it comes to tutoring maths to students with a wide range of abilities and levels. We use this to provide tailored lesson plans and personalise our tuition, which means each pupil feels completely supported and understood. You won’t be the only parent in Gerrads Cross looking into extra help for their child’s maths education, wanting to help guide your child to a brighter future can start with Maths Doctor. Contact us today by filling out the form to the right to take that first step, with absolutely no obligation or registration.
9. Maths Doctor tutors are extremely experienced and work in harmony with the syllabus your child is working to in their maths lessons at school in Marlow. What’s different is with a Maths Doctor tutor to hand your child will be provided with personalised tuition and tailored lesson plans that focus on the areas they may struggle with. Choosing to turn to Maths Doctor will mean the difference between your child achieving mediocre grades to achieving what they really deserve. You will see their confidence in not just maths but all subjects improve. Simply fill out the form to the right to contact us today and one of our advisers will be in touch.
10. If you feel your child’s school in Basildon isn’t pushing them to achieve what you know they can in maths, turning to the Maths Doctor for help makes perfect sense. With our highly qualified tutors on hand to provide one-to-one tuition that’s personalised to your child’s individual needs and that will focus on areas they struggle with and fill them with confidence in all areas of their education, you will quickly see the difference. Contact Maths Doctor today and we’ll give you a no obligation assessment that you don’t need to register for.


All Schools Meet Federal Testing Targets
Division falls short in two sub-groups
POSTED: 3:26 p.m. EDT, August 13, 2009
By: FCCPS Communications
At the individual elementary, middle and high school levels, Falls Church City Public Schools performed well on the Standards of Learning (SOLs) tests for the 2008-2009 school year. Each school made adequate yearly progress (AYP) in all target areas as defined by the federal No Child Left Behind Act (NCLB). The school division as a whole, however, made AYP in 25 out of 29 objectives, with a deficiency in reading and mathematics among economically disadvantaged students and Hispanic students.
AYP is determined primarily by achievement rates in mathematics and reading and by achievement rates among sub-populations determined by various factors such as socioeconomic status, race and disability. The school division’s testing target in reading for the 2008-2009 school year was 81 percent. The testing target in mathematics was 79 percent.
The passing rate in reading for the school division’s economically disadvantaged students was 69.1 percent, and the passing rate in reading for the school division’s Hispanic students was 71.9 percent. The passing rate in mathematics for the school division’s economically disadvantaged students was 71.1 percent and the passing rate in mathematics for the school division’s Hispanic students was 71.3 percent.
“We want all of our students to be proficient in all academic areas, and the testing results indicate a need for additional support,” Superintendent Lois Berlin said. “We have utilized federal stimulus funds to hire two specialists to work with our teachers and students with a goal of raising student mathematics and reading achievement rates. The school division has also teamed up with the Alliance for Youth to start a mentoring program to support both academic and social needs of students.”
Under NCLB guidelines, at least 50 students must meet sub-group criteria in order to be counted. In most sub-group categories, only the school division as a whole, rather than individual schools, has enough students who meet specific demographic criteria to be counted as a sub-group.
The Falls Church City School Board’s strategic plan includes a heavy emphasis on data-driven decision-making. Faculty and staff will look closely at the disaggregated student data to identify any areas of concern in an effort to tailor instructional practices to meet the needs of struggling students.


Roulette Wheel Numbers
Roulette Wheel has the numbers 0-36 in three colours: green, red and black. Zero is Green. Half of the numbers 1-36 are Red, and half are Black.
Red numbers of the Roulette Wheel are 1, 3, 5, 7, 9, 12, 14, 16, 18, 19, 21, 23, 25, 27, 30, 32, 34 and 36.
Black numbers of the Roulette Wheel are 2, 4, 6, 8, 10, 11, 13, 15, 17, 20, 22, 24, 26, 28, 29, 31, 33 and 35.
The Green number of the Roulette Wheel is zero. European Roulette only has one green zero. American Roulette also has a green double zero (00). Some online Roulette games also have triple zeros (000).
The sum of all the Red numbers is 332 and Black 334. Summed up, all the numbers of the Wheel are 666. This gives Roulette its nickname, “the devil’s game”.
How it Works
The mechanical Wheel (in a real-life brick-and-mortar casino) is made of wood and metal. The Wheel rests on precision bearings, carefully selected to keep the spin results random (non-biased). The ball, originally made of ivory, is nowadays a special plastic mix. The construction of a wheel is an extremely detailed process, as any imperfection would lead to the results not being random enough. Only a few companies make Roulette wheels for top-end casinos, among them TCS John Huxley whose tables are often seen at live online casinos too.
Virtual Roulette Wheels are coded like any online game, but much work goes towards the game’s random number generator. This piece of coding ensures that the spin results are random. These RNGs are nowadays verified by special testing laboratories, where millions (or even billions) of results are drawn and then analyzed to ensure that the Wheel’s results are random. Game providers like Microgaming and Netent provide simulated games to online casinos.
Typical Roulette Wheel odds for getting a winning number on a European Roulette game are:
- Red: 48.6% (18 out of 37 numbers)
- Black: 48.6% (18 out of 37 numbers)
- Odds: 48.6% (18 out of 37 numbers)
- Even: 48.6% (18 out of 37 numbers)
- Low (Manque): 48.6% (18 out of 37 numbers)
- High (Passe): 48.6% (18 out of 37 numbers)
- Zero: 2.7% (1 out of 37 numbers)
- Street: 29.7% (3 out of 37 numbers)
The odds are slightly lower for double and triple zero games as there are 1-2 more non-winning numbers on the Wheel.
How to Calculate Odds
First, see how many numbers there are on the Wheel. This is either 37 (European single zero games), 38 (two zeros) or 39 (three zeros). Then divide the number of winning results by how many numbers there are on the Wheel.
For example, the “first dozen” bet has 12 winning numbers. Therefore its odds in an American Roulette game with two zero fields (0 and 00) are 12/38 = 0.31578 = 31.6%.
Roulette is a game of luck, so there are no working strategies for it. Casinos maintain the wheels daily, so they don’t favour any numbers over the others. Online casinos, on the other hand, use random number generators that are tested to be fully random; thus, you can’t predict what number will come up next.
Try it Yourself
You can try simulated Roulette Wheels on many sites. You can, of course, choose any online casino and try playing Roulette for free. Roulette is the most popular table game at casinos, so you’ll find at least a dozen different games at each casino.
The other option is to visit Roulette-Simulator.info, which features a great Roulette simulator you can play for free. You can play the simulator’s virtual game as long as you like and get yourself familiar with the ins and outs of Roulette Wheels. The game even keeps track of your results (if you so wish) so you can try to gamble yourself on the game’s high score list!
Last updated: 2023/03/14


It’s late at night. You’re happily braiding along watching your favorite television program. You’re almost out of beads on several warps, but you’re not worried. Your braid is almost as long as you need. You keep braiding. You drop in the last bead and reach for your tape measure. So close! You just need to string a few more beads so you can finish up. You reach for the tube of seed beads and… NOOOOOOOO! It’s empty!
We’ve all been there. It’s so frustrating. The key to avoiding this agony is to take the time to accurately estimate how many beads you’ll need for your project before heading to the bead shop. Unless, of course, you’re coming into Design & Adorn. In that case, we’d be happy to do the math for you.
Let’s assume that you’re making a beaded kongoh gumi using seed beads and you’ll be using the same size beads on every warp.
For this type of beaded rope the math is based on the following ratio:
Length of Strung Seed Beads per Warp : Finished Length of Braid = 1:2
In other words, you need half your beaded braid length in strung beads per warp.
For example, if you want to make a 20” necklace you would string 10” of beads on each of your eight warps. This assumes you’ll use magnetic endcaps that fit over your beads and add a negligible length. If using a toggle clasp or other ending that will add length, be sure to subtract that from the total finished length before calculating how many beads you’ll need.
Now that you know how many beads to string on each warp, calculate how many total beads are needed for the project.
Length of Strung Beads per Warp X Number of Warps = Total Length of Strung Beads per Project
For our example necklace, we’ll multiple 10” of strung beads per warp by 8 warps and get 80” of strung beads needed for the project.
Up until this point it didn’t matter what size beads we were using, but now we need to make a choice. Let’s use size 8˚ seed beads. If you string up all the size 8˚ seed beads in one tube* you’ll get 24” to 26”. Let’s be conservative and call that 24” linear inches per tube. Now we can calculate how many tubes we’ll need to buy.
Total Length of Strung Beads per Project ÷ Inches per tube = number of tubes needed
For our example necklace we’ll take 80” of strung beads for our project and divide by 24” per tube to get 3.33 tubes. In this case we’ll round up and buy 4 tubes of size 8˚ seed beads.
Rebecca Ann Combs
PS: Remember that if you’re using a bead spinner you may prefer to have an extra 4-8 grams (about ½ tube) so you don’t have to spin down to the bottom of the bowl.
*PPS: All “per tube” counts are based on the tubes sold at Design & Adorn which are 2½” long and about ½” wide.


Last week was so much fun! We did our count down chains, Santa letters and mobiles, Triangle Christmas tree and worked on our gifts. We read books, talked about vowels and practiced our place value with tens and ones. Friday finished our week with a visit from St. Nicholas! What fun to hear the bells and find goodies in our shoes!
This week, will continue to be just as busy and hopefully just as fun! We are reading The Gingerbread Man and many varieties of it! We will be talking about the sequence and which ending is the best. We will continue with one and tens, and keep working on vowels! Besides all that, we will be putting the finishing touches on our Holiday program!
Friday, the children are supposed to “dress up” for the show. I suggest that the children wear regular uniform clothes to school and bring their other outfit with them. It is pizza day, after all, and we want them to look their best.
The performance is in the gym and begins at 2. Another suggestion is arrive a little bit earlier if possible. The show is generally pretty packed and so is the parking lot.
After the performance, you will be able to pick your children up from the classroom. That way we can ensure everyone goes with the correct family!
Warmly, Laura Sanders
Choose five of the six homework choices:
• Count how many days until Christmas. Show how many using tally marks.
• Draw a picture of a character from The Gingerbread man.
• Count how many light switches are in your home.
• Practice writing “an” family words
• Search for number words in a magazine or newspaper. Find five.
• Make up a dance for the Gingerbread story.
Chose a chore and have your child mark it off as they accomplish it daily.


TILES AND GAMERS
You can play the game OK with tiles, similar to those one from the Dominoes game. Up to four players can play. The tiles are in four colors (usually red, blue, green and black) with numbers from 1 to 13 over them, as every tile have two numbers. There are two additional tiles (with Star or J over them). The tiles are 106 total. (4 x 13 x 2 = 104 + 2 = 106 ) (2 black 1, 2 black 2, 2 black 3, ……, 2 green 13 etc.). Plus the two tiles with star (called fake OK).
Every player has a board for ordering of tiles. The tiles are closed and ordered by five in a heap, one next to the other (21 heaps x 5 pc. + 1)
For the determination of the OK cast a die, (2 times – the first time to determinate the heap, and the second time to determinate which tile from the heap will be OK) and then the game is open. The open tile (a number from the respective color), with 1 (bigger from the same color) is OK (for example if the open tile is black 1, OK is black 2 – two pc.). The OK could replace every other tile when making series (groups).
DEALING OF THE TILES
Someone of the players deal the tiles, as the first player have 15 tiles (because he is going to play first), and the other three players have 14 tiles each. Every player arranges his tiles on his board. With the arranging, if some player before to play have the same tiles, as the open tile (in the example – black 1), the result of the other player became with one point down (if the player has at least three points). The players are doing that before the end of the first round.
The player, who have 15 tiles play first. He cleans one tile for which he suppose, that he will not need in the making of the series (groups), as he puts her on his right side (between his desk and the desk of the player, who stands on his right side).
The players are making moves counterclockwise. Then plays the second player, who can take the tile, left by the previous player (the player who is on his left side) or to withdraw one tile from the heap in the middle (those tiles, which are not given to the players) and then also cleans one tile. Then plays the third player and after him, the forth player. That is the way to make round after round until the moment when one of the players “close” (order the tiles in series/groups as it is in the rules) or the tiles are finished.


We explain what algebraic language is, its origins and functions. Also, examples of algebraic expressions and what types they can be.
What is an algebraic language?
The algebraic language is the language of mathematics . That is, to a system of expression that uses symbols and numbers to express what we usually communicate through words , and that allow us to formulate theorems, solve problems and express proportions or formal relationships of a different nature.
The algebraic language was born, logically, together with algebra , the branch of mathematics that studies the relationship and combination of abstract elements according to certain rules. These elements can be numbers or quantities, but they can also be unknown values or certain numerical ranges, for which letters (known as unknowns or variables ) are used.
Originally, this field of knowledge was called al-jabr wa l-muqabala , that is, “the science of restoring balance”, as formulated by one of his fathers, the Persian astronomer, geographer and mathematician Al-Khuarismi. (ca. 780-ca. 850). The name came from his studying how to move a term from one side of an equation to the other, or how to add one to both sides to preserve proportion. Over time al-jabr came to Latin as algeber or algebra .
Seen in this way, then, the algebraic language is the language of algebra. The written forms that said language produces are known as algebraic expressions : any number, any equation are perfect examples of it. Using these types of expressions, then, we can “speak” the algebraic language, and communicate relations and operations that go far beyond the scope of mere arithmetic.
What is an algebraic language for?
As we have said before, the algebraic language is used to build algebraic expressions, that is, formulations in which numbers, symbols and letters are combined to express a logical and/or formal relationship , in which some quantities are known and others are unknown.
Algebraic expressions, then, are ordered strings of these signs, in which we will find numbers, letters, and arithmetic operators. Depending on what they are, we can distinguish between, for example:
- Unknowns (which express unknown values) or variables (which express non-fixed values), the latter being dependent or independent .
- Arithmetic signs (which express determined arithmetic operations).
- Superscripts or powers (which involve multiplying a number by itself a certain number of times).
- Roots or radicals (which involve dividing a number by itself a certain number of times).
- Functions (which express a dependency relationship between two values of two or more expressions).
Examples of algebraic expressions
The following are examples of algebraic expressions:
- 19465 + 1
- 9x + 2
- 6x . 2 (4+x)
- 2×3 _
- 8a + 4b = c
- y – 20(x) = ½
- F(x) = 2 (A, B)
- 4 (a + b)
- 6A + 2B – C = 0
- 4 ½ = 2
- 2y = x – 2
- 1/(y+x) . 5
- x 3 + 2y 2 + 9
- [ 5 3 . (a+b) ] – 7
- 9 + 9 + 9 + 9
- 5 + (1 – y) = 3
- y – x + 1


It is important for investors to know how to Calculate Profit And Loss In Forex because it is simple to do so.
Investors must first ascertain the investment’s original cost or purchase price in order to compute the percentage gain on the investment. The investment gain or loss is then calculated by deducting the investment’s acquisition price from its selling price.
Investors can ask their broker for the original purchase price if they don’t already have it. For every transaction, brokerage houses provide trade confirmations, either in print form or online, that include the original buy and sale prices as well as the investment’s financial information.
How to Interpret a Currency Quote
An exchange pair consists of two components. The first item is the “basic currency.” The second item is the “quote currency”. As a result, in the case of EUR/USD, the euro serves as the base currency and the US dollar as the quote currency.
At the time of writing, the EUR/USD quote is 1.0884. Accordingly, the current exchange rate for one euro is 1.0884 dollars.
Calculate Profit And Loss In Forex
Add the original purchase price to the selling price. Gain or loss is the outcome.
Divide the investment’s gain or loss by its initial value, which is typically its acquisition price.
To get the percentage change in the investment, multiply the figure by 100.
A loss on the investment occurs if the percentage turns out to be negative since the market value is less than the original purchase price, also known as the cost basis.
There has been a profit on the investment if the percentage is positive since the market value or selling price is higher than the initial purchase price.
Lets See How To Calculate Profit And Loss In Forex
Currently, the EUR/USD exchange rate is 0.9517/0.9522, where 0.9517 represents the sell price and 0.9522 represents the purchase price. Five is the spread.
Take the example of selling 10,000 EUR at 0.9517.
Accordingly, you exchanged 10,000 EUR for 9,517 USD (10000 EUR * 0.9517 = 9,517 USD).
Following your transaction, the EUR/USD market rate drops to 0.9500/0.9505. You choose to purchase 10,000 EUR at a rate of 0.9505 (9,505.00 USD = 10,000 EUR).
10,000 EUR were sold for 9,517 USD, and 10,000 EUR were then purchased for 9,505 USD.
Your earnings are $10.00 USD.
You can see that the current exchange rate is 115.00/115.05 (where 115.00 is the sell price and 115.05 is the purchase price) for the USD/JPY. Five is the spread.
You choose to purchase $10,000 at 115.05.
As a result, you spent 10,000 USD and earned 1,150,500 JPY (1,150,500 JPY = 10,000 USD * 115.05).
You decide to sell back 10,000 USD for 114.45 (10,000 USD multiplied by 114.45 equals 1,144,500 JPY) when the market rate of USD/JPY drops to 114.45/114.50.
10,000 USD were purchased for 1,150,500 JPY, and 10,000 USD were then sold for 1,144,500 JPY.
The math for your loss is 1,150,500 – 1,144,500, which is 6,000 JPY.
Keep in mind that you must translate your loss from JPY to USD.
To Convert this sum to US Dollars
6,000 JPY x 114.45 is $52.42 USD or
6,000 JPY * 1/114.45 is equal to $52.42 USD.
Pips, dollars, and cents are used to calculate gains and losses
Here are a few examples that illustrate the process for figuring gains and losses on foreign exchange.
We’ll start by presuming that the euro will appreciate in value relative to the dollar. As a result, we purchase 100,000 EUR/USD units at a cost of 1.1000. In order to execute this transaction, we are effectively paying 110,000 dollars to purchase 100,000 euros.
Say the exchange rate increases by 100 pip to 1.1100.
Our original investment of 100,000 euros is now worth 111,000 USD. We have a profit of $1,000 after deducting our investment of 110 000 dollars.
As a result, each pip is worth $10.
Or, let’s say we predict a drop in the euro’s value relative to the dollar. We exchange 100,000 units of the EUR/USD pair, or 100,000 euros, for 100,000 US dollars. At the quoted currency rate, 100,000 euros will buy $110,000 in US dollars (100,000 * 1.1000 = $110,000).
Assume that the market changes in our favour. EUR/USD decreases by 200 points to 1.0800.
We can profitably close out this trade. The new exchange rate of 1.0800 dollars per euro is used to convert the 110,000 dollars we currently own back into euros. At the new currency rate, the 110,000 dollars are converted back into 101,851.85 euros. To calculate the profit, deduct the 100,000 euros that were expended to open the transaction (1,851.85 euros).
It is necessary to convert the 1,851.85-euro profit back to dollars at the current rate of 1.0800. To obtain a profit of $2,000, multiply your profit in euros (1,851.85) by the exchange rate (1.0800). The 200 pip movement between the two means that each pip is now worth $10.
Calculating gains and losses in foreign exchange is as easy as repeatedly translating one currency into another, despite the math initially appearing complex. Foreign exchange trading is nothing more than exchanging one currency for another at the going rate in the hopes that you may return the transaction at a later date at a more advantageous rate, making a profit.
Speaking of gains, if you’re prepared to begin investing in either domestic or overseas equities, we can help. Visit our Broker Center, and we’ll assist you in beginning your investment adventure.
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By Patrick Barry
This booklet addresses a ignored mathematical quarter the place easy geometry underpins undergraduate and graduate classes. Its interdisciplinary portfolio of purposes contains computational geometry, differential geometry, mathematical modelling, machine technology, computer-aided layout of platforms in mechanical, structural and different engineering, and structure. Professor Barry, from his lengthy adventure of educating and examine, right here can provide a latest and coherent exposition of this topic region for various degrees in arithmetic, utilized arithmetic, engineering arithmetic and different components of software. Euclidean geometry is missed in collage classes or scattered over a few them. this article emphasises a scientific and entire build-up of fabric, relocating from natural geometrical reasoning aided by way of algebra to a mix of analytic geometry and vector tools with trigonometry, constantly in an effort to potency. The textual content starts off with a variety of fabric from the necessities of Euclidean geometry at a degree, and ends with an advent to trigonometric capabilities in calculus. Very many geometric diagrams are supplied for a transparent figuring out of the textual content, with plentiful challenge workouts for every bankruptcy. scholars, researchers and business practitioners would get advantages from this sustained mathematisation of shapes and significance from the true global of technological know-how that could bring up and support their mathematical information and talent
By Keith Critchlow
Can we think an international with out vegetation? Their attractiveness bargains us get pleasure from their colour, body spray, and shape, and their substance bargains medicinal advantages. plants additionally communicate to us within the language of the plant’s shape, supply cultural symbols in several cultures, and, on the maximum degrees, provide suggestion.
In this gorgeous and unique booklet, popular philosopher and geometrist Keith Critchlow specializes in a side of flora that has bought the least awareness. The flower turns into a instructor of symmetry and geometry (the “eternal verities,” as Plato referred to as them). during this feel, Critchlow tells us, we will be able to deal with plant life as resources of remembering―ways of recalling our personal wholeness, in addition to awakening our internal energy of popularity and awareness. what's glaring within the geometry of a flower’s face can remind us of the geometry that underlies all lifestyles.
Working from his personal flower pictures and with each geometric trend hand-drawn, the writer experiences the function of vegetation from the point of view of our interrelationship with the flora and fauna. His illuminating examine makes an attempt to re-engage the human spirit in its intimate relation with all nature.
By Peter H. Selby
If you want geometry and trigonometry as a device for technical paintings … as a refresher direction … or as a prerequisite for calculus, here’s a short, effective means that you can examine it! With this publication, you could educate your self the basics of airplane geometry, trigonometry, and analytic geometry … and find out how those themes relate to what you understand approximately algebra and what you’d wish to learn about calculus. You’ll paintings your manner via geometry, numerical trigonometry, equipment of trigonometric research, analytics, and limits—all the way in which as much as the "front door" of calculus. Geometry and Trigonometry for Calculus is among the Wiley Self-Teaching courses. It’s been proven, rewritten, and retested until eventually we’re certain you could educate your self the suggestions of geometry and trigonometry. And it’s programmed—so you're employed at your personal speed. No must haves are wanted. goals and self-tests inform you how you’re doing and let you pass forward or locate additional aid if you want it. widespread studies and perform routines strengthen what you examine.
By Koen Thas
The concept of elation generalized quadrangle is a normal generalization to the speculation of generalized quadrangles of the $64000 idea of translation planes within the thought of projective planes. nearly any recognized type of finite generalized quadrangles should be made out of an appropriate classification of elation quadrangles.
In this e-book the writer considers a number of facets of the idea of elation generalized quadrangles. certain consciousness is given to neighborhood Moufang stipulations at the foundational point, exploring for example a question of Knarr from the Nineteen Nineties in regards to the very proposal of elation quadrangles. the entire identified effects on Kantor’s leading energy conjecture for finite elation quadrangles are amassed, a few of them released right here for the 1st time. The structural conception of elation quadrangles and their teams is seriously emphasised. different similar themes, akin to p-modular cohomology, Heisenberg teams and lifestyles difficulties for definite translation nets, are in brief touched.
The textual content begins from scratch and is largely self-contained. many various proofs are given for identified theorems. Containing dozens of routines at a number of degrees, from really easy to really tricky, this direction will stimulate undergraduate and graduate scholars to go into the attention-grabbing and wealthy global of elation quadrangles. The extra comprehensive mathematician will specifically locate the ultimate chapters not easy.
By N. S. Hellerstein
This ebook is set "diamond", a common sense of paradox. In diamond, an announcement could be actual but fake; an "imaginary" kingdom, halfway among being and non-being. Diamond's imaginary values clear up many logical paradoxes unsolvable in two-valued boolean common sense. Diamond is a brand new strategy to clear up the dilemmas of upper arithmetic. during this quantity, paradoxes by means of Russell, Cantor, Berry and Zeno are all resolved. This publication includes sections: easy; which covers the vintage paradoxes of mathematical common sense and exhibits how they are often resolved during this new process; and complicated, which relates diamond to Boolean common sense, three-valued good judgment, Gödelian meta-mathematics and obstacle video games.
By Francis Borceux
This is a unified remedy of a number of the algebraic methods to geometric areas. The learn of algebraic curves within the complicated projective airplane is the usual hyperlink among linear geometry at an undergraduate point and algebraic geometry at a graduate point, and it's also a huge subject in geometric functions, equivalent to cryptography.
380 years in the past, the paintings of Fermat and Descartes led us to review geometric difficulties utilizing coordinates and equations. at the present time, this is often the most well-liked approach of dealing with geometrical difficulties. Linear algebra offers a good instrument for learning all of the first measure (lines, planes) and moment measure (ellipses, hyperboloids) geometric figures, within the affine, the Euclidean, the Hermitian and the projective contexts. yet contemporary functions of arithmetic, like cryptography, desire those notions not just in actual or advanced instances, but additionally in additional normal settings, like in areas built on finite fields. and naturally, why no longer additionally flip our realization to geometric figures of upper levels? along with all of the linear elements of geometry of their such a lot basic surroundings, this booklet additionally describes invaluable algebraic instruments for learning curves of arbitrary measure and investigates effects as complex because the Bezout theorem, the Cramer paradox, topological staff of a cubic, rational curves etc.
Hence the ebook is of curiosity for all those that need to educate or research linear geometry: affine, Euclidean, Hermitian, projective; it's also of significant curiosity to people who do not need to limit themselves to the undergraduate point of geometric figures of measure one or two.
By Lars-Erik Andersson
This can be an creation to the mathematical thought which underlies subdivision surfaces, because it is utilized in special effects and animation. Subdivision surfaces let a dressmaker to specify the approximate kind of a floor that defines an item after which to refine it to get a extra worthwhile or appealing model. a large amount of mathematical concept is required to appreciate the features of the resulting surfaces, and this publication explains the cloth conscientiously and carefully. The textual content is extremely available, setting up subdivision tools in a different and unambiguous hierarchy which builds perception and knowing. the fabric isn't limited to questions on the topic of regularity of subdivision surfaces at so-called awesome issues, yet offers a extensive dialogue of some of the tools. it's for this reason an outstanding instruction for extra complicated texts that delve extra deeply into designated questions of regularity. Read more...
By Rolf Berndt
Symplectic geometry is a significant subject of present learn in arithmetic. certainly, symplectic equipment are key elements within the learn of dynamical platforms, differential equations, algebraic geometry, topology, mathematical physics and representations of Lie teams. This ebook is a real advent to symplectic geometry, assuming just a common historical past in research and familiarity with linear algebra. It begins with the fundamentals of the geometry of symplectic vector areas. Then, symplectic manifolds are outlined and explored. as well as the fundamental vintage effects, similar to Darboux's theorem, more moderen effects and ideas also are incorporated right here, corresponding to symplectic potential and pseudoholomorphic curves. those principles have revolutionized the topic. the most examples of symplectic manifolds are given, together with the cotangent package deal, Kähler manifolds, and coadjoint orbits. additional valuable principles are rigorously tested, resembling Hamiltonian vector fields, the Poisson bracket, and connections with touch manifolds. Berndt describes a number of the shut connections among symplectic geometry and mathematical physics within the final chapters of the ebook. particularly, the instant map is outlined and explored, either mathematically and in its relation to physics. He additionally introduces symplectic aid, that's a huge software for decreasing the variety of variables in a actual method and for developing new symplectic manifolds from previous. the ultimate bankruptcy is on quantization, which makes use of symplectic the way to take classical mechanics to quantum mechanics. This part features a dialogue of the Heisenberg staff and the Weil (or metaplectic) illustration of the symplectic crew. numerous appendices supply historical past fabric on vector bundles, on cohomology, and on Lie teams and Lie algebras and their representations. Berndt's presentation of symplectic geometry is a transparent and concise creation to the foremost tools and functions of the topic, and calls for just a minimal of must haves. This ebook will be a superb textual content for a graduate path or as a resource for a person who needs to benefit approximately symplectic geometry.
By Jürgen Jost
In this booklet, I current an increased model of the contents of my lectures at a Seminar of the DMV (Deutsche Mathematiker Vereinigung) in Düsseldorf, June, 1986. The name "Nonlinear tools in complicated geometry" already shows a mix of concepts from nonlinear partial differential equations and geometric suggestions. In older geometric investigations, frequently the neighborhood elements attracted extra realization than the worldwide ones as differential geometry in its foundations presents approximations of neighborhood phenomena via infinitesimal or differential buildings. right here, all equations are linear. If one desires to contemplate worldwide facets, even though, often the presence of curvature Ieads to a nonlinearity within the equations. the easiest case is the only of geodesics that are defined by means of a approach of moment ordernonlinear ODE; their linearizations are the Jacobi fields. extra lately, nonlinear PDE performed a increasingly more pro~inent röle in geometry. allow us to Iist probably the most very important ones: - harmonic maps among Riemannian and Kählerian manifolds - minimum surfaces in Riemannian manifolds - Monge-Ampere equations on Kähler manifolds - Yang-Mills equations in vector bundles over manifolds. whereas the answer of those equations frequently is nontrivial, it will possibly Iead to very signifi cant leads to geometry, as options offer maps, submanifolds, metrics, or connections that are uncommon through geometric houses in a given context. a lot of these equations are elliptic, yet usually parabolic equations are used as an auxiliary device to unravel the elliptic ones.