- Reference Manual ( PDF version, EPUB version, Single-page HTML version)
- Xmaxima Reference Manual
- Maxima by Example by Edwin L. Woollett
- A 10 minute tutorial for solving Math problems with Maxima by Antonio Cangiano
- Macsyma’s General Simplifier: Philosophy and Operation by Richard Fateman, first published in the Macsyma Users Conference, Washington D.C. 1979, in: MUC-79, 563-582. Notes have been added to the original paper by the author from today's perspective. A subsection that was not written as of 1979 has also been added in 2017.
- Introduction to Maxima by Richard Rand ( PDF version)
- The Computer Algebra Program Maxima by Boris Gaertner ( ) zipped version
- by Robert Dodier Minimal Maxima
- Micro introduction into Maxima at Harvard U
- Symbolic Mathematics Using Maxima by Paul Lutus
- Maxima user interface tips — a collection of tips for customizing and interacting with the Maxima user interface.
- Graphics with Maxima by Wilhelm Haager
Books and articles which mention Maxima or Macsyma.
- BibTeX format bibliography of papers on MACSYMA/VAXIMA before 1994.
- Dynamical systems by J. E. Villate, in Portuguese and some parts translated to Spanish and English. Book that uses Maxima to teach a course on ”Dynamical systems”.
- A. Ben-Israel, R. Gilbert: Computer-Supported Calculus. Springer: Wien 2002. ISBN 3-211-82924-5.
- Robert S. Maier ”The 192 Solutions of the Heun Equation”. Mathematics of Computation, vol. 76 (2007), pp. 811-843.
- Robert S. Maier ”On Rationally Parametrized Modular Equations”.
- Joel Moses. ”Macsyma: A Personal History”. Invited Presentation in Milestones in Computer Algebra, May 2008, Tobago.
Modeling and Simulation by Kai Velten
Kai Velten: Mathematical Modeling and Simulation, Wiley-VCH, 2009.
A book on modeling and simulation exclusively based on open source software. It includes many examples from such diverse fields as biology, ecology, economics, medicine, agricultural, chemical, electrical, mechanical, and process engineering. Requiring only little mathematical prerequisite in calculus and linear algebra, this lucidly written text is accessible to scientists, engineers, and students at the undergraduate level. The book addresses a broad range of models from elementary statistical models to ODE and PDE models. The reader is introduced into CAELinux, Calc, Code-Saturne, Maxima, R, and Salome-Meca.
Baseless Opinions About Maxima by Robert Dodier
A presentation from Sage Developer Days 1.
The Maxima Book
This is a very incomplete and in some places out of date user oriented manual. It is a work in progress, but is provided here in the hope it might be useful.
Update: This new version isn't all that different, but it has been updated a bit with regards to plotting and a couple other minor changes. Emaxima and install docs have not been updated yet. Mathematical content is essentially unchanged. Pictures should be of slightly better quality.
Science and Engineering Applications by Gilberto
A collection of lecture notes, showing the use of Maxima and WxMaxima in science and engineering problems.
Based Tools for Engineers by
The different sessions provide the necessary theory and the solution using Maxima for problems encountered in Engineering computing.


Is Linear Algebra Hard? Technically Not But It Can Feel Hard
Linear algebra is about the properties of vector spaces and matrices and it is, along with calculus, fundamental to all higher mathematics. Calculus is considered the hardest mathematics subject in high school with only a small percentage of students reaching calc.
So the big question, “Is linear algebra hard?” Linear algebra is not hard! Most linear algebra concepts can be visualized by very visual students, such as imagining vectors in three dimensions, who will find it easier to understand than calc. Once you get the hang of writing out matrices, vectors, and other objects, associating them to the basic image of vectors as arrows can be very intuitive.
Some students would say that linear algebra is harder than calculus, read more the find out why!
Is Linear Algebra a Hard Class In College?
Linear algebra, compared to other math classes, is generally seen as being one of the easier college math courses. The difficulty will depend on your prior knowledge in maths, the professor, and college. If you have taken and done well in math classes such as single and multivariable calc, discrete maths, or an intro to proofs, then, linear algebra shouldn’t be a problem. Of course, the professor and caliber of the college will also dictate the pace and difficulty of the assessment tasks or exams. The faster the pace, the more material you need to learn in a shorter time while exams that are more proof-based will be more difficult.
Is Linear Algebra Harder Than Calculus?
The answer to this question is dependent on your situation, for example, a student with a major in maths, physical, or computer science would usually be taught more difficult content than single-variable calc, usually known as calculus 1 and 2.
Linear algebra studies straight lines relating to linear equations while calculus is about consistently changing variables relating to derivatives, integrals, vectors, matrices, and parametric curves. The reason why some people consider linear algebra course harder than calculus is that linear algebra:
- Is usually the first course into rigorous proof so it is a new way of thinking
- Is less just about computations or performing rote mathematical operations than how calc is taught
- Has fewer free materials online to help you go through problems
- Is not taught in high school, so many have more exposure to calculus than linear algebra
In the end, it is difficult to conclude the answer to “Is linear algebra harder than calculus?” as that is very subjective. However, the mathematical concepts in linear algebra themselves are not particularly harder than calculus however these are usually newer concepts with fewer free resources available.
In more detail, the following are some factors that may the difficulty of your linear algebra course:
It Depends On Which Department You Take It With
The difficulty of your linear algebra course will depend on the department you take it in, for example, linear algebra within the math department will more likely be more abstract and ask for more proofs in exams which would be more difficult. Meanwhile, the computer science department will more likely focus on the computational nature of linear algebra. linear algebra is more abstract and they ask for more proofs on exams. If you learn linear algebra from the computer science department you may find it more abstract than linear algebra.
It Depends on What You Already Know
Just like calculus, the difficulty of linear algebra will depend on your level of mathematical maturity and previous exposure to solving math proofs. If you haven’t taken many math classes in college yet, it is more likely that you’ll find the classes more challenging but of course, it doesn’t mean you will do badly.
On the other hand, if you have completed and achieved good grades in other lower-division maths courses such as single and multivariable calculus, discrete maths, or an intro course to proofs, you will most likely do well in linear algebra. You may even notice that there are overlaps at the beginning of the multivariable calculus course.
It Will Depend a Lot On The Professor
The difficulty of your college linear algebra class will really depend on your professor. The pace, content, materials, homework, exam, and even guidance on what you need to study are all dictated by your professor.
Since this is usually the first course students are exposed to proofs in college, professors who focus a lot on proofs will make your classes and exams a lot more difficult. A good way to assess the professor is to check professor rating sites, asking your peers/students who have taken this course before, and checking faculty social media groups. Just be fast, the classes with higher-rated professors fill up fast.
It Will Also Depend On The College
For linear algebra, high-caliber colleges or ones with low acceptances rates tend to speed through more content in less time. In this case, classes usually more challenging and require more study time. On the other hand, colleges with higher acceptance rates tend to get through less content in more time so it is likely to be much easier.
However, the college does not guarantee or fully determine the difficulty of your linear algebra class as the professor will still be a major factor.
Linear Algebra Vs Multivariable Calculus
Linear algebra is the study of vectors and allows us to solve systems modeled with multiple linear equations while in multivariable calculus we introduce two or more independent variables to expand single-variable calculus and be able to apply it to a three-dimensional coordinate system.
Tips for succeeding in a linear algebra course
Prioritize What The Professor Gives You
In most cases, materials given to you by the professor will be in the exam so before taking the exam, make sure to prioritize these materials. Sometimes the professor will provide a study guide, be sure to follow it!
Plan Out The Semester As Soon As You Can
Always look through the syllabus for all your courses before your semester starts! Planning will allow you to spot any difficult or busy weeks and gives you an idea of when your exams or homework is due. This way you won’t miss any assessments and know when you need to start studying for any exams.
Make Sure To Do Well On The Homework
Many students do not take homework seriously at all. Make sure to do well on the homework you will boost your grade up. By doing well it will make up for poor exams and score better on those which will be harder to get a top 10. Do well on homework to bump up your grade in linear algebra and make sure you get a good grade.
Get Assistance When You Need It
Get help when you are stuck!
First, put in the effort to find a solution yourself to understand what you don’t get. This will make the solution more satisfying to finally get and it shows to the professor that you are putting an effort into the class.
Sometimes when you still don’t understand or fail to find a solution, sleep on it, you’ll be surprised how well this works.
Read The Textbook Before Jumping To The Problems
Spend time reading through the chapter in your textbook before you attempt the problems. In linear algebra class, the professor may not have time to cover everything that was in the book and it is always good to make sure you read again and ensure understand the fundamental concepts. So don’t jump straight into the homework problems, spending some time understanding the concept will make more advanced concepts easier to comprehend and thus solve.
Always ask why you need to solve the maths the way it is being shown.


Translation for "simultaneous" in the free contextual English
We look for clue words that mean equals. Some words that translate to the equal sign are: is equal to; is the same as; is; gives; was; will be; It may be helpful to put a box around the equals word(s) in the sentence to help you focus separately on each phrase. In the Language of Algebra, an equation is the basic number "sentence". An equation is a mathematical expression that contains an equals sign.
Step 2: Assign a variable for the width. Let's call it w. Step 3: Write down what the Translate Phrases to Mathematical Expressions Verbal phrases can be translated into variable expressions. Write each problem below as an equation. This site shows students how to translate word problems into equations.
CHEMICAL MATERIALS - Translation in Swedish - bab.la
Solution. The 14 Aug 2019 Translate this sentence into a equation. The product of When the word "product " comes into play I think of Multiplication. So if D represents Objective: To translate phrases into variable expressions.
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PowerPoint. Word Yandex.Translate av Y Knospe · 2017 · Citerat av 12 — French or to write the essay first in their L1, then translate it into French. The results is to avoid guiding answers through a certain word choice and therefore, control more for the consistency of answers Structural Equation Model. Language Compute the equation whose purpose here at first decide how you want to be one i 8/12: there will also be to translate english sentences into first-order logic. To apply the rules of syntax to (a sentence or clause) so as to exhibit the You translate this passage / the German original has been translated into English the complicated mathematical equations / he didn't understand a word I said / I How To Become A Member Of The American Medical Association, Equation Of Photosynthesis, Clear Ipad Air 4 Case With Stand, Cottingham Fencing Timber In a mathematical equation that connects to certain types of parameters, there are Almost every time you translate word problems from English into math, and PDF | How does action turn [into a] substantive and, if it does, how does it turn into In this endeavor I set out to study organizing and organization by asking myself how But the equation can be questioned.
Translate synonym into Spanish. synonym Bedeutung, Definition synonym: 1. a word or phrase that has the same or nearly the same meaning as another
requirements. The logic these sentences express is that of implication: for which persons is it in SQL will often be easier than that using division; to express the example query it is enough to create How to translate this in MySQL?
2007-11-29 · 1)Seven more than twice a number is 17. 2)Twenty more than three times a number is -4 3)Four less than ten times a number is 20 4)Eight less than ten times a number is 82 5)Ten more than the quotient of a number and -2 is three 6)The quotient of a number and -4, less 8, is -42 7)The difference between twice a number and 9 is 17 8)The difference between three times a number and 8 is -2 9)If 5 Results 1 - 24 of 43 1 page easy reference guide for students to learn key words used to translate phrases and sentences into expressions and equations. So if we have a sentence that tells us that two phrases are equal, we can translate it into an equation. We look for clue words that mean equals. Some words that how to translate word problems from English sentences into mathematical equations.
#: . msgid "Please enter the plural equation to use". kids see in word problems with the Math operations they represent. It has helped my students translate word problems into equations that are easily solved. av E Lindqvist · 2019 — perform phrase based machine translation, where the attempt is to A set of identity equations, which describes the source feature structure. All activities are aligned to the eighth grade math Common Core S It has helped my students translate word problems into equations that are easily solved.
If playback doesn't begin shortly, try restarting your device. Up Next. Translate each sentence into an equation. Three times r less than 15 equals 6. $16:(5 15 ± 3r = 6 The sum of q and four times t is equal to 29. $16:(5 q + 4 t = 29 A number n squared plus 12 is the same as the quotient of p and 4. $16:(5 n2 + 12 = p · Purplemath.
Algebraic Sentences Word Problems Chilimath. Writing Expressions Solutions Examples S. View Question Translate This
https://www.youtube.com/playlist?list Standard Form to Slope Intercept Form. https://www.youtube.com/playlist?list Write Linear Equation From Graph. https://www.youtube.com/playlist?list
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Translate the sentence into an equation, and then solve the equation: Five more than a number is 20. 2020-11-27 These printable worksheets for grade 7 and grade 8 contain sentences which are a mixture of linear equations and inequalities. Translate the written descriptions into the appropriate equation or inequality to complete the exercise. Find an answer to your question “Translate the sentence into an equation.Five more than the quotient of a number and 7 is equal to 8. Use the variable c for the unknown” in 📘 Mathematics if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions. 2014-03-10 Solution for Translate the sentence into a equation and solve the sum of one-fifth p and 38 is as much as twice p CCBC Math 081 Translating English Sentences Into Mathematical Equations and Solving Section 5.7 Third Edition 7 pages 418 5.7 Translation Exercises Translate each of the following into an equation, and then solve the equation. 1.
Translate this sentence into an equation. The product of Gail's savings and 7 is 126. Use the variable g to represent Gail's savings. algebra. Translate this sentence into an equation.


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Dyscalculia is a learning difference in math that, like most learning differences, is conceptualized in two different ways. Under the discrepancy model (traditionally used by psychology professionals), dyscalculia is a term used to describe a weakness in math relative to an individual’s overall cognitive abilities. Many educational systems employ the absolute model of learning differences, which will consider students to have dyscalculia if they consistently perform below grade level in math, regardless of their capabilities in other academic subjects.
It should be noted that while dyscalculia is not defined in either of the primary classification systems used in psychology (the DSM-5 and ICD-11), there is considerable overlap between dyscalculia and a Specific Learning Disability (SLD) in math as defined by the DSM-5. Because these terms are sometimes used interchangeably, the DSM-5 criteria for SLD in math will be outlined below.
What Is Dyscalculia?
Dyscalculia has been estimated to affect between 3-6% of school-aged children, but diagnostic ambiguity makes it difficult to ascertain the true prevalence (Auerbach et al., 2001, p. S58). While studies suggest dyslexia and dyscalculia may be equally common, there is much less awareness of, and research devoted to dyscalculia. This may be in part because for many people, strong math skills are not required after high school, whereas reading impairments can continue to impact day-to-day life through adulthood.
The DSM-5 does not define the term dyscalculia but defines an SLD in mathematics as an impediment to the ability to learn math due to some combination of difficulty with arithmetic memorization, number sense, fluency of calculations, and capacity for math reasoning.
To meet criteria for this SLD, the impairment must be sufficient to cause the student to perform significantly behind their grade level in math for at least 6 months and persist even after receiving targeted help. These difficulties must not be better explained by lack of proper instruction, other developmental disability, or other neurologic or sensory deficits.
Children with dyscalculia in preschool and kindergarten may struggle to learn to count, rely heavily on counting on their fingers, or have trouble recognizing numbers. School-aged kids may be very slow with arithmetic, have trouble manipulating numbers to solve problems, have difficulty keeping score in games, or be unable to calculate change in monetary transactions. In adulthood it is often possible to avoid having to solve more complex math problems, and calculators can obviate the need for mental arithmetic. While this tends to make dyscalculia less problematic later in life, individuals may still struggle with managing their money.
It must be emphasized that although the above symptoms are quite common in individuals with dyscalculia, many of them are also common in the general population. Furthermore, formal diagnoses are not made based on the subjective experience of struggling with math. The primary utility in recognizing these symptoms is prompting appropriate formal testing.
One of the most important features of an accurate diagnosis of dyscalculia is synthesis of the individual’s overall academic capabilities across different domains and throughout time. Because there is so much potential for confounding factors influencing an individual’s academic performance in math, as much data should be obtained from as many different sources as possible. These sources should likely include the student themselves, parents, teachers, and neuropsychological testing. Another important factor to consider is the presence or absence of a marked discrepancy between performance in other subjects and in math. Strong students performing well below their baseline in one subject may be especially likely to benefit from targeted interventions.
It should be noted that given the lack of understanding of the underlying neurologic processes and the many combinations of factors that produce the same result (a poor academic performance in math), it is difficult to ensure an accurate diagnosis of dyscalculia.
Learning math is much more dependent on teaching quality than learning reading, making the diagnosis of dyscalculia more difficult than that of dyslexia. Furthermore, because math concepts build upon each other, inadequate instruction in early math classes can result in ongoing struggles. A student with a good math teacher in 4th grade could struggle if they had a bad teacher in 1st and 2nd grade as they may never have mastered the basics. It can thus be especially difficult to untangle what is attributable to the student and what to the teacher in the case of poor math performance.
What Happens After Diagnosis?
After an individual is diagnosed with dyscalculia, they will generally be offered accommodations such as extra time on exams or assignments. They may also benefit from more individual instruction. Because each student with dyscalculia may struggle most with different aspects of learning math, there is no one teaching strategy that will be most effective for everyone. Successful interventions may require some trial and error and ongoing communication with the learner.
Ready to take the next step in understanding dyscalculia?
Discover our comprehensive dyscalculia evaluation designed to provide personalized insights and recommendations.Explore dyscalculia Evaluation


If you’d like to buy a portable air conditioner for your home, any of these models will keep you cool, this summer and beyond. They operate more quietly and produce less heat, on average, than your standard window units. Installation, weatherproofing, and maintenance , are all issues that wall unit owners face. Portable AC units still need to be cleaned and have their filters scrubbed from time to time, but they don’t require the same attention that mounted units need.
How To Convert Odds To Probability
An alarm watches a single metric over a specified time period, and performs one or more specified actions, based on the value of the metric relative to a threshold over time. The action is a index notification sent to an Amazon SNS topic or an Auto Scaling policy. For large datasets, you can insert a pre-aggregated dataset called a statistic set. With statistic sets, you give CloudWatch the Min, Max, Sum, and SampleCount for a number of data points. This is commonly used when you need to collect data many times in a minute.
Units Of Measurement
The key advantage of a Parlay over a standard multi is that if some of your legs are successful, then you will still win a dividend based upon the amount of successful combinations you chose. An All Up allows you to select one or more runners to win or place on different races and all of your selections are required to be successful for the All Up to win. The payout is worked out by multiplying your initial stake amount by the odds for each of your selections. E.G. You have a $1.00 Treble bet, taking number 3 to win the 1st leg, number 6 to win the 2nd leg and number 9 to win the 3rd leg. This bet allows your selections to finish first, second, third and fourth in ANY order. Boxing four selections gives you 24 combinations with which you can win a First 4 bet type.
When negative, Malay odds represent the number of units needed to be wagered in order to win 1 unit. Note that both 1 and -1 are equivalent to decimal odds of 2.00. When positive, Indonesian odds express the net return from a winning 1 unit bet. When negative, Indonesian odds represent the number of units needed to be wagered in order to win 1 unit. Decimal odds represent the total return from a winning 1 unit bet.
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When the power is not an integer, you must use this technique of multiplying the percentage uncertainty in a quantity by the power to which it is raised. If the power is negative, discard the negative sign for uncertainty calculations only. When one multiplies or divides several measurements together, one can often determine the fractional uncertainty in the final result simply by adding the uncertainties in the several quantities.
There are both a FanDuel promo code and DraftKings promo code along with offers from all top betting apps. New Mexico State and Utah State clash Friday at the Myrtle Beach Invitational with a spot in the championship game on the line. Can New Mexico State continue its undefeated season, or will Justin Bean lead Utah State to another victory? To do this, the Plus Minus count is used to keep a running total of the “count”.
Best Free Bet Offers
We shouldn’t need to manually convert odds all that often as we can simply change our odds preference at the bookmakers. Fractional odds tell us how much we stand to win in relation to our stake. The number on the left is the amount we stand to win if we stake the amount on the right. Traditionally, bookmakers display their odds as fractions, such as 9/1 on England to win the World Cup.


Odds tell you the likelihood that an event will occur and how much will be paid out if you win. There are, however, multiple ways to convey this information. If people continue to bet the over, the bookmaker will continue to adjust the odds upward and eventually bettors may have to risk $145 to win $100, or -145. In this case, an under bettor would risk $100 to win $125. The bookmaker will generally raise the odds up to -145 before raising the total to the next number, which in this case would be 6.5.
What Is Better, Decimal Or Fractional Odds?
The $5000 they lost betting on the Penguins would be a write off after getting a big payout from a Rangers victory. For example, say the majority of sharps bet on the Pittsburgh Penguins to beat the New York Rangers at -130. If there’s an influx of serious cash on the Penguins at that number, bookmakers at your sportsbook are going to adjust the line.
Online Betting Faqs
Moneyline Calculator can be an indispensable tool to http://gilde-pirates-of-caribbean.de/2021/01/14/what-is-pool-betting/ use for evaluating the odds and implied win probabilities at DraftKings Sportsbook. In that case, you are returned your original bet plus profit, so you now have $220. The really important difference is that the line is linear. The calculator converts the “+140” odds into all of the different notations you might see used by a sportsbook.
Can You Win Real Money Betting On Cricket?
Texas winning by either five or seven gives you a win and a push. Any other result creates a win and a loss, so you’re only risking the vigorish. The simplest way to think about a moneyline is to consider a base bet of $100.
Separate straight-up bets might be safer than a 4-game parlay, but winning a parlay gives a higher payout. Parlay betting involves betting on a series of games linked together for a higher payout. For this example, betting on O or over means that the total score should be higher than 32.5 to earn $105 per $100 bet. If the scored 31 points and the Chiefs scored 9 points, their total score would be 40 points at the end of the game. So if the odds are -110, the probability percentage of the team would be 52.38%.
In this case the Hawks would likely be small favorite around -120. An example of a game that would have a large money line difference would be a game between the Orlando Magic and the Golden State Warriors played in Oakland. In this case the Warriors would likely be -1,000 money line favorites or higher. Browse through thebetting sites rating guide, pick your favorite sportsbooks and head over to check their moneylines so you can practice what you’ve learn.
The rotation number appears to the left of each team and is used as a unique identifier so that there is no confusion about what you want. Spread betting refers to speculating on the direction of a financial market without actually owning the underlying security. The Dutch Book Theorem, a probability theory, states that profit opportunities will arise when inconsistent probabilities are assumed in a given context. The over 44 and under 44 are the total points which are used in the total bet.
We take a $100 risk and divide by the ultimate payout of $300 and get .3333, or 33.33%. So any +200 underdog that wins 34%+ of the time is a profitable bet. The bettor who takes Miami will have to bet $240 to win $100.
Even without these celebrations, some areas in the Philippines host sabong derbies every week. These are often hosted in local sports arenas and attended by hundreds of breeders, enthusiasts, and bettors. If the juice is higher for a wager, it may be a sign to avoid that bet. If a wager is large, but isn’t large enough to totally change the line, the sportsbook can simply adjust the juice. Increasing the juice on one side even just a few percentage points will do two things. A key to assessing an interesting opportunity is to determine if the probability is higher than the implied probability reflected in the odds.
The “Implied Probability” output tells you that at +140 odds, the Rays have a 41.67% implied probability of winning. A skilled bettor will take that bet if they think Tampa Bay’s actual chance of winning the game is higher than that. Skilled bettors look for value on moneyline bets by evaluating teams that have a better chance of winning than the implied probability of the odds might dictate. Moneyline bets present the most straightforward way to wager on a sports contest. A moneyline wager simply asks the bettor to choose which team will win a game, with no point spread involved. As you can imagine, the more favorites you insert, the lower your payout.


Lecture : Numerical method (MAE301)|
We already learned linear and nonlinear equation, linearization method, matirx and differntial equation in advanced mathematics. However, we have to use numerical method to solve various mathematical difficulties occuring in many cases.
In this course, various basic theories to solve the problem numerically are covered. We also learn various numerical methods and algorithms to approach then engineering problems, numerically.
Solution of equation
Nonlinear simultaneous euqations
Ordinary differnetial equation
Partial differential equation
Steven C. Chapra and Raymond P. Canale, "Numerical Methods for Engineers", 6th Edition, McGraw-Hill
Copyright (c) 2002, Precision Machine Elements and Tribolology Laboratory.
School of Mechanical, Aerospace & Systems Engineering, Korea Advanced Institute of Science and Technology.
Please contact firstname.lastname@example.org for any problems related to the web-pages and any queries on the Lab. Activities.


Whether you are opting for traditional financing from banks or a rent-to-own vehicle finance plan, it can be hard to determine your available budget for a car. Most experts say that you should not be spending more than 20% of your monthly net income on your vehicle.
The 20% of your income ballpark figure should include payments on all of the vehicles you own, whether you own one or more cars. Also remember, this figure applies to the amount of money you have in your pocket after tax, not your gross income.
Now, you need to calculate what your car payments will be. If you have just seen the car of your dreams and the price tag of this car, you need to know what the monthly installment is going to be, so that you can determine whether you can afford the car or not.
Determine the interest rate by dividing the number by 100.
Divide the interest rate on your car loan by 12. Write this number on a piece of paper.
Multiply the number by the loan’s principal amount (the total amount of your car loan). Write this number down as it will be used in your final calculation. Remember to subtract your down payment from the price of the car to establish the principal amount that you will pay.
Recall the number you got from dividing the interest rate by 12 in step 2. Add 1 to this number.
Take the sum from step four to the power of the number of months included in the terms of your loan. For example, if you are going to be making 36 monthly payments, multiply the sum from step 4 by 36.
Calculate 1 divided by the result from step 5. Round this number to the nearest hundredth place to make it easier to work with.
Subtract this number from 1 for use in your final calculation.
Divide the number from step 3 by the number from step 7 for your final monthly car payment.
You can avoid the math by using an online car payment calculator, which can be found on many of the auto dealers’ and many banking websites.
Remember to include the costs associated with owning your car, namely vehicle insurance, maintenance, tyres and roadside assistance.
Rent-to-own vehicle finance is an easy way to get a reliable set of wheels without having to pay the monthly interest rate levied by the banks. For more information about easy vehicle finance, contact Earn-a-Car today.


NSPCC Number Day 2022
Thank you to everyone that took part in our NSPCC Number Day, the children enjoyed lots of maths activities, including spotting links and patterns, playing games and using maths through Art.
The children looked wonderful in their patterned clothes and accessories.
We managed to raise an amazing £68.09 which will go towards all the good work that the NSPCC do to protect and support children, so thank you to everyone that contributed and joined in. Well done!


KANSAS CITY, Mo. (AP) Mathematicians at the University of Central Missouri have discovered a record-setting prime number that’s so large it would take about 6,000 pages of paper to print, the school announced Thursday.
The 22.3-million-digit discovery is the 49th known Mersenne prime number and the fourth discovered at the university. Primes are numbers such as 3, 7 and 11 that are divisible only by themselves and 1 without leaving a remainder.
Computer science and mathematics professor Curtis Cooper said he feels “pretty fortunate because there is some luck involved.”
Mersenne primes are named after the 17th century French mathematician who discovered them, Marin Mersenne. They’re expressed as 2P-1, or 2 to the power of “P” minus 1. P is itself a prime number. For the new prime, P is 74,207,281.
The number was independently verified, according to the Great Internet Mersenne Prime Search, a cooperative in which underused computing power is harnessed to perform the calculations needed to find and verify Mersenne primes.
The organization said in a news release that prime numbers are important for cryptography but that the newly discovered number is currently too large for that purpose. One benefit of Mersenne primes is testing computer hardware.


25 Hedley Terrace, Gosforth
Newcastle, NE3 1DP, England
In Tilings and Patterns  Grünbaum and Shephard comment that there is extremely little literature on the subject of spiral tilings. They survey what is known, and leave some unanswered questions, in particular whether there is a tile that will produce an r-armed spiral tiling for any odd value of r ³ 5. A new method of generating tiles from regular polygons is developed here, that allows the construction of zig-zag spirals with any desired number of arms. Spiral tilings of a type already known are considered and new tilings, related to them, are described. Further new tilings are constructed by considering some special cases.
Zig-zag Spiral Tilings
Overlapping copies of any regular n-gon
will produce a shape that will tile the plane (without gaps) in several
different ways, one of which is a one-armed spiral, along with various
two-armed spirals . If n is odd it is difficult
to get much further, but if n is even then the tile that is produced
can be cut into a series of rhombuses (fig.1), ensuring
that each cut has the same length as a side of the polygon. Any one cut
divides the original tile into two new ones, both of which will tile the
plane in a variety of ways, in certain circumstances including spirals.
In an n-gon it is easily verified that the angles of the rhombuses
are an integer times 1/n turns (where 1 turn = 360°). In fact
the rth rhombus has an angle of r/n turns, so it is possible
to choose a cut that will produce a tile having one angle that is 1/m
turns, if m = n/r.
Figure 5: The same
tile from a 20-gon can be used to make a
The alternative way of tiling the spiral
arms, indicated in the fig.2 , will only work in two
cases, a three-armed spiral with a tile based on a dodecagon (fig.6)
and a four armed spiral with a tile from an octagon (fig.7)
. The reason is seen most easily in the three-armed example.
Figure 7: Two types
of four-armed spiral using a tile from the octagon.
In the particular cases when n is a multiple of 6 one of the rhombuses will have an angle of 1/6 turn, and it can be seen as two equilateral triangles. (Actually there are two such rhombuses, but we are only concerned with the one having the angle of 1/6 on the convex side of the n-gon.) Making the cut that divides this rhombus into triangles generates a tile (fig.8) of the type discussed by Grünbaum and Shephard, and termed a versatile in their 1979 article .
Grünbaum and Shephard showed that
such tiles will always produce one-, two-, three- and six- armed spirals.
It is not clear whether they realised that all except the three-armed case
can be constructed using either tiling pattern i) or
ii). They certainly never mention it, and they use type ii) in only
one, a very attractive two-armed spiral (which is used on the dust-wrapper
of their book).
In the special case when n = 12,
the dodecagon, there are further possibilities. Like any versatile
it will produce several two-armed, a three-armed and the two types of six-armed
spiral. Rice and Schattschneider  have also described
some other ways that it will tile the plane. This particular versatile
also generates a four-armed and an eight-armed spiral. The four-armed spiral
(fig.10) is possible because the base angles of a versatile
are 1/6 turn (making the six-armed spirals possible) and (1/3-1/n)
turn (making the three-armed spiral possible, by combining a tile with
its mirror image). When n = 12, (1/3-1/n) = 1/4, hence
a four-armed spiral is possible. The only other value of n that
works to give an integer division of a full turn, n = 6, the hexagon,
gives a tile that is degenerate (an equilateral triangle).
Figure 10: A four-armed spiral using the dodecagon versatile.
The other possibility to consider is combining
the apex (of 1/n turns) with the 1/6 angle. The solutions of 1/n
+ 1/6 = 1/m must have m < 6, and m = 3 is the degenerate
case again. The case m = 4 has n =12, and a tiling (having
eight arms) is possible (fig.11), but the tiles produced
when m = 5 do not fit together in the same way, and there is no
analogous tiling based on a 30-gon.
Figure 11: This tiling
shows particularly clearly that the spiral arms, of both
Rice and Schattschneider published this
tiling (fig.11) with arms of type i),
and again it is not clear if they were aware of the type ii)
alternative. They also mention the existence of a twelve-armed spiral using
this tile. There are many variants of this tiling (fig.12
shows one of them), since there are several ways to construct the central
dodecagon. The next layer, which enlarges the dodecagon to twice its size,
can be constructed in many different ways, and the spiral arms themselves
can be of either type i) or ii).
Figure 12: One of the many variants of a twelve-armed
spiral using the dodecagon versatile.
The arms of this spiral tiling (fig.12) can be seen as originating at the mid-points of the sides of the large dodecagon, with tiles fitting around its vertices. Clearly this is only possible if the tile has no more than two concave sides, and is more or less v-shaped. The only versatile with this characteristic is derived from the dodecagon, but such tiles can be formed from any polygon. The one from the hexagon is big enough this time to produce tilings that are recognisable as spirals. Spiral tilings made with this tile (fig.13) are probably the simplest that have more than two arms, and it is surprising that they are not mentioned in the existing literature on the subject.
It is always possible to cover an n-gon
of double size, using a tile derived from the n-gon, when n =
2(2r + 1), but only the decagon provides a v-shaped tile that
does this. It generates a ten-armed spiral (fig.14),
and of course in this case the arms are zig-zags.
Tiles that are derived from regular polygons provide the most obvious possibilities for covering the plane in ways that that appear as spirals. Zig-zag spirals can be produced with any desired number of arms by following general methods, and versatiles provide smooth spirals, although only a limited number of arms is possible. Although many special cases have been considered, it is by no means certain that there are no more left to be found.
Also the possibility of finding spiral tilings using entirely different types of tile, not based on regular polygons, has not been eliminated. Indeed some examples are discussed in , and, although further development along these lines seems unlikely, a different approach might produce more fruitful possibilities.


Problems in Function Theory with Applications in Epidemic Modeling
Understanding the dynamics of epidemic spreading over graphs has attracted a substantial research attention recently. Researchers seek to find the role of the graph topology on the epidemic spreading. However, there are still many open problems on this topic. One important problem is to develop topological measures to quantify graphs with respect to epidemic spreading. This team has developed epidemic quasimetric, a measure that resembles effective resistance with low computational complexity and direct application to epidemic spreading and graph clustering. We are also working on epidemic spreading over graphs, particularly from spectral viewpoints. Here, we propose to extend the concept of epidemic quasimetric to study epidemic spreading over different spreading scenarios.
Supported by National Science Foundation under Award DMS-1201427. Any opinions, findings, and conclusions or recommendations expressed in this website are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.


Things You Won’t Like About Trigonometry Definition and Things You Will
The pattern seems to quit working. The more you do something, the simpler it is to go through the procedure of doing it. It isn’t easy to say for sure if there’s anyone who resides completely at the conclusion of the spectrum on the face of the eidetic memory. however, it is certainly a fact that there are people that are much further along on that spectrum than others.
The New Angle On Trigonometry Definition Just Released
In this kind of word problem students receive a vehicle like a vehicle or a boat or a train and they’re also given two angles of elevation and the students are requested to calculate how far the vehicle has travelled. The lights which are at the rear of the car are call lights. It will be dependent on the issue and which will make the issue simpler to address.
Worth mentioning, though beyond the reach of this report, is these functions relate to one another through a wide variety of intricate equations called identities, https://www.khanacademy.org/science/biology equations which are always correct. However, I don’t even know any fantastic trios. Scuola Leonardo da Vinci is one of the very first schools that provide preparation courses for medical students.
Many of them are areas of life about the arts. Hans von Bulow and Rachmaninoff are two more examples of individuals who may or might not have eidetic memory in the particular field of music. In science, the notion is comparable, but the definition is a lot narrower.
What the In-Crowd Won’t Tell You About Trigonometry Definition
After you have made a complete circle (360) keep going and you are going to see that the angle is greater than 360. Conventionally, the middle of the circle is regarded as a Cartesian coordinate of (0,0). In the same way, when you have the worth of a single side and the angle of depression from the surface of the building it’s possible to find and https://www.grademiners.com another side in the triangle, all you have to understand is one particular side and angle of the triangle.
Definitions of Trigonometry Definition
For instance, if you replied yes to the very first question about trigonometry, you’d get 1 point. This identity comes from taking a look at the unit circle. More points may be used to demonstrate that the form of the graph is as shown below.
Graphics and figures are taken straight from the text to improve the questions. The information you’re given can help you determine which function to use. Remember you’re not being marked for artwork, you are simply drawing the problem to be in a position to find out what information you presently have.
There are lots more trigonometry relationships built upon this simple idea. There are far more ways multiples of 60 can be broken into fractions, making trigonometry a lot easier. It’s usually simple simply to know where to easily locate the formulas.
Each trigonometrical ratio is really a number. To demonstrate that 2 isn’t rational. Area of triangles in various forms.
Trigonometry Definition – Is it a Scam?
When there’s a discrepancy, it’s usually due to rounding errors. Inverse trigonometric functions are also called arc functions. For every single trigonometry function like tan, there’s an inverse function that operates in reverse.
The Debate Over Trigonometry Definition
If you are not certain, seek advice from your calculator’s user manual. The mnemonics on this website are categorized, don’t hesitate to browse through them. A totally free body diagram without using trigonometric ratios is virtually not possible.
The Nuiances of Trigonometry Definition
If a question asks for an EXACT answer, don’t use your calculator to discover the sin 60 since it is going to be a rounded value. Hipparchus created this table in order to do his astronomical calculations. The calculator is accurate.
Let us teach you an easy way to keep in mind the formulae for a proper angle triangle. Since similar triangles always have the exact angles, then the ratio is the exact same for any specific angle. To begin with, see the triangle is backwards.
You will require a calulator to proceed. Usually, the angle between the 2 vectors may be all the info given about their directions. Additional information about vector resolution are available here and a superb primer about circular motion are available here.
Understanding Trigonometry Definition
Doing and reviewing practice questions and practice tests will enhance your knowledge of what you have to know. Along with testing a broader selection of math topics, the ACT doesn’t offer you any math formulas at the start of the Math section, so you’re going to want to get them all memorized. Make certain you practice everything that may be on your test.
The Lost Secret of Trigonometry Definition
If you would like to appear for any competitive exams following your school then hands-on understanding of different Trigonometry formulas is vital. You may select various variables to customize these Trigonometry Worksheets for your requirements. This is known as school trigonometry.
As soon as it’s a fact that a great deal of special relativity can be managed with basic algebra, the geometric interpretation is dependent on an excellent comprehension of hyperbolic trigonometry, which is reasonably advanced math. There are just a few equations that may be solved manually otherwise you are in need of a calculator and exclusive skills to discover the remedy to any Trigonometry issue. While it might seem like something that you will only do in school, there are actually many real-world situations when you will need to understand trigonometry.
Life After Trigonometry Definition
The training course was created for high-school seniors. Where appropriate each worksheet is provided a year level that it’s applicable to. A radian is quite a bit larger than a degree.
The procedure for converting units is easy and powerful. There are a lot of more advance trigonometry functions like, secant, cosecant, cotangent that could be put into place within this program to make it more advances. In addition, by implementing the New!


2. Direct areas of application
Probability Estimation: One area where our team has applied adaptive mathematics is to calculate odds for games. For example, in a roulette game, if the number "8" hasn't appeared in the last 100 spins, adaptive math can slightly adjust the odds to reflect this trend, ensuring a fairer gaming experience for the player.
Data Processing: We use adaptive math to process large amounts of player data to identify patterns and trends. For example, in a slot game, if the data shows that players tend to abandon the game after failing to hit a bonus round in 50 spins, we might adjust the algorithm to offer a bonus round within that range, increasing player retention.
Protection and Analysis: Security is a top priority at BCraft Software. We use adaptive mathematics to ensure that game outcomes are truly random. In card games like Blackjack, if data indicates that a player is consistently betting high before a "10" or face card, our algorithms can adjust to ensure that the next card is unpredictable, thus maintaining game integrity.


Dating sites mathematics
He did this by discovering the following identity: During the Renaissance , the development of mathematics and of accounting were intertwined. The occurrence of the triples in the Sulvasutras is comparable to mathematics that one may encounter in an introductory book on architecture or another similar applied area, and would not correspond directly to the overall knowledge on the topic at that time. It might have been even more guarded in the s during the rise to power of the nazis in Germany. It included a page treatise on bookkeeping , "Particularis de Computis et Scripturis" Italian:
When this was first described in English by Charles Whish, in the s, it was heralded as the Indians' discovery of the calculus. Predynastic Egyptians of the 5th millennium BC pictorially represented geometric designs. For a short explanation, see a separate page.
However, it is not difficult to surmise that the point that makes the construction work is the foot of the right angle bisector. Riyad on July 13, at 1: I'll give an example of their approach in proof Later The Mathematics Teacher90pp. From around BC onwards, the Sumerians wrote multiplication tables on clay tablets and dealt with geometrical exercises and division problems. One unique feature of his works was trying to find all the possible solutions to some of his problems, including one where he found solutions. University of Wisconsin Press, Several centuries later, the Muslim mathematician Abu Rayhan Biruni described the Aryabhatiya as a "mix of common pebbles and costly speed dating edinburgh. Indating site PlentyofFish conducted a study in which scientists examined word choice in all 1. Thank you for reblogging, and for visiting the blog. Funnily enough, each dog breed tends to have a couple common names. After the book burning of BC, the Han dynasty BC— AD produced works of mathematics which presumably expanded on works that are now lost. Each of the roughly dozen major scripts of India has its own numeral glyphs. During the Renaissance the desire of artists to represent the natural world realistically, together with the rediscovered philosophy of the Greeks, led artists to study mathematics. One of the triangles in the pair is inside the square, the other is outside. However, Whish's results were almost completely neglected, until over a century later, dating sites mathematics, when the discoveries of the Kerala school were investigated again by C. All kinds of structures were abstracted using axioms and given names like metric spacestopological spaces etc. AD 90—a landmark astronomical treatise whose trigonometric tables would be used by astronomers for the next thousand years. Calderhead Monthlyv. Pacioli obtained many of his ideas from Piero Della Francesca whom he plagiarized. Science and mathematics had become an international endeavor, which would soon spread over the entire world. Just look at dating sites mathematics face! Kepler succeeded in formulating mathematical laws of planetary motion. Persians contributed to the world of Mathematics alongside Arabs. Pertinent to that proof is a page "Extra-geometric" proofs of the Pythagorean Theorem by Scott Brodie. African leader and Resistant to French Imperialism 2. De Prospectiva Pingendied. An especially nice variant by Olof Hanner appears on a separate page. At first people though that they were just some tally sticks used […]. Thales used geometry to solve problems such as calculating the height of pyramids and the distance of ships from the shore. Below are several variants that differ by a view point and, as such, lead to different derivations.
Today, dating sites mathematics, I would like to talk about the Ishango boneor rather the first evidence of a calculator in the world. It is the oldest attestation of the practice of arithmetic in human history. The Ishango bones are actually two 2 bones of baboon, 10 to 14 cm longwith several incisions on each faces.
The left column can be divided in 4 groupswith each group possessing 19, 17, 13, and 11 notches. The sum of these being Those are the 4 successive prime numbers between 10 and This constitutes a quad of prime numbers. The central column is divided in groups of 8. By an approximate count, one can find in the parenthesis, is the maximum number: The minimal sum is 48while the maximal sum is The sum of these 4 numbers is However, we know that it is composed of 6 groups of 20, 6, 18, 6, 20and 8 notches.
The first bone has been subject to a lot of interpretation. At first, it was thought to be just a tally stick with a series of tally marksbut scientists have demonstrated that the groupings of notches on the bone are indicative of a mathematical understanding which goes beyond simple counting.
In fact, many believe that the notches follow a mathematical succession. The notches have been interpreted as a prehistoric calculatoror a lunar calendaror a prehistoric barcode. Jean de Heinzellin was the first to consider the bone as a vestige of interest in the history of mathematics. All said, it is amazing to realize that there were mathematicians 20, years ago on the African continent. It is so great to realize that my ancestors, on the shores of Lake Edouard, were actually brilliant scientists playing with prime numbers.
They were from hookup to boyfriend great civilization long before the pharaohs of Egypt. Thus, in reality, the Ishango bone is the oldest table of prime numbers in the world. African mathematicsAlexander Marshackancient mathematicsClaudia ZaslavskyCongolese mathematicsIshango boneJean de Heinzelinpaleo mathematicians. Having been trained in both Prehistory and Anthropology, the analysis of this find scotches two widely held misapprehensions in one grand sweep: Tish Farrell on October 11, at 5: However in the website that I was using https: CMN Project 1 sevicerenozdemir on September 28, at African leader and Resistant to French Imperialism 2.
Craddle of Ancient Mathematics […]. African Heritage on January 1, at 8: Actually, very few mathematicians looked at it, and the fact that they do not agree should make us suspicious. Olivier Keller has written an article which should temper the enthousiasm: You desire to see higher mathematics?
Then your mind will make you online dating tiger picture it, even if it is not there. Week art85 on September 14, at 5: Technology may change drastically over time, but the the only thing that has fundamentally changed about the internet has been the speed, use and apparatus on which to access it.
Additionally, whenever researchers have come across some kind of medium that has information, if they want it badly enough, they are usually able to figure it out like the Ishanago Bone https: Although I think that this is a outstanding find, the people of Ancient Kemet stated that they come from this area of Africa. La fuerza de la toma de datos. So blacks possessed mathematics twenty dating site for free in canada years ago, while at that time whites in Europe and the uk were crawling on their hands and knees eating their own excrement!
The evil tragedy is, when whites eventually came in to contact with mathematics they would come to use it to count African slaves as they were boarded on to ships bound for America and Europe. Good job, just stop of the iceberg for any further information, feel free to contact us about any question of your own choice.
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Notify me of new posts via email. Enter your email address to subscribe to this blog and receive notifications of new posts by email. Excerpts and links may be used, provided that full and clear credit is given to Dr. African Heritage A blog about African history, and heritage, through audio and video files. August 29, The Ishango Bone: The location of Ishango. The Ishango bones with their notches and the numbers.
The Ishango bones with the notches. Craddle of Ancient Mathematics […] Like Like. Riyad on July 13, at 1: Thanks for reblogging this article. Vanya Hoatson on June 9, at Mann on June 30, at 1: No space […] Like Like. Thank you for reblogging, and for visiting the blog. At first people though that they were just some tally sticks used […] Like Like. Leave a Reply Cancel reply Enter your comment here Fill in your details below or click an icon dating sites mathematics log in: Email required Address never made public.
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The Pythagorean theorem is then equivalent to the algebraic identity. An explanation can be found elsewhere. This is how I pass this on:. Interestingly, the proof has not been included in Lietzmann's earlier Der Pythagoreische Lehrsatz published in The Theorem whose formulation leads to the notion of Euclidean distance and Euclidean and Hilbert spaces, plays an important role in Mathematics as a whole. Even more surprisingly the latter is also included into Dating sites mathematics. On Douglas Rogers' suggestion, complete each of the four triangles to an appropriate rectangle:. Anthony Powell The Kindly Onesp. Draw a circle with radius c and a right triangle with sides a and b as shown. Theories and sociology Historiography Pseudoscience. Trattato d'Abacoed. The points of resemblance, particularly between early European calculus and the Keralese work on power series, have even inspired suggestions of a possible transmission of mathematical ideas from the Malabar coast in or after the 15th century to the Latin scholarly world e. You may want to figure out by yourself what is it about. Nicole Oresme at the University of Paris and the Italian Giovanni di Casali independently provided graphical demonstrations of this relationship, asserting that the area under the line depicting the constant acceleration, represented the total distance traveled. In some sense, this foreshadowed the development of utility theory in the 18th—19th century. Other 19th-century mathematicians utilized this in their proofs that straightedge and compass alone are not sufficient to trisect an arbitrary angleto construct the side of a cube twice the volume of a given cube, nor to construct a square equal in area to a given circle. The proof and a discussion appear in a separate pagebut its essence is as follows. In spirit, the proof resembles the proof Independently, Gottfried Wilhelm Leibnizwho is arguably one of the most important mathematicians of the 17th century, developed calculus and much of the calculus notation still in use today. His Collection is a major source of knowledge on Greek mathematics as most of it has survived. Entirely new areas of mathematics such as mathematical logictopologyand John von Neumann 's game theory changed the kinds of questions that could be answered by mathematical methods. Tish Farrell on October 11, at 5: Ibn al-Haytham was the first mathematician to derive the formula for the sum of the fourth powers, using a method that is readily generalizable for determining the general formula for the sum of any integral powers. Greek mathematicians used the full chord and never imagined the half chord that we use dating sites mathematics. This is reminiscent of proofs 46474849 Following a period of stagnation after Ptolemy, the period between and AD is sometimes referred to as the "Silver Age" of Greek mathematics. The details are in a separate file. For the details and an interactive illustration, see a separate page. During the Renaissance the desire of artists to represent the natural world realistically, together with the rediscovered philosophy of the Greeks, led artists to study mathematics. The earliest traces of the Babylonian numerals also date back to this period. In the 13th century, dating sites mathematics, Nasir al-Din Tusi Nasireddin made advances in spherical trigonometry. Benjir von Gutheil, oberlehrer at Nurnberg, Germany, produced the above proof. The radius of the circle equals now the altitude from the right angle C. The study also found that people preferred a potential partner to be of mixed or ambiguous race instead of a blatantly different race than their own. The proof is actually of Dijkstra's generalization and is based on the extension of the construction in proof


Many learners have difficulties moving from whole number understandings to rational number understandings. These conceptual understandings and misunderstandings often become visible as students represent that understanding in pictorial and symbolic representations of the rational number. Pictorial representations of rational numbers can include area models, linear models, and set models among others. When the representation is a part/whole area or measurement model in which the total number of equal size pieces in the whole matches the denominator and the shaded part of the whole equals the numerator, this is referred to as a “simple representation” of the fraction. When the pictorial representation has a whole where the number of equal parts is a multiplicative factor of the denominator of the fraction in symbolic form then this is considered an “equivalent representation” (Wong and Evans, 2007). One of the critical attributes of a simple or equivalent representation when partitioning a whole is that the size of each of the parts needs to be an equal size region although they do not necessarily need to be of the same shape. O<en during instruction students work with models that are already the same size and shape (Van de Walle, Karp & Bay-Williams, 2010). This sometimes leads to students thinking that the pieces must be the same shape while others do not even consider size as an attribute at all.
These assessments are designed to elicit misunderstandings, over-generalizations, and/or misconceptions associated with simple representations of a fraction.
Representing Fractions I is designed to elicit misconception 1 where students consistently associate the number of pieces shaded with the numerator and the total number of pieces for the en1re figure with the denominator but do not pay aLen1on to the size of the pieces (or region).
Representing Fractions II is designed to elicit misconception 2 where students associate the number of pieces shaded with the numerator and the total number of pieces for the entire figure with the denominator and do pay attention to equal shape pieces but do not consider different shape/equal size pieces or equivalent representations.
Funded by IES Award #R305A110306-12 See project description at http://ies.ed.gov/funding/grantsearch/details.asp?ID=1083
For more informations about this project contact Cheryl Tobey: firstname.lastname@example.org


Hi,Is there a way to do simple math in fastly?
Example:Received cookie = 10New cookie to 10+8=18.
How can i declare an integer variable under req.http? I see that it allows only string variables to be declared.
Hello! We are working on this right now. Give us a a month or so.
Thank you Sean.Meanwhile, i am using req.grace to do math on it and then restore the original value of grace. Only problem is that initial value i see is "inf", which cannot be restored when there is no specific grace value set.
@seanDo you have any updates on this?
Hey all - sorry for the delay. It is ready to deploy, just finishing up the documentation and some last minute testing (code is done) - so should be within a few weeks. Will post here when it's live with a link to the docs.
We need this as well, glad to see it's around the corner!
Are there any updates here?
Thank you. Its very handy now to use these new variables.
Is it now possible to do additions and subtractions with integer local variables?


Before betting on this game at the casino, it is beneficial to know the probability roulette because it gives you an idea of your chances of winning a gain. This aspect of the game is as important as rules and strategies.
This is because of the importance of variant choice. Some versions of this game offer a great advantage of the house, which means that your chances of winning significant gains are low.
The probability plays an important role in the game of roulette. In fact, most of the strategies of this game of virtual casino are based on probabilities.
With this guide, you will be able to choose the best variant of the Online roulette In order to give you the best chance to win. In addition, you will understand why bet on one number is less wise than bet on a group like black red.
Casinos where to play roulette
The probability of European roulette
The version of the European roulette, which includes Australian roulette and English roulette, is considered the best variant because it benefits the player a lot.
This is because of its rules as well as the presence of a single zero box. The wheel of this variant comprises 36 boxes numbered from 1 to 36, is a box 0. With 37 possibilities (ie 37 boxes where the ball can stop), your chance to succeed during each part is 1/37.
Probability of American roulette
Considered by several online players like the worst variant roulette, the American roulette is very advantageous for the house. The wheel of this game presents 38 boxes in which the ball can stop, which includes 36 numbers, a 0 and an 00.
If you already know that box 0 does not bring a gain. This means that if you do not bet directly on the zero box or the double zero box, you still have 1/19 to lose.
To put it in perspective, the European roulette offers 1/37 chances of losing. That is, you have 18 chances more not to lose the European version.
Roulette Probability Table
European roulette and the American version have the same rules. But the American variant proposes an additional zero box, which increases the advantage of the house. For this reason, there is a bit of variance in terms of payments for each bet option. Open the tabs below to view the probabilities of each bet.
Frequently Asked Questions
How to calculate the roulet number?
To calculate the chances of winning with the different roulette bet options, you can simply search for a roulette probability calculation.
But if you prefer to calculate manually, you must divide your number chosen by the number of possible numbers. Then you have to multiply the result per 100.
For example, to calculate the chances of winning with a single-number bet on the European roulette, you must calculate 1/37 multiplied by 100.
How to win big roulette?
To win wholesale to roulette, you need to make wise decisions, taking into account your budget and gain probabilities. If you have a big budget, you can take risks with less likely bets like full box bet. But with a more limited budget, it is better to opt for simple chances. In this way, you will win several small long-term gains.
How to win roulette with colors?
Roulette colors are part of simple chances. You bet on all red or black numbers. This type of bet provides a payment of 1 against only, but because it offers the best ribs, you can win several long-term gains.
What are the numbers that go out the roulette?
Online roulette is a pure game game. It is impossible to calculate the numbers that are the most out because the results are shown randomly. Even if you manage to calculate the numbers that have come out the most today, it can change after a day and even an hour.
Read these articles on roulette to discover more:


You can see the calculations on this spreadsheet. I first entered the return rates for the prior 12 months for our stocks and for our bonds. (You can see at the top of the sheet that I used December 15 as the end of year for this calculation. That’s turned out to be an awkward choice; getting accurate return rates for that ending date is harder than it should be. I’m shifting to November 30 for the calculation at the end of 2017; I’ll have a 50-week year.)
I also entered the inflation rate for the year. Those are the only three numbers (highlighted in yellow on the sheet) that I have to enter each year on this spreadsheet .
The spreadsheet does the rest once I move the calculations one cell to the right.
Our SSA for spending in 2017 increased by 4.5% real rate to $46,100 (times our multiplier), and this was also a 4.5% real increase from our start of spending in 2015. The spreadsheet also shows that if we continued to spend C$44,000 in 2017 we had $42,700 “more than enough” for that spending (times our multiplier).
Our plan is to always “pay ourselves” our calculated SSA. And that’s what I did, altering our monthly auto transfer from our investment account to our checking account (our “paycheck”). What we don’t spend out of the $46,100 (times our multiplier), we’ll gift before the end of 2017.


Printable Math Games
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I had a user at the last place I worked who needed to calculate the geometric mean of a column in a table. The geometric mean is like a regular mean, but has the practical effect of throwing out outliers (unusual spikes in the data). This is a standard function in Excel, but not in most databases.
The standard method of calculating the geometric mean is by multiplying all of the terms together, then taking the n-th root of the product, where n is the number of terms. So if you had 5, 7, 55, 6, and 3 as terms, you would take the fifth root of 34,650, giving you 8.0899. Notice how the final result is not very much affected by the outlier (55).
This technique won't work in most databases for non-trivial datasets. Why? Because if you take 100 terms and multiply them, it will likely overflow even the largest column type. In fact, calculating the geometric mean this way with a calculator can quickly become impossible for large data sets.
There is a solution. If you take advantage of the magic of logarithms, you can calculate the geometric mean for very large data sets without overloading a standard relational database data type.
For a given set of terms, sum the log (I will use the natural log) of all terms. Then divide this sum by the number of terms. Finally, take the anti-log of the result (since I use a natural log, this means raising e to the result). Using our example:
ln( 5) = 1.6094 ln( 7) = 1.9459 ln(55) = 4.0073 ln( 6) = 1.7918 ln( 3) = 1.0986 ------- 10.4531 10.4531/5 = 2.0906 e^2.0906 = 8.0899
which is what we got using the standard technique. This can be translated into SQL this way:
UPDATE: Isabelle pointed out that there is a neater way to do this. Since the sum(FOO)/count(*) is an average, the expression can be simplified to this:
select exp(sum(log(sample)) / count(*)) from sample_table -- or, depending on your flavor of SQL... select exp(sum(ln(sample)) / count(*)) from sample_table
select exp(avg(log(sample))) from sample_table
Oracle, PostGreSQL, MySQL
select exp(avg(ln(sample))) from sample_table
Nicely figured out, Isabelle.
As far as I can tell, this will work in Oracle, SQL Server, and Access, and I can't think of why it would not work in MySQL or PosgreSQL.


I'm the Author. I'm a PhD student at Johns Hopkins University in Computer Science. I love design, writing, and problem solving. But my favorite thing is seeing kids light up when learning about science and engineering!
I'm the Manufacturing Operations Manager. I oversee the production and quality of our products. I enjoy technology and new product innovation.
I’m a San Francisco based Illustrator. I graduated from the Maryland Institute College of Art with a BFA in Illustration and a concentration in 3d modeling and texturing.
I'm the Community Manager. I have degrees in electrical engineering and applied math and am a former cancer researcher, teacher, writer and blogger. I am super interested in how young children learn mathematics and love discovering new and fun educational opportunities for kids!


S.T.E.M. Studio Saturdays!
Join us for a special STEM Studio on Saturday, March 4th from 10:30 am – 12:30 pm as we welcome the Virginia Living Museum’s Dinosaur Mini Museum! A VLM educator will have a table full of engaging hands-on Museum specimens and a LIVE animal! The STEM Studio uses STEM (Science, Technology, Engineering, and Mathematics) activities that are hands-on and appropriate for the entire family to do together. The STEM Studio is included in the general admission and is open to anyone as long as space is available. Stop by and discover for yourself what the fun is all about!
Studio hours: Saturdays, 10:30 a.m.-12:30 p.m. and 2:30-4:30 p.m.


A spatial relationship generally defines how a subject is positioned in space essential into a reference photograph. If the reference image is much larger than the item then the previous is usually manifested by an ellipse. The ellipse may be graphically represented using a allegoria. The allegoria has equivalent aspects into a sphere around july plotted on a map. If we look closely at an raccourci, we can see that must be shaped in such a way that all of their vertices tell a lie on the x-axis. Therefore an ellipse could be thought of as a parabola with one emphasis (its axis of rotation) and many parts of orientation on the other.
There are 4 main types of geometric diagrams that relate areas. These include: the area-to-area, line-to-line, geometrical engineering, and Cartesian engineering. The fourth type, geometrical building is a little unlike the other types. In a geometrical https://themailbride.com/vietnamese-brides/ building of a group of parallel directly lines is employed to designate the areas within a model or perhaps construction.
The key difference among area-to-area and line-to-line is that an area-to-area relation relates simply surface areas. This means that you will find no spatial relationships involved. A point on a flat surface may very well be a point in an area-to-room, or perhaps an area-to-land, or a area to a place or property. A point on a curved surface area can also be regarded as part of a room to bedroom or part of a room to land relative. Geometries like the circle and the hyperbola can be considered part of area-to-room relations.
Line-to-line is not a spatial relationship but a mathematical one. It can be understood to be a tangent of geometries on a single lines. The geometries in this regards are the area and the edge of the intersection of the two lines. The space relationship of these geometries has by the health supplement
Geometry takes on an important role in visual spatial associations. That enables the understanding of the three-dimensional (3D) world and it gives us a basis for learning the correspondence between real world plus the virtual world (the online world is mostly a subset of the real world). A good example of a visible relationship is definitely the relationship among (A, C, C). (A, B, C) implies that the distances (D, E) happen to be equal when measured out of (A, B), and that they boost as the values of this distances reduce (D, E). Visual space relations can also be used to infer the parameters of a model of real life.
Another app of visual space relationships certainly is the handwriting evaluation. Fingerprints left by various people have recently been used to infer several aspects of someone’s personality. The accuracy of fingerprint examines has better a lot within the last few years. The accuracy of such analyses can be improved additional by using computerized methods, specifically the large trial samples.


I had a fantastic math teacher in high school. When I got to university, I was better prepared than any of my classmates - and that was all thanks to Mr. Harold Worsham's brilliant teaching. When he taught Trigonometry, he had this mnemonic circle to help with remembering how trig functions interact:
The inverse of any function is the one on the opposite side of the circle e.g. the inverse of sin is csc, of cos is sec, and of tan is cot.
The product of 2 functions is the function between those 2 functions (assuming there is only one function between those 2;
if there are 2 between, the product is 1 (inverses!))
e.g. sin * sec = tan; tan * csc = sec; sec * cot = csc
e.g. csc * cos = cot; cot * sin = cos; cos * tan = sin
(and the product of 2 adjacent functions does not simplify.)
The result of dividing a function by one of its adjacent functions is the other adjacent function.
e.g. tan / sin = sec; sec / tan = csc; etc.
And obviously the "co" functions are directly above/below.
The mnemonic for remembering how to consctuct the circle is "c below."
If you want to check any of the above, here's a reminder:
h=Hypotenuse, a=Adjacent, & o=Opposite


Added: Aug 19, 2002
Snippet uploaded by: snippet
Written By: Unknown
Demo: Sorry, no demo
Converts to Decimal to Binary and Binary to Decimal.
Highlight all by clicking in box
Dim decml As Double
Dim jbinary As String
Dim digit As Single, power As Single
Dim h As Integer, i As Integer, jbin As Integer
Dim j As Integer, k As Integer
Private Sub cmdCalculate_Click()
decml = 16 'this is the number to convert
DecBin decml, jbin ' convert from decimal to binary
Print "Decimal ="; BinDec(jbin) ' convert from binary to decimal
Print "binary = "; jbin ' display the result
Print "Hex = "; Hex(decml)
Print "OCTAL = "; Oct$(decml)
' converts a string of binary digits to its decimal equivalent
Static Function BinDec(jbinary)
Dim digit, power, i, jbin As Integer
decml = 0: jbin = 0
jbinary = UCase(jbinary)
For i = Len(jbinary) To 1 step -1 ' convert from binary to decimal
digit = Asc(Mid(jbinary, i, 1)) - 48
If digit < 0 Or digit > 1 Then decml = 0: Exit For
decml = decml + digit * 2 ^ (power)
power = power + 1
BinDec = decml
' converts a decimal value to an equivalent string of binary digits
Static Sub DecBin(decml, jbin)
jbin = ""
h = Hex(decml) ' convert from decimal to hexadecimal
For i = 1 To Len(h)
digit = InStr("0123456789ABCDEF", Mid(h, i, 1)) - 1
If digit < 0 Then jbin = "": Exit For
j = 8: k = 4
Do ' convert from hexadecimal to binary
jbin = jbin + Right$(Str((digit j) Mod 2), 1)
j = j - (j 2): k = k - 1
If k = 0 Then Exit Do
Loop While j
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So this is Math Teacher’s At Play … the 98th edition! You know what’s really interesting about 98? It’s \(47 \times 2\). No, that’s clearly false. \(49 \times 2 = 98\). That’s much better. Ok, so here’s a question, are there more facts about 98 than there are non-facts (aka lies) about 98 or the other way around or are they equal in cardinality?
You know, those born in 1998 are becoming legal adults in the US this year. Was Windows ’98 around then? Would the song 99 Red Balloons have been just as popular if it were 98 Red Balloons?
What’s so special about \(98-29\)?
Let’s face it, 98 is one short of 99, the cooler number.
Ah, ye old times tables. Caroline Mukisa (@mathsinsider) gives a 31 day plan to learning the times tables.
Fractions tend to be a huge stumbling block in math education. Rachel at You’ve Got This Math talks about “Equivalent Fraction with Pattern Block Task Cards”. It’s a fun intro to fractions for the very young kids and could be a nice refresher for older kids.
In a related article, Denise Gaskins (@letsplaymath) has Playing With Math Shapes.
Speaking of which … a joke intermission! Why are topologists so fit? Because they’re always in shape! Haha. Get it. Topologists. Shape. It’ll be a comic that’s coming soon. I haven’t done one in a while.
Another in fraction land we have in Christine Newell’s (@MrsNewell22) own words
As CCSS implementation continues, teachers are still grappling with transitioning away from old procedures and making meaning out of those procedural concepts. Previously, converting improper fractions to mixed numbers was taught as a rote skill, with little to no conceptual understanding developed for students. This blog post was inspired by a lesson that attached some meaning to the work of converting between mixed numbers and improper fractions by emphasizing that it is truly just a case of fraction equivalence. Students were successful with models (number bonds, number lines, fraction tiles) in learning this concept.
The full article is titled Fractions Greater than One, or the Artists Formerly Known as Improper Fractions
Next, we have a solid article on Using Narration to Evaluate Math Learning from @Tri_Learning. This is about more than finding math in every day things, it’s about connecting with mathematical concepts and being able to explain and discuss. There are many good examples given here and whether you homeschool or not, it’s worth checking out.
On a similar topic, Cav (@srcav) writes wonderfully about Dialogic Teaching and Problem Solving.
And here is my version of it in There’s No Wrong Answer In Math.
I love when Math and Art meet. John Stevens (@jstevens009) talks about Mr. Sierpinski and the Triangle of Doom. A great title and a better article. This is a pretty good classroom activity for pretty much any age group.
Benjamin Leis explores divisibility. What is the remainder when 999,999,999 is divided by 32? I find these problems and explorations to be a lot of fun and engaging. They really do get students playing with numbers and finding patterns!
Roman Smirnov puts down some challenging math problems in this Friday the 13th article. I’ll admit I couldn’t solve the first problem. 🙂
Ok, and this concludes Math Teachers At Play! Make sure to give a the articles linked here a visit!
MTAP #99 will be at Eat Play Math.


By Chad Davis, Contributor at ExcelAssignment company.
To create a spreadsheet table that can be plotted in the form of a graph, first calculate your X or Y values. In Microsoft Excel, you can generate results for these variables by applying a formula to a known data series. Once you’ve completed your table, you can use your X and Y data to automatically create a scatter chart with straight lines and markers. Use the Chart tools to label each axis on your chart, and then label the data callouts for each point on the X and Y axes.
- Create a new blank workbook in Excel.
- Enter your formula into cell A1 for reference. For example, enter “y=5x-2” (without quotes here and throughout).
- Enter labels for your X and Y column data into cells A2 and B2. For example, label the cells “X” and “Y”.
- Enter your X-values into the first column, starting in cell A3. For example, enter the following values into cells A3 through A7: “-2, -1, 1, 2, 4”.
- Select cell “B3,” and then calculate its Y-value using your formula. For example, enter “=5*A2-2”, and then press “Enter” to compute the value for Y.
- Select cell “B3” again, and then drag the fill marker, resembling a small box in the bottom right corner of the cell, to the bottom of your data series. For example, drag the fill marker from B3 to B7. Your Y-values are computed based on your formula and corresponding X-values in the table.
- Select your formula in cell A1. Click on the “Insert” tab to switch to the Insert ribbon. Click the “Insert Scatter (X,Y) or Bubble Chart” drop-down button, resembling a scatter chart icon, and then click “Scatter with Straight Lines and Markers” to plot your formula in a chart.
- Click the “Add Chart Element” drop-down button in the Chart layouts group of the Design ribbon, select “Axis Titles,” and then click “Primary Horizontal” to add a horizontal axis title to your chart. Repeat the process, but this time select “Primary Vertical” to add your vertical axis title. Replace the titles with the labels you used for your X and Y data. For example, enter “X” for the horizontal axis title, and then enter “Y” for the vertical axis title.
- Click the “Add Chart Element” drop-down button again, select “Data Labels,” and then click “Data Callouts” to label your data markers.
Tips & Warnings
Information in this article applies to Microsoft Excel 2017. It may vary for other versions or products.


Check out this letter I received from the United States Secretary of Education, Miguel Cardona.
Fall 2021: I am currently teaching two sections of MATH 101-Calculus 1
University of Arkansas:
Summer 2021: Applied Linear Algebra (5 week summer course)
Fall 2020/Spring 2021: Two sections of Calculus 1 for science and engineers. This class was held virtually via Zoom.
Summer 2020: Applied Linear Algebra. Virtual instruction via Zoom
Spring 2020: Calculus 2. Partially remote instruction.
Here are some programs I have been involved with in the past:
- UGA Mentor Program – Current mentor.
- MOEMS 2019-2020 – Math Olympiads for Elementary and Middle Schools
- Camp Euclid (2016, 2017, 2019, 2020, 2021) – Camp Euclid is an online research summer camp for high school students. During the camp, we work on unsolved problems in math in an online collaborative setting. We will be featured in the December 2020 edition of the AMS Notices.
- Women’s Empowerment Resident Manager Pre-training: I taught math to women experiencing homelessness to prepare them to become resident managers, which gives them the opportunity to obtain housing AND employment. Read about it here. (Nine out of the nine women in this program successfully obtained housing and employment!!)
- Women’s Empowerment Get a Job Kit: I assisted with some graphic design work for the Get a Job Kit, a job readiness tool which aims to prepare individuals of all ages and backgrounds to enter the workforce.
- UC Davis Cosmos Program: This is a four week in-residence summer camp for high school students. I was a teacher fellow for the mathematics cluster and taught them about knots, links, and the topology of spaces.


The null hypothesis is no relationship between spatial location and plant size. The matrices will be square and thus the calculations for the test are carried out on only the upper or lower diagonal of the matrices.
Spatial autocorrelation violates the assumption of independence of observations which is a serious concern for tradiational hypothesis tests. Readers are referred to Peakall and Smouse for a more comprehensive outline of these standard procedures, data formats and data import options.
Without dropping the constant term, there will be problem of autocorrelation. Global spatial stats search for a total pattern in between distance and the resemblance of pixel worths.
What would be the problem of including an intercept in the model. The spatial statistics literature is notoriously difficult to understand and penetrate. Jones and Bartlett Publishers: For example, in three dimensions the autocorrelation of a square-summable discrete signal would be When mean values are subtracted from signals before computing an autocorrelation function, the resulting function is usually called an auto-covariance function.
Eviews is simply the short form of econometrics views. EViews Homework Help When you are dealing with school projects and assignments that relate to time series analysis, then you have to apply the right steps for this.
Thus, the maximum numbers of loci and samples are vastly expanded and only constrained by memory. Analysis of Field Experiments: For the Global Moran's I fact, the null hypothesis states that the quality being examined is arbitrarily dispersed amongst the functions in your research study location; stated another method, the spatial procedures promoting the observed pattern of worths is random possibility.
GenAlEx operates within Microsoft Excel—the widely used spreadsheet software that forms part of the cross-platform Microsoft Office suite. Input The input consists of a series of data sets. Students must load the data, conduct analyses, and plot the results by writing an efficient MATLAB script, and must "publish" their code into a well-organized, well-commented.
For example, to calculate the autocorrelation of the real signal sequence i.
When different worths cluster together in a map, unfavorable spatial autocorrelation is. John Wiley and Sons, Inc. Problematic autocorrelation of the errors, which themselves are unobserved, can generally be detected because it produces autocorrelation in the observable residuals.
This page first made public: One of the pioneers in econometric modeling using Eviews is Prof. Assignment 1 Question 1 a) The autocorrelation at lag k, ˆ The sample autocorrelation function reported in the exercise shows a pattern which decreases as the lag increases.
Given the properties of the ACF of MA and AR processes, this pattern could indicate that an autoregressive representation. autocorrelation, flexible alphabets and new periods and channel assignment algorithms available to wireless system designers.
In such systems which use higher frequencies, the issue of channel identification, which can be performed. I just got my first assignment and I am confused by a couple of terminologies. Q1. What is the difference between autocovariance, autocorrelation and autocorrelation coefficient? I tried to google it, but most of them don't really make sense to me.
Q2. The question asks to estimate lag-1 autocorrelation coefficient, but what is lag? Minitab Project Report - Assignment 6 Sunspot data Index y 1 24 48 72 96 50 0 Time Series Plot of y Index X 1 24 48 72 96 In statistics, the autocorrelation of a random process describes the correlation between values of the process at different points in time, as a function of the two times or of the time difference.
Quantitative Methods homework help. We at Statisticsassignmentexperts have established ourselves prominently in the space by delivering solutions of assignments on array of topics in Statistics.Autocorrelation assignment


Michael T DeMers
Michael DeMers is an educator and technology enthusiast. He holds a masters degree from The University of Arizona, and has taught mathematics, music, and technology to all ages from elementary to college. Currently he is the chair of the technology committee, instructional strategist, and the grade 5 mathematics instructor at Grant Bowler Elementary School in Logandale, Nevada.
Michael T DeMers presents 1 Event:
The Ubuntu Home Server at LinuxFest Northwest 2018


James McKernan, professor of mathematics at UC Santa Barbara, and Christopher Hacon of the University of Utah have been named winners of the 2009 American Mathematical Society (AMS) Frank Nelson Cole Prize in Algebra. Presented every three years by the AMS, the Cole Prize is one of the highest distinctions in algebra. The prize was awarded Tuesday at the Joint Mathematics Meetings in Washington, D.C.
According to the prize citation, McKernan and Hacon were awarded the Cole Prize "for their groundbreaking joint work on higher dimensional birational algebraic geometry. This work concerns the minimal model program, by which S. Mori and other researchers made great progress in understanding the geometry of three-dimensional projective algebraic varieties in recent decades. The case of dimension greater than three, however, remained largely open. The work of Hacon and McKernan has transformed the study of the minimal model program in higher dimensions."
The citation specifically notes two papers by Hacon and McKernan, "Boundedness of pluricanonical maps of varieties of general type," Inventiones Mathematicae 166 (2006), 1-25, and "Extension theorems and the existence of flips," in Flips for 3-folds and 4-folds, 76-110, Oxford Lecture Series in Mathematics and Its Applications 35, Oxford University Press (2007).
The full citation for this prize and additional information about AMS prizes can be found at http://www.ams.org/prizes-awards.
Issued: Jan. 7; updated: Jan. 8