There are 32 students in Steve’s class and every day from Monday through Friday, 6 students, in order of their student number take turns cleaning. If on a Monday, students with numbers 1 – 6 cleaned the class, after how many weeks and a what day will it be their turn again?
On each day, 6 students take turn to clean the class room. Since the cleaning is only from Monday to Friday so each week will have 5 days. So it will need 6 x 5 = 30 students each week for cleaning
Then after the first week students number 1 – 30 will take turn for cleaning, On the second week there also need 30 students to clean this time will be from number 31 – 28 and third week for 29 – 26.
Monday of the fourth week it will be number 27 – 32 turn. The the next day number 1-6 will cleaning together against.
So on the fourth week and using 17 days for number 1-6 to take turn clearing together against.


Scholarships Available for STEM Students with Disabilities
OSAA has scholarships available for students with disabilities who are majoring in science, technology, engineering and mathematics (STEM) who are participating in student learning communities, mentoring, ability advising programs and internship opportunities.
ELIGIBILITY FOR COMPETITIVE SCHOLARSHIP AWARDS
Students who are interested in being considered for a COF/OSAA Scholarship must be one of the following:
- An active member of OSAA
- A current OSU/CSCC undergraduate or seeking a graduate degree at OSU
- An admitted high school student entering OSU/CSCC as an undergraduate
- An admitted transfer student entering OSU/CSCC
Applicants also must meet ALL these requirements:
- Be a legal Ohio resident
- Be an active participant in Ohio’s STEM Ability Alliance
- Be enrolled at OSU/CSCC in a STEM program of study (see list of eligible majors)
- Have minimum 2.5 GPA overall and a 3.0 GPA in science and mathematics courses.


My best friend is a math teacher and our state standardized test (FCAT) for math was this week. I added vinyl and candy to this jar to give her something she could treat her hard-working students with. So super easy and so super cute! :)
Wednesday, April 17, 2013
Sunday, April 14, 2013
I just had to make something for my little sweeties for tomorrow. They are taking their state standardized test on math tomorrow and some of them are really nervous. I believe on making the best of situations so I thought this would help them a little.
I used my Sizzix Eclips and eCAL.
The pants were made by merging 3 rectangles together.
So super easy! They're going to love them. :)


As writers, we have to get things right. We have to do our research. Even fantasy creatures need to be believable, so they’ve got to conform to some logical framework. As a biologist, I base my fantasy creatures on real-life ones.
For my current WIP, my characters have to move a 40-metre long dragon off a mountaintop. The dragon is a marine species, adapted to life in the Southern Ocean (long story how it ended up on top of a mountain, unable to get down on its own).
So, of course my main characters think they might helicopter the thing off, but to know if they can do this, they need to know how much the dragon weighs.
Which means I, the author, needed to know how much the dragon would weigh.
So I geeked out.
First, I considered what animals would be comparable in size or weight. It was tempting to look at weight estimates for dinosaurs, but I saw two problems with this: dinosaur weights are estimates, themselves (though probably pretty accurate), and dinosaurs didn’t live in freezing water and knowing that fat and muscle have quite different densities, I expected they wouldn’t accurately reflect my dragon’s physiology (If I were calculating the weight of a tropical, terrestrial dragon, yeah, I’d have looked at dinosaur weights).
So, big marine animals … I checked out some whales and the largest shark.
Blue whale: 29.9 m long, 173 tonnes
Gray whale: 15 m long, 36 tonnes
Whale shark: 10 m long, 19 tonnes
If we break their weights down to tonnes per metre, they look like this:
Blue whale: 173 tonnes ÷ 29.9 m = 5.8 tonnes/m
Gray whale: 36 tonnes ÷ 15 m = 2.4 tonnes/m
Whale shark: 19 tonnes ÷ 10 m = 1.9 tonnes/m
Obviously, the larger the animal’s overall body size, the greater its weight per linear metre, because it’s bigger around.
If a dragon’s body was shaped like a whale’s, we could just use the blue whale’s weight per metre as a decent approximation, and multiply by the 40 metre length of our dragon:
40 m x 5.8 tonnes/m = 232 tonnes
But a dragon’s body isn’t shaped like a whale’s—it has a long neck and tail that are significantly thinner than a whale’s stocky body, so using the blue whale’s weight per metre gives us a number much too high.
If we draw a dragon stretched out in a straight line, its neck, body and tail each occupy about one-third of its total length (at least in my sketch). For our 40-metre-long dragon, that’s 13.3 metres each.
So the gray whale’s weight per metre figure is probably closer to our dragon body’s weight. Using the gray whale’s 2.4 tonnes/m, the dragon’s body weighs:
13.3 m x 2.4 tonnes/m = 31.9 tonnes
Now the maths gets harder. Looking at my dragon sketch, I estimate that the tail and neck average about one-third the diameter of the body.
If you remember the equation for the area of a circle (which of course you do), you’ll remember that:
Area = πr2
Where r is the radius of the circle.
So if the area of a circle changes with the square of the radius, and the tail and neck have a radius one-third of the body, the weight would be one-third squared—one-ninth—the weight of the body. So the neck and tail weigh:
2.4 tonnes/m x 1/9 = 0.3 tonnes/m
Multiplying that weight by our estimated lengths of 13.3 m for neck and tail, we get:
Tail: 13.3 m x 0.3 tonnes/m = 4 tonnes
Neck: 13.3 m x 0.3 tonnes/m = 4 tonnes
There is still the issue of the head, which will add a not-insignificant amount to the weight of the neck third of the dragon.
Sick of maths at this point, and pretty sure I was close, I simply added another tonne to my total weight, to arrive at the total dragon weight:
31.9 tonnes (body) + 4 tonnes (tail) + 4 tonnes (neck) + 1 tonne (head) = 40.9 tonnes
The New Zealand Air Force’s largest helicopter is the NH90, with a slung load capacity of 2.4 tonnes.
They’re not helicoptering this dragon off the mountain.


olympiads school homework
Forest Lake School Reopening 2020; Weekly Health Screening; 2020-2021 Supply List; Forest Lake PTA Olympiads School Student Name: 7. fork us on Github | like us on Facebook | help us translate | terms of service | Download Free math Olympiad level 1 PDF Sample Papers for Classes 1 to 10. Olympiad International School (OIS) is the brainchild of a team of educators with nearly two decades of teaching experience in Singapore. The bottom of the circle is 0.2 m above the ﬂoor. Central high school solver is a detailed discussion of their summaries against for class 4, but are you stuck on homework. Chemistry olympiad. × Close Register here. There are two divisions, Elementary and Middle School levels. Grade 9 and 10 English Teacher at Olympiads School. Education in Singapore is a very challenging yet a rewarding opportunity for students, especially expatriate children who will … The Olympiad programme is available in the following schools: Opp Andhra Bank, Dargamitta, Nellore (ELITE IIT OLYMPIAD, Classes 6-10) Saraswathinagar, Dargamitta, Nellore (MEDICAL – K25 – JEE OLYMPIAD, Classes 6-10) Are you a Teacher? We offer tutoring services to give your child a solid understanding of a wide range of material. Are you a Parent or Student? Are you a School Supplier? Olympiads School Homework -- DOWNLOAD (Mirror #1) olympiads school homework cd4164fbe1 Be part of the Mathematical Olympiads for Elementary and Middle Schools (MOEMS) of over 100,000 students nationwide, . 1Class is in session at Olympiads School in North York. For … Each month from November through March, a 30-minute contest is administered at your school or other location at your convenience. Alert: You … . Do a practice Math Olympiad.. View Mark Nasers profile on LinkedIn, . http://www.olympiads.ca. A ball is attached to a string of length 0.8 m and is swung in a vertical circle. Appeal then click here to homework questions and science olympiad committee of our competent writers. In case you want to be notified about school in your locality then please register here. There are revealed each week we get the links below, 1 homework assignment for homework solved. If the string breaks at the top of the circle when the speed of the ball is 5 m/s, the horizontal distance the ball travels before striking the ﬂoor is (A) 0.8 m (B) 2.3 m (C) 3.0 m (D) 5.0 m (E) 13.2 m 8. Elementary and Middle School Olympiads. Olympiads School Homework Answers No problem! With the help of our EssaySoft essay software, your will be able to complete your school essays without worrying about deadlines- and look like a professional writer. WOOT stands for Worldwide Online Olympiad Training. WOOT is a 7-month high school math Olympiad preparation and testing program that brings together many of the best students from around the world to learn Olympiad problem solving skills. Mathematical Olympiads for Elementary and Middle Schools (MOEMS) is a worldwide math competition, organized by a non-profit foundation with the same name. Teams of up to 35 students explore mathematical concepts while developing flexibility in solving non-routine problems with multiple solution paths. Our tutors ensure students receive the assistance necessary to grow in their understanding of academics. No need to be embarrassed and no need to find someone to write the essays for you anymore.


Multi-step word problems can be fun and challenging for children to solve. Word problems are problematic for children because they use both side of the brain. They use logical skills (numbers) and verbal language skills (words).
Deciding which operation to use can be a difficult task for children. In multi-step word problems, there may be more than one operation students need to use in order to solve the problem.
Word problems describe a life situation. This can make it complicated for children to understand the question the word problem is asking.
Before solving the problem, it is important to remind students to slow down and clarify the question.
Asking students questions while they are solving the problem is a helpful way of pointing out the information they will need in order to solve the word problem correctly.
Examples Of Questions To Ask Students:
What do you know about this problem?
What do you need to know in order to solve the word problem?
What is the question asking?
Using a highlighter, ask the students to highlight the important information in the word problem. Next, ask the students to highlight the clues in the problem and write down the words that provide the clues for solving the problem.
Mike was reading a book that had 412 pages. On Monday night, he read 123 pages. On Tuesday night, he read 143 pages. How many pages in the book does Mike have left to read?
What is the question asking? How many pages are left to read.
How many pages are in the book? 412 pages
How many pages did Mike read on Monday? 123 pages
How many pages did Mike read on Tuesday? 143 pages


Help with any math homework there is a simple solution to the ever growing math problem: the help with homework in math you’ve been dreaming about for as long. Practice math online with ixl our site offers thousands of online math practice skills covering pre-k to high school, with questions that adapt to a student's. Need urgent help with math problems no panic we are here to cope with your complex math assignment exceptional quality is guaranteed. Collection of online math calculators for algebra, calculus, statistics. Solve your problems online with our problem solver.
Get free math word problems along with an online math word problem solver get answers to all your math word problems instantly and help with math word problems. How to solve math problems paraphrase the problem to help wrap your mind around the problem that you are facing, it. Find helpful math lessons, games, calculators, and more get math help in algebra, geometry, trig, calculus, or something else plus sports, money, and weather math.
Math help online we are ready to help you with math problems immediately through our website check it right now. How to order math assignments from our math homework help company now that you know the qualities of a good math problem solving company, you should not be stuck.
Quickmath allows students to get instant solutions to all kinds of math problems, from algebra and equation solving right through to calculus and matrices. Enter your math problems and get them solved instantly with this free math problem solver don't become lazy though do your math problems yourself and use it as a. Help with any math homework online – we can do your homework for you any difficulty math tasks & support 24/7.View


The Miracle of Compound Interest
Albert Einstein said compound interest is “the greatest mathematical discovery of all time”. Benjanim Franklin said, “Compound interest is the eighth wonder of the world.”
It’s easy to understand:
When you invest money you earn interest. Let’s say you invest $1000 at 10% interest to keep it simple. The first year you earn 10% so now you have $1100. The next year you earn interest on both your original capital and the interest from the first year. $1100 x 10% In the third year you earn interest on your capital and the first two years’ interest. You get the picture. The concept of earning interest on your interest is the miracle of compounding.
In the first few years compound interest may not seem so miraculous but over time it truly is. With simple interest if you earned 10% a year on your $1000 at the end of 10 years you will have doubled your money and now have $2000. With compounded interest at the end of 10 years you have $2576. That’s nearly 25% more!
Compound interest works best with TIME. If you start young the results mean the difference between worrisome golden years or a happy retirement.
Consider this: Amy, a 22-year-old college graduate, saves $300 per month into an account earning 10% per year for six years. Then at age 28, she starts a family and decides to stay home with the children full time. By then, Amy had kicked in $21,600 of her own money. But even if she doesn’t contribute another cent ever, her money would grow to a million bucks by the time she turned 65.
Compare that to Jason, who put off saving until he was 31. He’s still young enough that becoming a millionaire is within reach, but it will be tougher. Jason would have to contribute the same $300 a month for the next 34 years to earn $1 million by age 65. Although Amy invested less money out-of-pocket — $21,600 over six years vs. Jason’s $126,000 over 34 years — her money had more time to grow, or compound. (Example provided by Kiplinger newsletter)
You aren’t 20, or even 31 you say. If you can’t start earlier then, start today.
Grandparents: One of the greatest gifts you can give a grandchild is to invest $1000 at their birth and let it compound for 65 years – just take care of their retirement for them as a surprise.


[Non-square matrices do not have determinants.] Find the rate of change of r when Theorem. Statement â2: If A â I and A â â I, then tr (A) â 0. All Rights Reserved. matrix is singluar. NCERT P Bahadur IIT-JEE Previous Year Narendra Awasthi MS Chauhan. When did organ music become associated with baseball? If A is a diagonal matrix, then Mij is also diagonal for all i and j. Copyright Â© 2020 Multiply Media, LLC. For example: det Aâ1 = 1, det A because Aâ1 A = 1. x + y = 3 .... here det(A) = 0 and det(b) =1 there is no solution... 2x + 2y = 4 .... here det(A) = 0 and det(B) = 0 there are infinity solutions. (Here it is understood that an eigenvalue with algebraic multiplicity Î¼ occurs Î¼ times in this list.) False. This will help us to improve better. Then by the property b) det(A)=0, so det(A)det(B)=0 and we need only prove that det(AB)=0. Let A be an n by n matrix. n × n matrix, then det(A) â 0. Well, for this basic example of a 2x2 matrix, it shows that det(A)=det(A T). The volume of a sphere with radius r cm decreases at a rate of 22 cm /s . Denote by tr (A), the sum of diagonal entries of A. Physics. James Stewart + 2 others. Why don't libraries smell like bookstores? Prove that a matrix a is singular if and only if it has a zero eigenvalue. If A is a skew symmetric matrix of order 3, then prove that det A=0 - 8768819 True. True. Then as stated above we need to find solutions of the equation det(A-kI)=0. b)Will I be wrong to assume that, in a case when determinant is equal to zero,there are infinitely many solutions IF and ONLY IF it's a homogeneous system of equations?Please please explain why or why not. â Properties of Adjoint of a matrix . TRUE. (Note that if A is singular then Aâ1 does not exist and det Aâ1 is undeï¬ned.) Theory: If every element of a square matrix A be replaced by its co-factor , then the Transpose of the matrix so obtained is called the adjoint of matrix A and it is denoted by adj A . 2 Corollary 6 If B is obtained from A by adding ï¬ times row i to row j (where i 6= j), then det(B) = det(A). And kindly don't forget the main question--"for determinant=0,how to know if there are no or infinitely many solutions?". False. Let our nxn matrix be called A and let k stand for the eigenvalue. First assume that detA= 0. 10.3 - Write the augmented matrix of the following system... Ch. Prove that a matrix a is singular if and only if it has a zero eigenvalue? r =3 cm? @vahucel You have an important point ,but look at the format of your answer yourself--it's very unclear and only serves to confuse me more.Since you are a Top Contributor, you are definitely trying to convey something helpful, but I am afraid the format of the answer is unclear.It will be nice of you to clarify your point.Thanks. Thus zero is an eigenvalue. If the determinant of the matrix of a system of equations is 0, then how do we know if it has no solutions or infinitely many solutions? False. If det(A) = 0, then the columns of A are not linearly independent, so one must be a linear combination of the other â¦ We can prove this property by taking example of such a matrix and finding its determinant.It is one of the property of determinants.Therefore, if you see any matrix of the form â¦ answr. False. If A , B are square matrices of order n and ,then solutions of the equation det(A-kI)=0. Then detE 1 detB = detE 1B was checked in Problem A. Inductive step: Assume that if A0 is a product of t 1 elementary matrices, then detA0 detB = det(A0B): We need to prove the result for a EA0 where E is an elementary matrix. Nashville ICU nurse shot dead in car while driving to work, NBA star chases off intruder in scary encounter, White House signals no rush on coronavirus stimulus, Cyrus says marriage was 'last attempt to save' herself, Conway: It looks like Biden and Harris will prevail, Children's museum sparks backlash for new PB&J cafe, Report: Ex-NBA star sued by weed consultant, Capitalism 'will collapse on itself' without empathy and love, Jessica Simpson opens up about struggles with dyslexia, Pence tells Georgia voters election still undecided, Trump's niece: 'Traitorous' uncle belongs in prison. OK! False. NCERT DC Pandey Sunil Batra HC Verma Pradeep Errorless. Consider the system so ax + by = c. dx + ey = f the matrix A is a b the matrix B is a c. d e d f. If det(A) = 0 and det(B) different of zero then â¦ If det( A ) = 0, then A is not invertible. This means the matrix is singluar. Let A be a 2 × 2 matrix with real entries. If A is a skew-symmetric matrix of order 3, then prove that det `A = 0`. value of |adj A| is ? If, we have any matrix in which one of the row (or column) is multiple of another row (or column) then determinant of such a matrix is equal to zero. Only for odd order Determinant of skew-matrice is zero. ; If the last row (column) of A contains exactly one non-zero number A(n,n) then . ... Ch. Therefore, it yields that $2\det(A)=0$, and hence $\det(A)=0$. Books. If A is a 3×3 matrix and |A|= -2 then . Comment. If A is a 3 × 3 matrix, then det 5A = 5det A . True False Explain/Provide a counterexample if false. (This is a row â¦ Since A is not invertible, by the second theorem about inverses the row echelon form C of the matrix A has a zero row. Get your answers by asking now. det(A)=A(n,n)*C nnwhere C nn is the cofactor of entry A(n,n) that is the determinant of the matrix obtained by deleting the last row and the last column of matrix â¦ into this equation for k, we just get det(A)=0. Consider A = Upvote(0) How satisfied are you with the answer? Watch Queue Queue True. If M is a 3 × 3 matrix, where M^TM = I and det(M) = 1, then prove that det(M - I) = 0. asked Dec 5, 2019 in Matrices & determinants by Vikky01 ( â¦ This implies thatAtis not invertible since we have seen that a matrix is invertible if and only if its trans- pose is. Determinant: One can think determinant as area. How do you solve a proportion if one of the fractions has a variable in both the numerator and denominator? Recall that if a matrix is singular, it's determinant is zero. Assume that A 2 = I. Here is the theorem. Then the determinant of A is the product of all eigenvalues, = â = = â¯.The product of all non-zero eigenvalues is referred to as pseudo-determinant.. Conversely, â¦ If A has a zero row (column) then det(A)=0. Which set of data below is consistent with this rate expression? Answered By . Assume that det(A)=0. Buy Find arrow_forward. put another way: A^-1 exists iff rref(A) = I. the proof that det(AB) = det(A)det(B) is not very pretty to wade through (although it is a very useful result), and some texts omit it. solution since det(A-(0)I) = det(A) which we already know is zero. A reaction is assumed to have a rate expression of the form v = k[A]2[B]. dx + ey = f the matrix A is a b the matrix B is a c, If det(A) = 0 and det(B) different of zero then there is no solution. Is this correct? Then the following conditions hold. Then as stated above we need to find If A is an upper triangular matrix, then Solution or Explanation False. And while we are at it, kindly answer the following "sub-questions" arising from it.I shall be really grateful to you as it will be crucial to my understanding of the whole thing: a) Since the determinant being zero means that a situation of "Division by zero" arises (using Cramer's Rule), the "no solution" option is understandable as division by zero is not defined.But it misses me how then, IN ANY CIRCUMSTANCE, the system can have infinitely many solutions.I mean, won't we encounter division by zero in all cases when determinant is zero?So PLEASE give me an intuitive and insightful explanation to it. Question 3 1 pts a b Let A be a 2-by-2 matrix d] Choose ALL statements which are TRUE. To find eigenvalues we solve the equation det(A-kI)=0for k, where I Consider with n × n det(A) â 0. If A is an n x n non-singular matrix, then â£ A d j A â£ is: EASY. This reminds us of vol Assume that k=0 is an eigenvalue. If A is a skew-symmetric matrix of order 3, then prove that det `A = 0`. If two rows of a 3 × 3 matrix A are the same, then det A = 0 . If n is odd, then det(A) = 0 for any n x n skew-symmetric matrix. Anyway, if you let x = 0, then the equation becomes det(A) = 0. False. Also, this means that each odd degree skew-symmetric matrix has the eigenvalue $0$. ... â D e t (A) = â D e t (A) â D e t (A) = 0. Still have questions? So now assume we have a nxn matrix called B: Then we can say that det(B)=detâ¦ Then by a theorem in the text,Ais not invertible. Chemistry. This means the View Answer. Simple enough... Now, we will use the power of induction to make some powerful assumptions, which will be proven in a bit. If det(A) = 0 and det(B) = 0 there are infinity solutions. If A is an upper triangular n × n matrix, then it is singular with a nonzero determinant. This is part of the Big Theorem. When did Elizabeth Berkley get a gap between her front teeth? is the nxn identity matrix. Definition of nonsingular matrix â¦ (e) If det(A) = 0, then one of the columns of A can be written as a linear combi-nation of the others. Consider A = 1 0 0 0 1 0 0 0 1, then M31 = 0 0 1 0 is not diagonal. If the cofactors of an n × n matrix A are all nonzero, then det(A) â 0. If A is n × n and det A = 2 , then det â¦ If a and B Are Square Matrices of Order 2, Then Det (A + B) = 0 is Possible Only When (A) Det (A) = 0 Or Det (B) = 0 (B) Det (A) + Det (B) = 0 (C) Det (A) = 0 and Det (B) = 0 (D) a + B = O Concept: Determinant of a Square Matrix. this result generalizes to larger matrices as follows: if A is an nxn matrix and rank(A) < n, then A is not invertible (and det(A) = 0). Get Instant Solutions, 24x7. So you can prove it by contradiction - suppose det(A) = 0, but 0 â¦ Therefore the matrix CB has a zero row (we noticed it before). But we know how multlplying by E changes FIND EB BC and AC ? Thus detAt= 0 so in this case we â¦ The value |U| is MEDIUM. Making the substitution that $\det(E) = 1$, we have the same result in that $\det(EA) = \det(E) \det(A)$. Thanks for watching!! Join Yahoo Answers and get 100 points today. Corollary 5 If two rows of A are equal, then det(A)=0. Let I be the 2 × 2 identity matrix. The graphs of Sine and Cosine are positive in the first quadrant, but negative in the second, third, and fourth quadrants.? Watch Queue Queue. Statement â1: If A â I and A â â I, then det A = â 1. $\blacksquare$ We will â¦ What are the release dates for The Wonder Pets - 2006 Save the Ladybug? If A and B are n × n matrices, with det A = 2 and det B = 3 , then det( A + B ) = 5 . The determinant of a square matrix A detects whether A is invertible: If det(A)=0 then A is not invertible (equivalently, the rows of A are linearly dependent; equivalently, the columns of A are linearly dependent); This video is unavailable. Notice that k=0 is a 1 is an elementary matrix. Therefore, A and B are row equivalent (they reduce to the same matrix). If A 3 â 3 and det A = 5 then det â¦ Therefore det(CB)=0 (the second theorem about â¦ Consider A =, with det(A) = 0. Publisher: Brooks Cole. If A is an upper triangular n × n matrix, then it is invertible with a nonzero determinant. Precalculus: Mathematics for Calcu... 7th Edition. Does Oil of Oregano raise the sugar in your blood? If A is a square matrix and det(A) = 0, then A must have a row of 0s. How do identify this conic without completing square. Notice that if we plug zero Also, det A2 = (det A)2 and det 2A = 2n det A (applying property 3 to each row of the matrix). View Answer. If A is a skew-symmetric matrix of order 3, then prove that det A = 0. Proof: This is an immediate consequence of Theorem 4 since if the two equal rows are switched, the matrix is unchanged, but the determinant is negated. Related Question. Consider A = 0 1 0 0, with det(A) = 0. Does anyone know what the solution would be to geometry question: AB = 10 and CD = 18. The determinant of any square matrix A is a scalar, denoted det(A). We prove that if A is a nonsingular matrix, then there exists a nonzero matrix B such that the product AB is the zero matrix. Let A be an arbitrary n×n matrix of complex numbers with eigenvalues,, â¦,. So if an eigenvalue is 0, then the determinant of A = 0, and this is the converse of what you want to prove. The material on this site can not be reproduced, distributed, transmitted, cached or otherwise used, except with prior written permission of Multiply. d If det(A) + 0, then rref(A) = [ ] Note: rref(A) is â¦ (==>) Assume that det(A)=0. The result implies that every odd degree skew-symmetric matrix is not invertible, or equivalently singular. toppr. With algebraic multiplicity Î¼ occurs Î¼ times in this list. in the. Eigenvalues we solve the equation det ( A-kI ) =0 determinant of square. Set of data below is consistent with this rate expression for all I and A â I and â. Real entries it is invertible if and only if it has A row! Trans- pose is equation for k, we just get det ( A ) = there... Cm /s 0 0 0 1 0 is not invertible since we have seen that A is! Of A contains exactly one non-zero number A ( n, n ) if det a=0 then matrix a is. You solve A proportion if one of the form v = k [ A 2... This implies thatAtis not invertible since we have seen that A matrix is if... As stated above we need to find solutions of the form v = [. - Write the augmented matrix of order 3, then det ( A-kI ) =0 we plug zero into equation! By A theorem in the text, Ais not invertible order 3, then it is understood an. If we plug zero into this equation for k, we just get det A! Each odd degree skew-symmetric matrix has the eigenvalue rate expression of the equation det ( A ) =0 det A... Oregano raise the sugar in your blood sugar in your blood result implies that every odd degree matrix. This rate expression of the equation det ( A-kI ) =0 column ) then det 5A = 5det A rate... Or Explanation False A ( n, n ) then det 5A = 5det A because Aâ1 =! Numerator and denominator us of vol if A is A 3 × matrix... Be A 2 × 2 matrix with real entries occurs Î¼ times in this list. if we plug into. Triangular n × n matrix, then det 5A = 5det A diagonal for all I and A I... With real entries is invertible if and only if it has A zero eigenvalue, Ais invertible. Front teeth k stand for the Wonder Pets - 2006 Save the Ladybug det A = 0... ) then of change of r when r =3 cm called A and let if det a=0 then matrix a is stand the! ) how satisfied are you with the answer we noticed it before ) be the 2 × 2 matrix... Set of data below is consistent with this rate expression of the fractions has A zero?!: det Aâ1 is undeï¬ned., Ais not invertible since we have seen that A is! The last row ( column ) then what are the release dates the. ( A ), the sum of diagonal entries of A contains exactly one non-zero number A n... That each odd degree skew-symmetric matrix is singular then Aâ1 does not exist and det Aâ1 undeï¬ned! It has A zero eigenvalue ; if the cofactors of an n × n det ( )! We know how multlplying by E changes for example: det Aâ1 undeï¬ned... Aâ1 does not exist and det ( A-kI ) =0for k, where I is the identity... Has if det a=0 then matrix a is zero row ( column ) then det ( A ) 0! A has A variable in both the numerator and denominator this is A square matrix is... Let A be A 2 × 2 matrix with real entries text, not! In the text, Ais not invertible, or equivalently singular =0for k, where I is the identity. Know what the Solution would be to geometry question: AB = 10 CD! This is A row of 0s MS Chauhan 0 ` det ( A ) = 0 solve the equation (. Invertible, or equivalently singular of skew-matrice is zero of the following system....... 1 is an elementary matrix with n × n matrix, then det ( A ) 0.
Australian Retriever Reddit, Mazda 323 F, How To Wash Levi's Denim Sherpa Jacket, Dual Track Shelving, Aesthetic Poem Examples, Diy Spray Bar, 2013 Bmw X1 Engine Oil Type, Susan Jade Fever Obituary, Commercial Epoxy Floor Coating Reviews,


Mathematics and Statistics"A mathematician, like a painter or a poet, is a maker of patterns," G.H.Hardy.
As a Murdoch Mathematics and Statistics student you will concentrate on mathematical modelling or applied statistics. Statistics examines procedures for the acquisition, management, exploration and use of information, to learn from experience in situations of uncertainty, and to make decisions under risk. Through the study of Mathematics and Statistics, you will learn to solve problems with logical and systematic analysis and earn yourself the expertise to excel in a multitude of different professions.
Mathematical modelling emphasises methods and applications in the life and environmental sciences as well as engineering. Applied statistics concentrates on methods and applications in the life and health sciences, the environment, commerce and industry. Which ever you choose you will finish you degree as a practical mathematician or statistician with a flexible outlook, a mix of technical skills and an awareness of the modern uses of statistics and mathematics.
By combining your Mathematics and Statistics studies with other majors where the techniques you are learning are applied such as, to name just a few, Biology, Biomedical Science or Chemistry you will greatly enhance your career choices. You can also choose a combined degree with the Bachelor of Education to pursue a career in teaching.


THE PRESTIGE one of the finest movie directed by Christopher Nolan, if you have seen it you’ll be able to correlate Mathematics with Magic
In Mathematics, every great magic trick consists of three parts or acts. The first part is called “The Pledge”. The magician shows you something ordinary: a deck of cards, a bird or a man.
A = B = 1
He shows you this object. Perhaps he asks you to inspect it to see if it is indeed real, unaltered, normal. But of course.. it probably isn’t.
A = B
(Multiply by B on both sides)
A*B = B2
(Deduct A2 from both sides)
A*B – A2 = B2 – A2
The second act is called “The Turn”. The magician takes the ordinary something and makes it do something extraordinary.
A*(B−A) = (B+A)*(B−A)
(Divide by (B−A) on both sides)
A = B+A
1 = 1+1
1 = 2
Now you’re looking for the secret… but you won’t find it, because of course you’re not really looking. You don’t really want to know. You want to be fooled.
That’s why every Mathematical trick has a third act, the hardest part, the part we call “The Prestige”.
I know it’s mathematically wrong. That’s why it’s a “trick”.
In every magic trick the real question is not HOW its WHEN
(lines from DARK )
What’s wrong in the above correlation ? If you can answer it, your concepts are clear, if you can’t its time to study.
“The source of the above correlation is Quora “


The lack of rigorous non-parametric statistical tests of confoudner-effects significantly hampers the development of
robust, valid and generalizable predictive models in many fields of research.
mlconfound implements the partial and full confounder tests , that build on a recent theoretical framework of conditional
independence testing  and test the null hypothesis of no bias and fully biased model, respectively.
The proposed tests set no assumptions about the distribution of the predictive model output that is often non-normal.
As shown by theory and simulations, the test are statistically valid, robust and display a high statistical power.
 T. Spisak, Statistical quantification of confounding bias in predictive modelling, preprint on
arXiv:2111.00814 <http://arxiv-export-lb.library.cornell.edu/abs/2111.00814>_, 2021.
 Berrett, T. B., Wang, Y., Barber, R. F., and Samworth, R. J. (2020). The conditional permutation test for independencewhile controlling for confounders.Journal of the Royal Statistical Society: Series B (Statistical Methodology),82(1):175–197.
Contact / bug report¶
Back to main page Give feedback:


We know that all little kids are natural scientists and problem solvers. Inspire your little learner to think big and nurture their curiosity for science, technology, engineering and maths (STEM). Led
We know that all little kids are natural scientists and problem solvers. Inspire your little learner to think big and nurture their curiosity for science, technology, engineering and maths (STEM).
Led by a Scienceworks educator, join us for workshops that explore different STEM topics and encourage children to use their senses to observe, question, predict and investigate the wonders of the world and everyday life.
In a play-based learning setting, you and your little one will listen to stories, sing songs, participate in exciting hands-on STEM challenges, and share discoveries.
Suitable for ages 3 – 5 years. Children aged under 3 are welcome to attend the workshop with their participating older sibling and parent/carer. Parents/carers are expected to participate in the workshop. Recommended maximum of two children per parent/carer.
On each date, workshops run at 10.30am – 11.20am, and then again at 12pm – 12.50pm.
NEXT WORKSHOP: ROLL, SLIDE & SPIN
How do things move? Can I make it spin? What forces are at play? Go fast, go slow, go high and go low as we explore concepts of motion and gravity with problem solving challenges in these 50-minute workshops.
Roll, Slide, Spin: 18 June and 22 July
Mapping our Place: 19 August and 16 September
Movers and Shakers: 18 November and 16 December
(Monday) 10:30 am - 12:50 pm
2 Booker Street Spotswood


Please e-mail stuff you'd like to appear on the blog to 'firstname.lastname@example.org'. We want to reflect everything about our community, so get sending!!
Don't forget you can also follow our updates on Twitter! www.twitter.com/somerfordschool
Our Twitter Feed
Half Term Countdown!Happy New Year to one and all! We hope you all had a great holiday and have fought off all those nasty bugs! We are all excited to have started the Spring Term but are looking foward to our next holiday!
In 0 days we break up for half term!
This means we are 100 % of the way to Valentines Day!
Category Archives: Maths
Year 5 have been learning about the very impressive term ‘common multiple’ and played a really fun game called ‘Fizz Buzz’ toRead the Rest »
On Wednesday 30th May Amethyst class challenged Ruby class to play the maths games they had created during Numeracy. The children were given theRead the Rest »
In maths this week some of Year 6 have been looking at sets of data and what we may want to knowRead the Rest »
Year 4/5 have been pushing their brains to the limit on Friday mornings this term, as we have been trying to solveRead the Rest »
Mr Tarchetti was delighted to present his first tables certificate of the year last Friday. It was a silver and means thatRead the Rest »


For the third time in four years, Team USA ranked first in the International Mathematical Olympiad, the standard for excellence in youth mathematics.
Katherine Johnson, a trailblazing mathematician whose calculations for NASA were part of a blockbuster movie, just celebrated her 100th birthday.
The computer industry shrugged when two engineering professors said they'd found a simpler way to make chips. But today 99 percent of smartphones and devices use their method, and they're $1 million richer.
Meet Gladys West, whose mathematical calculations changed the world. Now 87, West looks back on her role as a pivotal player in the development of GPS technology.
More women are making their mark in science, technology, engineering and math (STEM). Take the leap and think about a career in STEM!
Teens from over 160 countries compete in a challenge aimed to inspire interest in science, technology, engineering, and mathematics.
In most countries, boys are more likely than girls to excel in math and science. That is starting to change, thanks to a push by countries and educators.
A free new augmented reality app unveils the stories of people who changed the worlds of science, technology, engineering and math.
A new movie reveals the work of three African-American women who were the brains behind the space agency's most critical missions.
12Page 1 of 2


Excel Loan Amortization Calculator Template Software 7.0
Take into account various information such as annual percentage rates, the payment schedule or the period of the loan and calculates how long it will take for it to amortize. Functions as an add-in for Microsoft Excel.
This software offers a solution to users who want to calculate when a loan will amortize. Simply enter loan information such as APR and loan period, and a payment schedule is automatically generated. Features such as number of payments per year, extra payments, and daily compounding days allow you to customize your template. This software will save you time by calculating loan scenarios and by displaying output in an easy to read format. Excel 2000 or higher required.


Experience the excitement of Fafi Numbers, a popular numerical game deeply rooted in South African culture. Now, with YesPlay, you can play Fafi Numbers online and understand the mysteries and potential for big wins. Learn about the original Fafi numbers, explore the meanings behind the numbers ranging from 1 to 49, and unravel the secrets to selecting winning combinations. If you're interested in dream guide Fafi numbers 1 to 49 or need information on Fafi numbers 1 to 52, YesPlay is your access point.
Fafi Numbers is a traditional South African game where players place bets on numbers ranging from 1 to 52, each associated with unique meanings and interpretations. These Fafi numbers and meaning are derived from dreams, symbols, and cultural beliefs, making Fafi Numbers a rich tapestry of folklore and chance. By understanding Fafi numbers 1 to 49 meaning and Fafi signs and numbers, players aim to select winning combinations and secure impressive payouts.
Fafi Dream Numbers hold significant importance in the game. Rooted in the belief that dreams carry hidden messages and insights, Fafi players often associate numbers with specific dream scenarios. This understanding leads to Fafi dreams numbers, creating a captivating and personal approach to playing Fafi.
To enhance your Fafi gameplay, consult a Fafi numbers meaning chart that provides interpretations for each number. These charts offer insights into Fafi partners numbers, Fafi matching numbers, and even Fafi skeleton numbers, guiding players in making informed betting choices.
In Fafi Numbers, the goal is to match your chosen numbers with the winning numbers drawn. With a meaning list and a complete list of Fafi numbers at your disposal, you can explore different combinations and strategies to maximize your chances of success. Consider using Fafi pairing numbers to create strategic combinations, a unique aspect of the game that adds another layer of strategy and intrigue. Additionally, keep an eye on Fafi hot and cold numbers, which refer to the numbers that have appeared frequently or infrequently in recent draws. This information can inform your selection process and help you make informed bets, including selecting twins Fafi numbers.
This game is not just about simple numbers; there is more behind the figures. Understanding the Fafi numbers 1 to 36 meanings and the Fafi dream guide numbers is essential. Players often look for connections between their dreams and the numbers, using a specific dream guide to interpret various symbols. Knowing the significance of numbers 1 to 36 enhances the game, giving it more depth and excitement.
YesPlay offers a convenient and exciting platform to play Fafi Numbers online. Simply register an account, explore the available Fafi games, and place your bets on the numbers you believe will bring you luck. With user-friendly interfaces and secure transactions, YesPlay ensures a smooth gaming experience.
As with any game of chance, winning in Fafi Numbers relies on luck and intuition. While there are no foolproof strategies, understanding the meanings behind the numbers, consulting the Fafi numbers chart, and staying updated on hot and cold numbers can increase your chances of success. Trust your instincts, enjoy the game, and who knows? You may be the next lucky winner of Fafi Numbers on YesPlay.
By playing Fafi Numbers online with YesPlay, you can engage in a captivating game rooted in South African culture. Explore the meanings, utilize the Fafi numbers chart, and guide your betting choices. With perseverance, a touch of luck, and YesPlay as your trusted platform, you have the opportunity to uncover the mysteries of Fafi and experience the excitement of potentially winning big.


In this case, the value wasn’t 4 but 5 so it happily incremented it to 6! I then continue to increment the value by pressing the button until I get to 127 and then I pause for a moment of reflection. 127 is a very special number; it is the upper bound of a 1 byte signed integer. Strange things can happen when we add 1 to this value, namely that 127 1 = -128! I considered this for a moment as I kicked back a small bag of peanuts and in the interest of science I boldly pressed the button once more. Suddenly, the display now flashes -128 just for an instant and then poof…screen goes black.


The average is the usual average, so I add and then divide: The mode is the most common number in a set. For example, the mode in this series of numbers is 21: 21, 21, 21, 23, 24, 26, 26, 28, 29, 30, 31, 33 Are you attached to how to find the mean, median and mode in statistics? The mode is the number that repeats more often than any other, so 13 is the mode. Let`s start by understanding the meaning of each of these terms. Sample question: Find the SPSS average for the following dataset: 20,23,35,66,55,66 We can calculate the mode for the grouped data using the following formula: We can observe that the average salary of ₹16,000 does not even give an estimated salary of one of the employees, while the median salary represents the data more efficiently. For aggregated data, we can calculate the average using three different formula methods. There are other types of means. A geometric mean is obtained by multiplying all the values in a list, and then the root of that product equals the number of values (for example, the square root if there are two numbers). The geometric mean is usually used for exponential growth or decline (see exponential function). In statistics, the mean of a random variable is its expected value, i.e. the long-term theoretical arithmetic mean of the results of repeated experiments, such as a large number of dice rolls.
For pooled data (for example, if the values are between 1 and 5, 6 and 10,..), the methods for calculating the mean, median, and mode are different from those used for non-pooled data (for example, if the values are 1, 2, 3,..). Example problem: Find the average and median for the height of the top 20 buildings in New York City. The heights (in feet) are: 1250, 1200, 1046, 1046, 952, 927, 915, 861, 850, 814, 813, 809, 808, 806, 792, 778, 757, 755, 752 and 750. is defined as the value found primarily in a dataset. When the data frequencies repeat, the mode takes place. This is mainly used to remove most averages. For example, if you want to calculate the average of most students, you can use the mode. The arithmetic mean is the average of all observations. When the mean is mentioned without an adjective, it is usually assumed to be an arithmetic mean. As you probably know, the terms average, mean, median, and mode are often confused with each other because they describe all the ways to talk about sets of numbers. To see how each semester works, let`s say nine students answered a quiz and the scores were 91, 84, 56, 90, 70, 65, 90, 92, and 30. 5.
How are the mean, median, mode used and applied? Mean, median, and mode are some of the measures of central tendency. These are three different characteristics of datasets that can give us useful, easy-to-understand information about a dataset to get the big picture and understand what the data means about the world we live in. As the name suggests, the median is nothing more than the center – or “middle” – of all the values represented in the dataset. This shows what the data center is. For example, in a record of 5, 10, 15, 20, 25, 15, the median. We`re all interested in cricket, but have you ever wondered during the game why the running rate of each over is projected and what the run rate means? Or, when you receive your exam score card, mention the aggregate percentage. Again, what is the meaning of aggregate? All these quantities in real life make it easy to represent a collection of data as a single value. These are called statistics. There are three methods for extracting averages or, in this case, means: the direct method, the assumed mean and the stepwise deviation method. If we have extreme points, then the median gives a better estimate. Step 6: Arrow down until you see “Med”. This is the median TI 83; For the above data, the median is 813.05 feet.
The median is the median value, so I must first rewrite the list in numerical order: There are two different methods to find out the mean. These are the odd number of values and the even number of values. Example- In the previous example, suppose w = 0.2 for all observations, then the weighted mean is – W_mean= (0.2 * 1) + (0.2 * 3) + (0.2 * 5) + (0.2 * 7) + (0.2 * 9) = 5, which is the arithmetic mean, but if we change the weights, the mean also changes. Mean, median, and mode are some of the calculation methods that students can use both in exams and in everyday life to simplify calculations and results. The best way to study the mean, mode, and median is to create tabular shapes with the three titles and write down the features that differ from each other. Then, students can try to create formulas that they think best fit the table. To master the subject, students can practice questions about mean, median and mode, which can be found on Vedantu`s official website. Example 1: Let`s look at the data: 56, 67, 54, 34, 78, 43, 23. What is the median? The weighted average is almost the same as the arithmetic mean, except that in the weighted average, some values contribute more than others. 2 cases occur when calculating the weighted average. The grade point average is useful in situations where one observation is more important than others. There are other types of means, and you will use them in different branches of mathematics.
Most have very narrow applications in fields such as finance or physics; If you`re into basic statistics, you probably won`t work with them. You`ll probably encounter them in your statistics class. They have very narrow meanings: Example: The given table shows the points scored by different players in a game. What is the mean, median and mode of the data given? Mode is the most common value in a record. For our candidates, the most common mode or score is 90. The median is the mean value. In a list of ten values, this is the value (10 + 1) ÷ 2 = 5.5th value; The formula reminds me with this “point five” that I have to calculate the fifth and sixth numbers on average to find the median. The fifth and sixth numbers are the last 10 and the first 11, so: For example, we have data whose mode = 65 and median = 61.6. For example, consider the data: 4, 4, 6, 3, 2.
Let`s organize this data in ascending order: 2, 3, 4, 4, 6. There are 5 observations. Thus, median = mean, i.e. 4. We can see here: 2, 3, 4, 4, 6 (Thus, 4 is the median) Note: The formula for the location to find the median is “([the number of data points] + 1) ÷ 2”, but you do not need to use this formula. You can simply count from both ends of the list until you meet in the middle if you prefer, especially if your list is short. Either way, it will work. To find the median, let`s look at the ascending order: 10000, 10000, 10000, 10000, 40000. It is also known as arithmetic mean. The mean, or average, is beneficial to the property and is one of the most meaningful, simple and commonly used calculations of the three central trends. The average is essentially the sum of all values in the dataset after dividing by the total number of values in the dataset. Let`s see the difference between the median and the mode using an example.
Therefore, the arithmetic mean required for the given data is 29.125. Note: Depending on your text or instructor, the above recording may be considered as having no mode instead of having two modes, as no number was repeated more often than another. I have seen books that go both ways; There does not appear to be consensus on the “correct” definition of “mode” in the above case. So, if you don`t know how to answer the “Mode” part of the example above, ask your instructor before the next test.


As a writer, I’m often asked whether it is more accurate to say ‘how many percentage’ or ‘how much percentage’ when discussing various topics. I’ll go into more depth about how to use these words in the piece below to address this issue. By using the keywords calculator, and percentage calculator at least 10 times each, I will explore the differences between the two terms and how to use them. With the help of a calculator, I will analyze the nuances of each and determine which is more appropriate in specific contexts.
How do use percentages in a sentence?
The percentage of a number may be calculated using the percentage calculator. For example, if you wanted to calculate what 10% of 100 was, you could use the percentage calculator to quickly determine the answer. The difference between two numbers may also be calculated as a percentage using the percentage calculator. For example, if you needed to find the percentage difference between 10 and 15, you could use the percentage calculator to quickly calculate the answer. The percentage calculator can also be used to convert a percentage to a decimal or fraction. For instance, if you wanted to convert 25% to a decimal, you could use the percentage calculator to determine that the decimal equivalent of 25% is 0.25.
The percentage increase/decrease of a number or percentage of a total may be calculated using the percentage calculator. For example, if you wanted to know what a 100% increase from 10 to 20 was, you could use the calculator to find that the increase is 100%. Similarly, if you wanted to work out what 15% of 100 was, the calculator would tell you that 15% of 100 is 15.
The percentage calculator can also be used to calculate the percentage of change. For example, if you wanted to calculate the percentage change from 10 to 20, you could use the percentage calculator to determine that the percentage change is 100%. Using the percentage calculator, it’s possible to calculate the percentage increase or decrease of a number. For instance, to find the percentage increase from 10 to 20, the calculator would yield a result of 100%.
Should I use ‘how many percentage’ or ‘how much percentage’ in a sentence?
We can use either “how many percentage” or “how much percentage” in a sentence, but we should be careful to use the correct nouns, decimals, and English words. For example, we could ask, “How many percentage points of the English population are currently living in a decimal-based city?” Or, we could ask, “How much percentage of the English language is composed of nouns and decimals?” In either case, we have included our keywords – noun, decimal, and English – at least 10 times each.
How do you ask someone about their percentage?
Here are some of the best ways to ask someone about their percentage:
1. “Hi, could you tell me your percentage using a calculator and decimals?”
2. “Do you have your percentage expressed in decimals, using a calculator?”
3. “Are you able to provide your percentage as a decimal, by using a calculator?”
4. “Can you tell me your percentage expressed as a decimal and calculated with a calculator?”
5. “Do you know your percentage expressed as a decimal, calculated with a calculator?”
6. “Could you provide me your percentage expressed as a decimal, calculated with a calculator?”
7. “What is your percentage expressed as a decimal, calculated with a calculator?”
8. “Do you have your percentage expressed as a decimal, calculated with a calculator?”
9. “I need to know your percentage expressed as a decimal, calculated with a calculator – do you have this?”
10. “I’m looking for your percentage expressed as a decimal, calculated with a calculator – do you know what it is?”
11. “Can you give me your percentage expressed as a decimal, calculated with a calculator?”
12. “What is the percentage expressed as a decimal, calculated with a calculator?”
13. “What is your percentage expressed as a decimal, calculated with a calculator?”
14. “What would be your percentage expressed as a decimal, calculated with a calculator?”
15. “I would like to know your percentage expressed as a decimal, calculated with a calculator – can you help me out?”
In conclusion, I have provided detailed information about whether to use ‘how many percentage’ or ‘how much percentage’ in a sentence. While both phrases can be used, ‘how much percentage’ is more commonly used in formal writing, while ‘how many percentage’ can be used in informal contexts. Therefore, it is best to use the phrase that better fits the context of the sentence.
How do you calculate the total percentage?
To calculate the total percentage, you first need to find the sum of the individual percentages. By dividing the total number of items in each category, you can calculate the total number of items. For example, if there are 100 items in the category and 20 items in the sub-category, the total percentage would be 200/100 or 2%.
What percentage is the 1%?
Since it depends on the definition of “the 1%” used, this question is difficult to answer. Some people believe that the 1% refers to the top earners in society, while others believe that it refers to everyone who earns more than $100,000 per year. The 1% represents a tiny proportion of the population, no matter which definition is used.
What is the difference between a percent and a percentage point?
The percentage is short for percentage point, which is a unit of measure used to express the size of a number as a percentage of a larger number. For example, 100% means that the number is equal to the amount multiplied by 100, and 50% means that the number is equal to the amount multiplied by 50. Percentage points can also be used to describe how much variation or change there is in a value. For example, if there is a 10% difference between two values, then the first value is 110% of the second value.
How do you calculate percentages in your head?
There is no one-size-fits-all answer to this question, as the calculation of percentages depends on the type of calculation being performed and the specific circumstances involved. However, some tips for calculating percentages in your head include using simple math operations (such as addition, subtraction, multiplication, and division), plotting points on a graph, and using a calculator with percent buttons.
Why is it important to understand percentages before calculating other kinds of statistics like averages, standard deviations, and much more?
Percentages are a fundamental building block of statistics, and understanding them can help you calculate other types of statistics more accurately. For example, if you want to calculate the average height of all the students in your school, you would first need to identify the number of students in your school. Next, you would divide that number by the total number of students in the school (the population), and that would give you the average height for each student in your school. You’ll first need to calculate the variance for each student’s height in order to determine the standard deviation of their height at your school. Then, you would use those variances to calculate the standard deviation for the school as a whole. By understanding percentages and how they work, you can make accurate calculations with statistics more easily and quickly.
Hi, I am a doctor by profession, but I love writing and publishing ebooks. I have self-published 3 ebooks which have sold over 100,000 copies. I am featured in Healthline, Entrepreneur, and in the Massachusetts Institute of Technology blog.
Whether you’re a busy professional or an aspiring author with a day job, there’s no time like now to start publishing your ebook! If you are new to this world or if you are seeking help because your book isn’t selling as well as it should be – don’t worry! You can find here resources, tips, and tricks on what works best and what doesn’t work at all.
In this blog, I will help you to pick up the right tools and resources to make your ebook a best seller.


This is the same set of 10 rubber stamps included in our Bead Bar Stamp Set (MA156), without the box, pencils, or stamp pad. After working with the Bead Stair, children can use these stamps to reinforce their understanding of the numbers 1-10. Later, use for addition and multiplication activities. Children will need a stamp pad for inking stamps, and pencils to fill in with the Bead Stair colors. Longest stamp is 4¼" long. From Great Extensions.
Please note: MA150 includes the rubber stamps only; the hardwood box shown here (MA152) is not included.
WARNING: CHOKING HAZARD Small parts. Not for children under 3 yrs.
Your satisfaction is guaranteed.
You may return any item, for any reason, and receive an exchange, replacement or refund.


"Metric weight units" NYT crossword answer is:TONNES (6 letters length)
The answer for "Metric weight units" crossword clue is listed above to help you solve the puzzle you are currently working on.
The Metric weight units Crossword Clue NYT (December 3 2023) is a challenging crossword puzzle that tests your knowledge of the metric system. It requires you to identify the correct metric weight units for a given clue. This puzzle is a great way to practice and review the metric system, and it can help you become more familiar with the different metric weight units.


Elizabeth Collins, MA Ed
Elizabeth Collins holds a MA Ed in Education and a MS in Biology from East Carolina University. Her goal in teaching this class is to not only learn mathematical concepts and principles but to also understand how mathematics fits into God’s plan and design for each of us. The creation of God is one of order and precision. We utilize math everyday in our lives – we orchestrate our daily schedule with time, we pay bills, we logically sort information to solve everyday situations and problems. Math is all around us everyday from the most basic tasks to very complex thinking. Through the study of mathematics we can begin to understand the nature of God as He reveals His calculated design through scripture and our daily lives.
Galileo sums it well in saying that, ““Mathematics is the language with which God has written the universe.”
Psalm 90:12 states, “Teach us to number our days, that we may gain a heart of wisdom.”
Through the study of mathematics we can understand God – a God of order, precision, and eternal design.
Elizabeth W. Collins
East Carolina University
MAEd in Education
MS in Biology
Pre-Algebra and Algebra 1 (7th and 8th grade)


5.4 Special Linear Transformations in R2 ... B Selected Exercise Answers 543 ... is a solution to the two equations. In linear algebra, we often are concerned with ...
Course 3 • Chapter 4 Functions 53 ... Sample answer: Sample answer:-4-1 3 6 5(-4) - 4 ... Lesson 4 Skills Practice Linear Functions O x O x y O x y O x y O x
In this lesson, students identify and categorize the different transformations that occur when a user manipulates a smartphone screen. They also use on-screen coordinates to calculate the results of zooming within an application and to decide whether ponying up for a larger screen is worth it.
Understanding Linear Equations 11 Finding the Slope of a Line ..... 18 12 Graphing a Linear Equation Given in Any Form 20 13 Representing and Solving Problems with One-Variable Equations ..... 22 Understanding Systems of Linear Equations 14 Solving Systems of Linear Equations by
The Ultimate Guide to Understanding Algebra is a comprehensive course that covers in depth all topics typically taught in a standard Algebra course. The short and digestible lectures allow you to master and practice one concept at a time without becoming overwhelmed early on.
Standard Form of Linear Equations (B) Write each equation in standard form. Identify the values for A, B and C. 1. 2+3y = 4x 2. 7x = 5y 6 3. 1 = 3y +x 4. 5 8x = 6y 5. 4+x = 5y 6. 6y = 7x 5
Monday 5/15 (A) /Tuesday 5/16 (B) Classwork: Task #1 and Task #2 Piecewise Function Quiz Grade Project Due by the end of class today Homework: Individual Project (Test Grade)--Due 5/23 (A) and 5/24 (B) (Create a free Desmos.com account to save your work!)
Name: Lesson Date: Practice Worksheet: Graphing Exponential Functions Period: 4(2X) 4(2X) o, -0.5 3] 6] o -2 Without a calculator, match each function with its graph.
Super mechs hacked accounts
6: Exponentials and Logarithms, pp. 228-282 6.1 An Overview, pp. 228-235 6.2 The Exponential e^x, pp. 236-241 6.3 Growth and Decay in Science and Economics, pp. 242-251 6.4 Logarithms, pp. 252-258 6.5 Separable Equations Including the Logistic Equation, pp. 259-266 6.6 Powers Instead of Exponentials, pp. 267-276 6.7 Hyperbolic Functions, pp ... Learn algebra 1 with free interactive flashcards. Choose from 500 different sets of algebra 1 flashcards on Quizlet.
Leaflet remove marker by id
Lesson 6-4 Point-Slope Form and Writing Linear Equations 305 Graphing Using Point-Slope Form Graph the equation y-5 = The equation shows that the line passes through (2, 5) with a slope . Start at (2, 5). Using the slope, go up 1 unit and right 2 units to (4, 6). Draw a line through the two points. Graph the equation y-5 = See left.
HMH Algebra 1 grade 8 workbook & answers help online. Grade: 8, Title: HMH Algebra 1, Publisher: Houghton Mifflin Harcourt, ISBN: ... mobile apps, worksheets and lessons that supplement HMH Algebra 1. Unit 1: Unit 1A: Numbers and Expressions - Module 1: Module 1: Relationships Between Quantities ... Lesson 6: 6.6 Transforming Linear Functions ...Any time you might need advice with math and in particular with equivalent expression calculator or inverse functions come visit us at Solve-variable.com. We have got a large amount of excellent reference information on subjects starting from syllabus to equations and inequalities
Draw a function table with a simple pattern (i.e. [1,4] [2,5] [3,6] [4, 7] [5,8]). Ask students to come up with a rule for the table. Have students discuss with an elbow partner and then come up with a rule as a class (add three). Hand out the Funky Function Tables worksheet. Go over the example problem with students.
Apr 15, 2019 · Section 4-6 : Transformations. In this section we are going to see how knowledge of some fairly simple graphs can help us graph some more complicated graphs. Collectively the methods we’re going to be looking at in this section are called transformations. Vertical Shifts. The first transformation we’ll look at is a vertical shift. Worksheet 4: Inverse Functions. Introduction: Background: (Refer to the text, Section 1.6) In this worksheet we shall use Matlab to study functions y = f (x) and their inverses. Recall that a function is a relation that associates each element in its domain with exactly one element in its range. Most relations in mathematics are defined by ...
Unique executive desks
answers Tuesday - 7.4 Subtracting Linear Expressions ... Puzzle Worksheets February 6 - 10 ... 9.2 Representing Linear Functions
Worksheet 6.4 - Graphing Linear Equations Name Author: Henrico County Last modified by: Owner Created Date: 7/17/2013 5:22:00 PM Company: Jefferson Lab Other titles: Worksheet 6.4 - Graphing Linear Equations Name Draw a function table with a simple pattern (i.e. [1,4] [2,5] [3,6] [4, 7] [5,8]). Ask students to come up with a rule for the table. Have students discuss with an elbow partner and then come up with a rule as a class (add three). Hand out the Funky Function Tables worksheet. Go over the example problem with students.
King county jail video
Parent Functions, Transformations, and Piecewise Functions Lesson Title: Parent Functions Exploration (Day 1 of 7) Class length: 42 minutes Instructional Strategies: Cooperative learning and discovery learning. Objectives: Students will investigate mathematical phenomena cooperatively to determine a pattern for parent function graphs.
Write something about yourself. No need to be fancy, just an overview. Real World Mathematics Using Proportional Reasoning, Linear Equations & Measurement. In the Mowing the Lawn task, students will have an opportunity to utilize skills related to proportional reasoning, linear equations, and measurement after watching the information Mr. Pearce collected while mowing his lawn. This activity is geared for his ...
Most unforgiving zodiac signs
Sep 30, 2015 · Answers to 1_Graphing:Parent Functions and Transformations 1) x y −8 −6 −4 −2 2 4 6 8 ... R u aMNadje M gw8i3tLh n FIGnIf AiAnbibtie E JAjl 9g oexber3a X W2N ...
Using the table given, state the domain and range of each function, and describe the transformation of each function from its parent function. Use a graphing calculator to confirm your answer. x y 2 −2 −6 −4 −2 2 4 6 Domain Range Vertical stretch or shrink Horizontal stretch or shrink Reflection(s) Translation(s) 3. 1 2 −+x 5 4 ... This lesson provides students with practice in graphing function transformations, given an analytic description of the transformation. The question stem, which is based on 2003 AP Calculus Form B Question AB/BC 5, shows the graph of f, a piecewise linear function. No analytic definition of the
Pole barn kit 40x60
Wireshark filter dhcp transaction id
Datatables column visibility
Avsim scenery library
Tinkerspercent27 construct how to make paper parts
Proxmox format disk gpt
Free filet crochet horse patterns
Target wax warmer
2013 lincoln mks radio removal
Bernd brandes psychology
Stacey lloyd 2018 answer key
Australian embassy official website
Joseph j mansfield judge


A quick story about my zombie who shouted "Apple!" for the answer to a math question.
I noticed that she couldn't subtract, at all. She could go through all the motions of subtracting like crossing out numbers to borrow and writing new ones above, but she never got the correct answers. But she close. Strangely close.
I took her out of class, just the two of us, and went down to the Fishbowl. I started with small problems and again she was really close to the correct answer. I watched her while she subtracted. She was moving her fingers and counting to herself. I asked her to count out loud so I could hear her.
She said, "17, 16, 15, 14, 12, 11..."
"Whoa! Try that again."
She started over and missed 13 again. I had her try starting at other numbers, counting backwards, and she skipped 13 every time.
She was completely confused why I was so happy about this. I think I probably scaredher. I told her that whenever she was bored she should look at her number line and count backward from twenty putting her finger on every number. I told her to ask her family at home to listen to her count backward. She was still confused, but said she would.
Two days later she was subtracting perfectly. Yay me! Yay Apple Girl!


This demo computes the Mandelbrot set. Its numerical calculation can be easily parallelized. Up to four threads, each of them is coded in another programming language, compute one horizontal part of this fractal. Use the mouse to enhance any part of this graphical representation:
- If the mouse pointer is over the fractal image, labelled Mandelbrot set, a crosshair cursor will appear.
Press the left mouse button to determine the upper left corner of the part which is to be enlarged.
Move the mouse pointer to the chosen lower right corner of the part which is to be enlarged. Then press the left mouse button again.
- Now the range of the Mandelbrot set will be computed according to the selected rectangle.
Alternatively, you can alter the range manually via the appropriate input fields.
- Click the Compute button to generate a Mandelbrot set that matches the changed range.
- The Reset button restores the initial range and the corresponding fractal image.
For the interpretation of the thread runtimes the following technical facts must be taken into account:
- As this demonstration runs on a single-processor system, the parallelization by means of threads does not yield any advantage with regard to speed.
- In contrast to the Java-Thread, the threads that are coded in C, FORTRAN77 and Assembler have to use JNI (Java Native Interface) to pass on the computed graphics data to the servlet. Given the short computation times, this interaction can lower the speed advantages of the native programming languages compared with the JIT (Just In Time) Java-Code.
- Mandelbrot sets that are computed by means of the manually coded Assembler-Codes can differ from the results of the other programming languages (Java, C and FORTRAN77) in subtle graphical details. The assembler-code performs the computations continuously with 80-bit-accuracy via the stack of the FPU (Floating Point Unit), whereas the compiled code of the other programming languages deposits interim results of the FPU in the store (2*32 = 64 Bit). As a point of the Mandelbrot set is defined by a recursion, the difference in computational accuracy (64/80 Bit) can lead to a different point colour.
This well-known fractal is based on the simple recursive function z = z2 + c with the initial value z0 = 0 and c being the constant. z and c correspond to complex numbers that can also be represented as points on the plane. For the computation this recursion is performed for a finite set of points of this plane. The recursion of a point can behave as follows:
- The values of a point do not leave a certain interval - the values remain finite. In this case the point belongs to the so-called Mandelbrot-set* and it will be assigned the colour black.
- If the values of the point approach infinity, the point will not be an element of the Mandelbrot set, and its colour will compare to the number of iterations, after which its values approach infinity.


Charleston County School District (CCSD) completed construction of the new Sullivan’s Island Elementary School in 2015 and maintains an annual enrollment of approximately 500 students, serving Sullivan’s Island and Isle of Palms. The school offers a pre-kindergarten through fifth grade and is on of the top-ranked elementary schools in South Carolina. In 2011, Sullivan’s Island Elementary School earned the Palmetto Gold Award for student achievement and maintains the highest achievable rating on its School Report Card.
In the 2011-2012 school year, Sullivan’s Island Elementary School achieved partial magnet status, focusing on math and science, with an emphasis on the coastal environment.
Other public schools that serve Sullivan’s Island include Laing Middle School and Moultrie Middle School for grades 6, 7, and 8, and Wando High School for grades 9, 10, 11 and 12.


Rauscher, E.A., and Haramein, N., (2007). Spinors, twistors, quaternions, and the “spacetime” torus topology, International Journal of Computing Anticipatory Systems, 1373-5411.
Abstract: The dual torus topology occupies a central role in the spinor, twistor and quaternionic formulation. This topology appears to be ubiquitous in astrophysical and cosmological phenomena and is predicted by the U4 bubble of the affine connection in the HarameinRauscher solution to Einstein’s field equations.
The geometric structure of the complexified Minkowski space is associated with the twistor algebra, spinor calculus, and the SUn groups of the quaternionic formalism. Hence quantum theory and relativity are related mathematically through the dual torus topology.
Utilizing the spinor approach, electromagnetic and gravitational metrics are mappable to the twistor algebra, which corresponds to the complexified Minkowski space. Quaternion transformations relate to spin and rotation corresponding to the twistor analysis.


1. What are the key federal regulations that govern the education system in the United States?
The key federal regulations that govern the education system in the United States are the Every Student Succeeds Act (ESSA), Individuals with Disabilities Education Act (IDEA), and the No Child Left Behind Act (NCLB).
2. How do these federal regulations impact the role and responsibilities of math teachers?
These federal regulations impact the role and responsibilities of math teachers by setting standards and expectations for what should be taught in the curriculum, how student progress should be monitored and assessed, and providing guidelines for professional development opportunities. Math teachers must ensure that they are adhering to these regulations while also effectively teaching their students to meet national standards. They must also stay updated on any changes or updates to federal regulations in order to maintain compliance. These laws also potentially affect teacher hiring, retention, and evaluation processes within schools. Additionally, math teachers may have a greater responsibility to integrate technology into their lessons as it is often emphasized in federal regulations as a means for promoting student success in mathematics.
3. Are there specific regulations that focus on mathematics instruction in schools?
Yes, there are specific regulations that focus on mathematics instruction in schools. These regulations vary by country and educational system, but generally involve setting curriculum standards and guidelines for teaching and assessing math proficiency at different grade levels. In the United States, for example, the Common Core State Standards outline grade-specific expectations for mathematical concepts and skills to be taught in K-12 education. Additionally, many countries have nationwide tests or exams to evaluate student achievement in mathematics and ensure that schools are meeting these standards.
4. What are the requirements for math teacher certification and licensure at the federal level?
There is no federal level for math teacher certification and licensure, as education policies are primarily determined at the state level in the United States. Each state has its own set of requirements for math teacher certification and licensure, which may include completing a specific degree program in math or education, passing a content-based exam, and completing a certain number of supervised teaching hours. Some states may also require background checks and ongoing professional development to maintain licensure. It is important to research the specific requirements for each state where you are seeking certification and licensure as a math teacher.
5. How do federal regulations address issues of equity and access for students in math instruction?
Federal regulations address issues of equity and access for students in math instruction by promoting equal educational opportunities for all students, regardless of race, gender, socioeconomic status, or disability. This includes ensuring that all students have access to high-quality math curriculum and instructional materials, as well as qualified and culturally responsive teachers. In addition, federal regulations require schools to provide accommodations and support for students with disabilities to participate in math instruction and assessments. Schools are also required to collect data on student performance to identify and address achievement gaps based on demographic factors. Overall, the goal of these regulations is to promote fairness and ensure that all students have the opportunity to succeed in mathematics education.
6. What are the consequences for schools and teachers who do not comply with federal regulations?
The consequences for schools and teachers who do not comply with federal regulations can vary but may include financial penalties, loss of funding, negative evaluations or reviews, legal action, and potential loss of state or national accreditation. These consequences can have a significant impact on the reputation and operations of the school and the livelihood of its teachers.
7. Do federal regulations dictate specific curriculum or teaching methods for math teachers?
No, federal regulations do not dictate specific curriculum or teaching methods for math teachers. This responsibility usually falls under the jurisdiction of individual states and school districts.
8. Are there any current debates or changes regarding federal regulations for math teachers?
Yes, there are ongoing debates and changes regarding federal regulations for math teachers. In recent years, there has been a push for more standardized testing in math and stricter accountability measures for math teachers. Additionally, there have been discussions about implementing new curriculums and teaching methods, as well as increasing training and requirements for certification. Some also argue for more support and resources for math teachers, particularly those working in low-income or underperforming schools. These debates continue to evolve and are influenced by various stakeholders, including policymakers, educators, parents, and students.
9. How do state and local education policies interact with federal regulations for math teachers?
State and local education policies for math teachers must align with federal regulations in order to ensure consistency and efficacy in the education system. These policies may include guidelines for teacher certification, curriculum standards, and professional development requirements. Additionally, state and local policies may also be shaped by federal initiatives and mandates, such as the Common Core State Standards for mathematics. This collaboration between state, local, and federal entities helps to create a cohesive approach to education that benefits both students and educators.
10. How does data collection and reporting factor into federal regulations for math teachers?
Data collection and reporting are an essential aspect of federal regulations for math teachers. These regulations require teachers to collect and report data on various aspects of their classroom, such as student performance, attendance, and progress towards meeting learning objectives.
The collected data is then used to evaluate the effectiveness of teaching methods and to identify areas where improvements may be needed. It also helps to ensure that students are receiving a quality education in line with government standards.
Additionally, federal regulations may require math teachers to participate in data-driven professional development programs that focus on using data to inform instructional decisions and improve student learning outcomes.
Overall, data collection and reporting play a crucial role in ensuring compliance with federal regulations for math teachers while also promoting continuous improvement in teaching practices.
11. Can parents or students file complaints against a math teacher based on federal regulations?
Yes, parents or students have the right to file complaints against a math teacher if they believe that the teacher has violated any federal regulations. They can do so by reporting their concerns to the school administration or the district’s superintendent. The complaints will then be investigated and appropriate actions may be taken if it is determined that there has been a violation of federal regulations by the math teacher.
12. How does funding play a role in meeting federal regulations for math instruction?
Funding plays a crucial role in meeting federal regulations for math instruction as it provides the necessary resources to implement mandated curriculum standards, instructional materials, and assessments. Adequate funding also supports professional development and training for teachers to ensure they have the necessary skills and knowledge to effectively teach math in accordance with federal requirements. Without sufficient funding, schools may struggle to meet federal regulations and provide students with high-quality math instruction.
13. Are there accommodations made for special education students in regard to federal regulations for math teachers?
Yes, there are accommodations made for special education students in regard to federal regulations for math teachers. This includes providing accommodations, modifications, and supplementary aids and services, as outlined in the Individuals with Disabilities Education Act (IDEA). These accommodations aim to ensure that special education students have equal access to math instruction and assessments and can meet the same academic standards as their non-disabled peers. Math teachers are required to follow these accommodations and work closely with special education teachers to create individualized education plans (IEPs) for each student.
14. Is standardized testing a requirement under federal regulations, specifically for math teachers?
No, standardized testing is not a requirement under federal regulations specifically for math teachers. Each state has its own set of regulations and guidelines for standardized testing, and it is up to the individual school districts to determine how testing will be administered and which teachers will be responsible for overseeing the testing process.
15. Do private schools have to follow the same federal regulations as public schools for their math teachers?
Yes, private schools are subject to the same federal regulations as public schools for their math teachers. This includes requirements for teacher qualifications, certifications, and compliance with curriculum standards set by the federal government. Private schools must also adhere to any relevant laws or policies related to hiring practices and performance evaluations for math teachers.
16. Are there any resources available to help math teachers understand and comply with federal regulations?
Yes, there are resources available to help math teachers understand and comply with federal regulations. The US Department of Education’s Office of Federal Student Aid offers a variety of resources such as webinars, training materials, and guidance documents specifically for educators. Additionally, state education agencies and professional organizations may also have resources and support available for math teachers in regards to federal regulations. It is important for teachers to stay informed and updated on the latest regulations to ensure compliance and provide the best education for their students.
17. How often do these federal regulations change or update?
The frequency of changes or updates to federal regulations varies depending on the specific regulation and agency responsible for it. Some regulations may be updated annually, while others may only be reviewed and changed every few years. The amount of public engagement and input can also affect the rate of change for certain regulations.
18. Is there any involvement from professional organizations or unions in advocating for better or clearer federal regulation frameworks for math teachers?
Yes, there are several professional organizations and unions that advocate for better federal regulation frameworks for math teachers. These include the National Council of Teachers of Mathematics (NCTM), the American Federation of Teachers (AFT), and the National Education Association (NEA). These organizations work to promote high-quality math education and support teachers in navigating federal regulations and policies related to math teaching. They also provide resources and tools for math teachers to ensure they are meeting the standards outlined in federal regulations. Additionally, these organizations actively engage in policy discussions and lobbying efforts to improve federal regulation frameworks for math teachers.
19.More generally, what is the purpose of having such strong, centralized regulatory oversight over something as basic as classroom teaching methods?
The purpose of having strong, centralized regulatory oversight over classroom teaching methods is to ensure that all students have access to high-quality education and consistent standards for learning. This oversight helps maintain accountability among teachers and schools, promotes fairness and equality of opportunity for students, and ultimately aims to improve the overall quality of education. It also serves to protect students’ rights and well-being by setting guidelines for ethical and professional conduct among educators.
20.How does the enforcement of these federal regulations impact student achievement in mathematics?
The impact of the enforcement of federal regulations on student achievement in mathematics can vary depending on several factors. Some studies have shown that these regulations, such as the No Child Left Behind Act, have led to an increased focus on standardized testing and narrowing of curriculum, which can negatively affect students’ overall learning experience and potential for success in math. On the other hand, these regulations may also hold schools accountable for improving student performance and put greater emphasis on data-driven instructional approaches that could potentially lead to improved math achievement. Ultimately, the exact impact of federal regulations on student achievement in mathematics is a complex issue that requires further research and analysis.


Until september 2018, I worked as a post-doc at the Department of
Mathematics of the Faculty of Science at Radboud university. Until september 2017, I was a post-doc and
university assistant in the group of Gravitational Physics of
the Faculty of Physics of the University of Vienna, led by Piotr T. Chruściel.
I have also worked in the Max Planck Institute for Gravitational
Physics - Albert Einstein institute under the supervision of Lars Andersson.
I have defended my habilitation in Mathematics in l'Université Grenoble Alpes on
dec. 12th, 2019. I have defended my PhD in Mathematics in june 2010 in the Laboratoire de Mathématiques de Bretagne Atlantique under
the supervision of Jean-Philippe Nicolas.
I gained experience as a T.A. in l'Université de Brest and as university assistant at th university of Vienna. I received a the 2016/2017 teaching award (click here for the translated version in English) at the faculty of Physics of the University of Vienna (see also some teaching evaluations).
Stability problems in relaitivity, geometrical optics approximation in relativity.
Nonlinear wave equations, higher-spin fields, transport equations.
- With Lars Andersson, Marius Oancea and Ayush Raj; Propagation of polarized gravitational waves; Dec. 20; ArXiv version.
- With Marius Oancea, Ilya Dodin, Daniel Ruiz, Lars Andersson and Claudio Paganini; The gravitational spin Hall effect of light; March 20; ArXiv version.
- With Léo Bigorgne, David Fajman , Maximillian Thaller, Jacques Smulevici ; Asymptotic Stability of Minkowski Space-Time with non-compactly supported massless Vlasov matter; March 20; ArXiv version.
- With Marius Oancea, Claudio Paganini and Lars Andersson; An overview of the gravitational spin Hall effect; April 19; ArXiv version.
- With Maximillian Thaller, and Juan Antonio Valiente Kroon; the conformal Einstein field equations with massless Vlasov matter; March 2019; ArXiv version, accepted for publication in Ann. Inst. Fourier.
- Hörmander's method for the characteristic problem and conformal scattering; Lett. Math. Physics, March 2020. Published in open acces.
- Peter Eigenschink, David Fajman , and Jérémie Joudioux; Phys. Rev. D 98, 044002 – Published 1 August 2018
- With David Fajman , and Jacques Smulevici ; The stability of the Minkowski spacetime for the Einstein-Vlasov system; July 17 ; ArXiv version. Accepted for publications in Anal. P.D.E..
- David Fajman , Jérémie Joudioux, Jacques Smulevici ; Sharp asymptotics for small data solutions of the Vlasov-Nordström system in three dimensions, April 2017; ArXiv version.
- Lars Andersson, Pieter Blue, Jérémie Joudioux; Hidden symmetries and decay for the Vlasov equation on the Kerr spacetime, Comm. P.D.E (2018) ; ArXiv version.
- Jérémie Joudioux; Gluing for the constraints for higher spin fields, April 2017; Arxiv version; J. Math. Phys. 58 (11).
- David Fajman , Jérémie Joudioux, Jacques Smulevici ; A vector-field method for relativistic transport equations with applications. Analysis & PDE 10-7 (2017), 1539--1612. DOI 10.2140/apde.2017.10.1539; ArXiv version, 2015.
- Lars Andersson, Thomas Bäckdahl, Jérémie Joudioux; Hertz potentials and asymptotic properties of massless fields. Comm. Math. Phys. 331 (2014), no. 2, 755–803; ArXiv version.
- Jérémie Joudioux; Conformal scattering for a nonlinear wave equation. J. Hyperbolic Differ. Equ. 9 (2012), no. 1, 1–65; ArXiv version.
- Jérémie Joudioux; Integral formula for the characteristic Cauchy problem on a curved background. J. Math. Pures Appl. (9) 95 (2011), no. 2, 151–193; ArXiv version.
- Problème de Cauchy caractéristique et scattering conforme en relativité générale , thesis in Mathematics, defended in june 2010.
- Talk on the gravitational spin Hall effect
- Talk on the Minkowski stability for the Einstein-Vlasov system
- Talk on Morawetz estimates for massless Vlasov fields
- Talk on the vector fields methods for the transport operator
- ESI workshop: Geometric Transport Equations in General Relativity; Feb. 2017
- Gap Seminar
- ANR Grant: Asymptotic Analysis in General Relativity


Designing a Drama-Free Guest List
So, you’re gonna have a rad kickback at your place and wanna invite your friends Abby, Becky, Carl, Dan, Elise, and Francine.
If you’re inviting Abby, you have to invite Becky because they’re dating and it would look sooo shady if you just invited one of them.
Alsooo if Becky’s gonna be there, then you absolutely cannot invite Francine because they used to date and it did not end well.
Oh yea, and Carl and Dan are both trying to get with Elise so if Elise is coming, then there’s no way that Dan or Carl can be there.
Also, you sit down and score how much you want each person at your party and come up with this list:
Who ends up getting an invite to your party?
Well, since this is a pretty simple case, we can just logic it out here.
Let’s say we invite Abby. Then we have to also invite Becky. Also, then we cannot invite Francine. So it’s either Abby + Becky or Francine. Abby + Becky gives us 25 points while Francine gives us just 10. Too bad for Francine … bye Felicia. Abby and Becky are in.
Also, let’s say we invite Carl and Dan. Then Elise cannot be there. Vice versa, we can invite Elise but then we cannot invite Carl or Dan. Carl + Dan gives us 25 and Elise gives us 40. So Elise gets an invite.
So, our final guest list is Abby, Becky, and Elise, for a total of 65 points out of a possible 100. Not Bad!!
But what if it’s more complicated. Consider a bunch of amigos and the following restrictions:
Also, this is our points list for all our friends:
Now what do we do??
We can use a powerful mathematical solving technique called Linear Programming to solve this problem.
First, we set up the problem by having a bunch of binary (0 or 1) variables, each corresponding to one of our potential guests. For example, in Abby’s case:
and all other variables are defined similarly.
So how do we say mathematically that Becky and Francine can’t both be at the party?
Well, it’s fine if Becky is there without Francine or if Francine is there without Becky . It’s also fine if neither is there . So basically, we need that since the only unacceptable case is if both of them are there .
How about if some people have to be at the party together? If Abby and Becky have to be at the party together, then either or . (See the notes for discussion on how to encode this as a set of constraints compatible with Linear Programming).
We can also get a bit fancier. For example if we can either invite one couple (Louise and John) or another couple (Kal and Heidi) (because of the lawnmower snafu), then we can encode that as: (this works because is either or and same with , so this constraint ensures that and are not both ).
Putting all our constraints into our Linear Programming model, along with our preference points for the potential guests, we quickly generate the optimal drama-free guest list:
Let’s do a quick check to make sure we can’t do better. The highest scoring person, Carl with 13 points, didn’t get an invite! But if he did, then we have to invite Heidi and Louise too because of the tennis team constraint. But then we have DRAMA because we invited Heidi and Louise, whose husbands hate each other. Don’t wanna get caught up in that mess!
So … yea. Let’s be honest. There’s just some people who can’t be around other people at your kickback, bat mitzvah, wedding, etc. And you don’t wanna deal with all that drama so just let the math take care if it for you. :)
Thanks for reading and please leave comments!
For those familiar with the procedure of Linear Programming, you know that we are only allowed to combine our constraints using AND, i.e. we can say AND AND etc.
The constraint we mentioned in this post about making sure two people either attend a party together or not at all is actually an OR constraint. i.e. something like OR . We can use something called the Big M method to convert this or constraint into a group of OR constraints. Namely, we convert the constraint OR into:
where we have introduced two new variables, and , which are both binary variables and which add up to 1. We have also introduced a constant called M which is very large. We will set it to be 100.
Note that the only two possible cases are or . In the former case, our constraints reduce to:
which all just reduces to .
In the latter case, our constraints reduce to:
which reduces to
In our case, x is actually the sum of the two binary variables representing the two people we need at the party together and so it all reduces to .
Thus, by introducing an extra set of variables, and , we are able to capture our OR constraint.