# Tagged Questions

Use this tag when you want to determine the thinking that is needed to solve a certain type of problem, as opposed to looking for a specific answer to a question.

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### What is the optimal strategy when playing head or tail per team

Introduction Once a week, we are playing head or tail in my favorite bar. There are $N$ people in the room and each person is guessing whether ...
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### Solving a polynomial with modular arithmetic.

$x^5+ax^4+bx^3+cx^2+dx+e=0$ Assume that $a,b,c,d,e$ are not arbitrary and that they are known. I was wondering if it were possible to reduce or 'simplify' this using some modular arithmetic. It ...
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### is A an even number?

Let $a,b,c,d$ be positive integers such that $(3a+5b)(7b+11c)(13c+17d)(19d+23a)=2001^{2001}$ hence, prove that $a$ is even. I tried to approach this problem reducting it modulo 6. From which we ...
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### How long would it take Mustafa to do the job alone? [closed]

Murat and Mustafa can do a job together in fifteen days. After they have worked together for five days, Mustafa leaves the job. Murat completes the job in sixteen days. How long would it take ...
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### Solving for $x$ in $x + \frac{s}{s^2+4} = \frac{2x}{s^2+4}$

How would I go about solving for $x$ in this equation? $$x + \frac{s}{s^2+4} = \frac{2x}{s^2+4}$$
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I'm trying to improve my knowledge of statistics and develop my intuition for solving statistical problems. While doing so I've worked on the following exercise: There are 20 players in a checkers ...
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### Related Rate of Cylindrical Cone (Filling + Leaking)

So, we are only told of how to solve related rates with one underlying problem. Either a cone is leaking or Being filled up at some point $x$ but I never encountered both working at the same time. ...
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### Explain the thought process to a given solution for $\frac{1+n}{2^n} =\frac{3}{16}$ please

Part of the given solution to a question leaves me baffled: "...solve the equation $$\frac{1+n}{2^n} =\frac{3}{16}$$ We can check (simply by plugging in values of $n$) that if $\leq n \leq 5$, ...
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### Resources for solving Euclidean geometry problems using symmetries

I know a number of books that treat geometry from the viewpoint of transformations/symmetries. However, very few of them actually teach someone to solve Euclidean geometry problems using said ...
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Knowing $2\pi r =\dfrac{h}{m \left(\sqrt{\frac{e^2}{mr}}\right)}$, How do I prove $r = \dfrac{h^2}{((2\pi)^2m e^2)}$? I started by dividing both sides by $2\pi$ to get $r = \dfrac{h}{m\left(\sqrt{\... 1answer 16 views ### Given an integer$i\in\{1,\ldots,NM\}$, find its place in a matrix of size$N\times M$? The integers$N$and$M$are positive. Given the matrix$\mathbf{A}=\left[\mathrm{a}_{nm}\right]$defined as follows:$\mathrm{a}_{nm}=m+(n-1)M$for all$m\in\{1,\ldots,M\}$and$n\in\{1,\ldots,N\}$. ... 2answers 37 views ### How can I solve this nature log equation?$ln(x+2)=e^{(x-4)}$Is there any way to solve this equation without graphing or using GDC ? Thank you 1answer 25 views ### Recover Marginal Distribution subject to a Constraint I want to identify the marginal of a normal distribution subject to a restriction. Take two normally distributed random variables$x,y$. Their pdfs are denoted by$\phi(x)$and$\phi(y)$. The moments ... 0answers 81 views ### In a sweepstakes giveaway scenario, how does having 2 chances to win the same prize affect the overall odds? In a sweepstakes giveaway scenario where total entries are expected to result in final odds of 1:93,150.685 for/against a single entrant (after adjusting for multiple entries) and can be won by either ... 1answer 28 views ### Finding the number of multiples [closed] I have recently been doing problem solving in math, and I came across this problem: Determine the number of positive multiples of$6$or$9$or both, less than$1000$. I appreciate any help. Thanks! 1answer 82 views ### Finding the Determinant of a particular Matrix I've come across the question of finding the determinant of the$(n\times n)$matrix, given by $$A:= \begin{pmatrix} x & 1 & 1 & \dots & 1 \\ 1 & x & 1 & \dots & 1 \\ \... 2answers 46 views ### Example of inverse semigroup with at least two idempotent elements We say that the semigroup S is inverse semigroup if for any s\in S there is a unique t\in S such that sts=s,\ tst=t. Suppose that E(S)=\{e:\ e\in S,\ e^2=e\} and define$$s\sim t\... 1answer 62 views ### Counting and Abstract Problem Solving [closed] Suppose that you have a bucket holds fiv-sev c, and one holds tw-one c. How could you use them to measure out thre c of water? 2answers 62 views ### Solve equation of inverse functions I have two different functions$y_1=f_1(x)$and$y_2=f_2(x)$, both invertible but quite complex. I am able to find their inverse functions numerically, i.e.$f^{-1}_1(x)$and$f^{-1}_2(x)$, by ... 0answers 49 views ### How do I derive the cubic formula? (without substitutions) I've heard of a number of ways that people have derived a cubic formula (I've even heard of a number of different ways to show the formula itself too). What I want to know is how to derive it without ... 2answers 22 views ### Survival bias and probability Imagine the following situation: A new virus is discovered that is believed to have infected 20% of the population. Anyone infected with the virus has a chance of 50% of dying in their sleep every ... 1answer 27 views ### How can we solve this system of linear inequalities? Let$c_i$be a given non-negative integer for all$i\in\{1,\ldots,n\}$. I would like to find the non-negative integers$a_i$and$b_i$for all$i\in\{1,\ldots,n\}such that: \begin{align} \begin{... 0answers 23 views ### Probabilities of each waitlist person Coming from this,10$Applicants for a exclusive club membership. I found that you can use total probability to consider existing and old members leaving/returning as members in the club, ended up ... 1answer 22 views ### Mpg to l/100km conversion problem? We have two vehicles A: old truck that does 17 mpg (13.84 l/100km) B: old car that does 47 mpg (5.00 l/100km) We are looking to replace one of these vehicles with a new one (of the same size)... 1answer 17 views ### Finding the rate at which the space diagonal of a cube is decreasing This is the context of the question: I'm assuming by the space diagonal (although I'm not sure) to be the area of the right-angled traingle created by the diagonal. Let this space be$V$, then we ... 1answer 73 views ### If$y'+y=|x|$and$y(-1)=0$, what is$y(1)$? If$y'+y=|x|$and$y(-1)=0$, what is$y(1)$? I calculated the integrating factor to be$e^x$. Then$e^x y'+ e^x y=e^x |x|$hence$\frac {d(e^x y)}{dx}=e^x |x|$hence$d(e^x y)=e^x|x|dx $... 4answers 89 views ### How to find unknowns$w_1,w_2,w_3$that satisfy$t=w_1f_1 + w_2f_2 + w_3f_3$? For any$i \in \{1,2,3\}$, let:$w_i \in [0,1]$is an unknown number such that$\sum_{i \in \{1,2,3\}} w_i = 1$.$t$is a known number in$[0,1]$. Suppose that$t = 0.8$.$f_i$is also a known ... 1answer 37 views ### Let$S=[0,1) \cup [2,3]$and$f:S \to \Bbb R$be a strictly increasing map such that$f(S)$is connected. Which of the following statements is true?$f$has exactly one discontinuity.$f$has exactly two discontinuities.$f$has infinitely many discontinuities.$f$is continuous. I know theorems related to connectedness and continuity ... 1answer 44 views ### solve$54 x + 16 y = 2400\$ for integer values of x,y

How to get integer values for x and y that satisfy: $$54 x + 16 y = 2400$$ Someone told me that I can do it using Euclid-Wallis algorithm, but I don't understand it so, if there isn't any else ...