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.

learn more… | top users | synonyms

0
votes
1answer
31 views

Lifetime of exponential variable of a battery

Suppose that the operating lifetime of a certain type of battery is an exponential random variable with parameter $\theta=2$ $($measured in years$)$. Find the probability that a battery of this type ...
1
vote
0answers
65 views

Natural Numbers Equation

I am trying to find the $(k_1,k_2,...,k_N)$ tuples solutions to an all natural numbers equation in the following form : Given $n\in\mathbb{N}^{*}$, $N\in\mathbb{N}^{*}$ and $n_i\in\mathbb{N}^{*}\leq ...
1
vote
1answer
31 views

Random variable of a store

The weekly profit in thousands of dollars of Miller's Office Supply Store is random variable X whose cdf is given as follows: $F(x)=0$ for $x<0$; $F(x)=(3/32)(2x^2-x^3/3)$ for $0 \leq x \leq 4$; ...
2
votes
3answers
63 views

The game of craps and dice

The game of craps involves the repeated tossing of a pair of dice. In the game of craps, Nancy throws a five on ther first tos of a pair of dice. ["Five" means that the sum of the number ofr dots on ...
0
votes
2answers
52 views

Problem Solving Question? Sum of the squares

The sum of the squares of two numbers is 247 and the product of the two numbers is 21. How would I find all possible values for the sum of the two numbers?
0
votes
2answers
32 views

Solving an equation

Integrating gives $$\ln\frac{250-X}{40-X} = 210kt+c_1\qquad\text{or}\qquad \frac{250-X}{40-X}=c_2e^{210kt}.\tag{10}$$ When $t=0, X=0,$ so it follows at this point that $c_2 =\frac{25}{4}$. Using ...
0
votes
1answer
57 views

Help , Word Problem

Bob and Bob played golf against each other in a tournament. A marshall keeping their score had a difficult time because both players were named Bob. The scores the marshall recorded were the correct ...
4
votes
2answers
113 views

Primes $p$ such that $p^2$ divides $x^2 + y^2 + 1$

Call a prime $p$ awesome if there exist positive integers $x$ and $y$ such that $p^2$ divides $x^2+y^2+1$. Observation: $2$ is not awesome, because $x^2+y^2+1\not\equiv 0$ (mod $4$). But $3$ is ...
0
votes
2answers
81 views

How to solve age word problems?

Roy is now 4 years older than Erik and half of that amount older than Iris. If in 2 years, roy will be twice as old as Erik, then in 2 years what would be Roy's age multiplied by Iris's age? Is ...
0
votes
1answer
123 views

Math Question on Guess and Check strategy

We always liked poking around Grandpa's attic whenever we had a family reunion. We found all sorts of neat stuff up there. Once we found a bunch of baseball cards, so Grandpa said, "Just divide 'em up ...
1
vote
1answer
69 views

very simple math question

I have this very simple math question: Each person starts working life on a salary of $5000$ dollars and then benefits form an annual increment of $250$ dollars over $40$ years of his career. My ...
0
votes
2answers
39 views

Mod Problem solving

I can't do this last question of my homework that's due in tomorrow. Can anyone hint me on what to do? Suppose $p$ is prime and $k$ is a positive integer Show that if $p$ is odd and $x$ is an ...
0
votes
0answers
56 views

Finding the coefficients of a partial differential equation after a change of coordinates.

I'm stuck in one of the mathematical steps of my physical problem. I've been following the derivation of my equations (starting at section 4) from this article Symmetric Euler-Angle Decomposition of ...
0
votes
2answers
87 views

Playing Detective

Four suspects were assembled in the director's office, having been accused of a devious crime: turning off the light switch during Mr. Buehler's business presentation. It was known that only one of ...
0
votes
0answers
53 views

The trace of a wedge product of matrices

I'm trying understand a computation on Besse's book (p. 371). I already know the curvature operator $R:\bigwedge^2\to\bigwedge^2$ may be written in block diagonal form relative to the direct sum ...
2
votes
1answer
32 views

Calculate the area of this object problem

Stuck on the last questions of my homework that's due in tomorrow. Somebody help. I think it's to do with integration but i can't do it. Can anyone give me a hint?
9
votes
1answer
292 views

Prove that this particular sequence contains an infinite number of sixes

Given the sequence $$2,7,1,4,7,4,2,8,\ldots$$ which begins with $2, 7$ and is constructed by multiplying successive pairs of its members and adjoining the results as the next one or two members of ...
5
votes
1answer
79 views

Is this a problem that has already been solved?

I have a question paper with $n$ True/False questions and I don't know the answer to any of those questions. My objective is to find the answer key of the question paper. All I have is a machine which ...
4
votes
3answers
104 views

Difficulty in solving challenging trig equation

Find $\theta$ on $[0, 2\pi)$ such that $$\cos{\theta}^{\sin{\theta}^{\cos{\theta}^{\dots}}} = 2 + 2\sec^2{\theta}\tan^2{\theta} - \sec^4{\theta} - \tan^4{\theta}$$ I'm not sure on how to tackle this ...
1
vote
2answers
45 views

Find square roots upto infinte times

Evaluate : $\sqrt{1+ 2 \sqrt{1+3 \sqrt{1+\dots\infty}}}$ Is it possible to solve in the following way : Let $x=\sqrt{1+ 2 \sqrt{1+3 \sqrt{1+\dots\infty}}}$ $x^2= 1+ 2 \sqrt{1+3 \sqrt{1+\dots\infty}}$ ...
1
vote
2answers
72 views

Is this Chinese card game solved?

There is a card game here in China, use a standard 52 card deck of cards. Draw four cards and use any elementary operators $(+,-,\times, \div)$, and only use each card value once to get a result of ...
2
votes
0answers
77 views

What are the zero-divisors modulo 12 [closed]

I have tried to answer this problem and have had no success
0
votes
1answer
43 views

Infinetly many primes of form $4k+3$ [duplicate]

Prove that there are infinitely many primes of the form $4k + 3$ (where $k$ is an integer). Note that it is a special case of "Theorem 6 (Dirichlet). Let a and b be positive coprime integers. Then ...
0
votes
0answers
15 views

Prime factorization and its product of a square and a cube [duplicate]

Suppose that n≥2 is an integer with the property that whenever a prime p divides n, p2 also divides n (i.e., all primes in the prime factorization of n appear at least to the power 2) Prove that n can ...
0
votes
1answer
56 views

Greatest common divisor of $3$ numbers

Let $a,b, c$ belong to $\mathbb Z$ such that $(a,b,c) \neq (0,0,0)$. Define the [highest common factor] greatest common divisor ${\rm gcd}(a, b, c)$ to be the largest positive integer that divides $a, ...
8
votes
3answers
178 views

Existence of a certain subset of $\mathbb{R}$

To every real $x$ assign a finite set $\mathcal{A}(x)\subset \mathbb{R}$ where $x\not\in \mathcal{A}(x)$. Does there exist $\mathcal{W}\subset \mathbb{R}$ such that: $$1.\;\;\mathcal{W}\cap ...
5
votes
4answers
269 views

Some Questions regarding preparing for Math Olympiads (searched but didn't get answers)

Many questions have been asked on this site regarding preparation for olympiads like the Putnam. I've read those questions and accordingly decided to start with Engel's "Problem Solving" but I have a ...
0
votes
1answer
47 views

Solving $\int\sqrt{1+(-2ax+b)^2}\;dx$

List item What solution $$\int\sqrt{1+(-2ax+b)^2}\;dx$$Unable to develop anything ...$~$:'( I tried completing squares, but can not move much.
0
votes
0answers
20 views

The radius of a circle grows at a rate of $ 30$ cm/s, that rate increases the area of ​​the circle with respect to time?

I would like to address the question The radius of a circle grows at a rate of $ 30$ cm/s, that rate increases the area of ​​the circle with respect to time? I know I have to derive, but where I ...
4
votes
3answers
61 views

Elementary set theory problem - I get an incorrect result

The problem given is this: $\bigcap_{i \in I}(A_i \cup B_i)$ and $(\bigcap_{i \in I}A_i) \cup(\bigcap_{i \in I}B_i)$ I am asked if they are the same. Here is the reasoning I used: for the first ...
-2
votes
1answer
77 views

What is the next letter in the series? [closed]

What is the next letter in the series? O-T-T-F-F-S-S-E-N-? Answer option: A. T B. E C. O D. N Please describe your solution. Thanks for your help.
0
votes
1answer
34 views

How many smallest number moves need to measure 6 liter of water?

You are given two (unmarked) containers of capacity 9 liter and 4 liter and a huge tank of water. Need is to get measure of exactly 6 liter, of water. A move is either filling a container completely ...
-2
votes
3answers
61 views

How to know number of eggs in this problem?

A women took a certain number of eggs to the market and sold some of them. The next day through her poultry industry, the number left over had been doubled, and she sold the same number as the ...
0
votes
0answers
54 views

Matheletics '13 challenges

I was trying to solve the challenges proposed on Matheletics '13. I'm having trouble solving Hockey Classics, Special Arrangement and Permutation. Can anyone point out the idea I can't see, pls?
0
votes
1answer
37 views

Combinations with multiple kids

In a certain country, it has been found over many years that $55$% of the babies born there are males. For a family in that country with five children, what is the probability that (i) the two ...
1
vote
0answers
52 views

When does a ball in a game of brick breaker never hit the remaining breaks?

I have a block size 2N*2N and some squares are filled with bricks and some aren't. I have a ball that travels distance 1 in the x and y direction and bounces off with perpendicular direction if it ...
0
votes
2answers
33 views

Using plant to find depth of water (triangles)

John and Chris were out in their row boat one day, and Chris spied a water lily. Knowing that Pat liked a mathematical challenge, Chris announced that, with the help of the plant, it was possible to ...
1
vote
2answers
44 views

2 states, 2 interarrival distribution Renewal Process.

Karlin and Taylor (1975): 18. Consider a stochastic process $X(t)$, $t \geq 0$, which alternates in 2 states $A$ and $B$. Denote by $\xi_1, \eta_1, \xi_2, \eta_2, \ldots,$ the successive ...
0
votes
3answers
64 views

Proving this inequality

I am having trouble with proving an inequality. Assume we have two positive real numbers $a$ and $b$ such that $a+b=1$ and numbers $x > 0$ and $y > 0$. Prove: $$\frac{2}{\frac{a}{x} + ...
1
vote
1answer
26 views

Finding F(x) given any reals x and y

I have a problem and I think I know how to solve it so here it is: Determine $F(x)$ if, for all real $x$ and $y$, $F(x)F(y)-F(xy) = x+y$. I tried a couple of cases and these were my results: When ...
0
votes
1answer
35 views

Linking 5 communities by plane, train, and bus

Every pair of communities in a country is linked directly by exactly one mode of transportation: bus, train or airplane. All three modes of transportation are used in the country; no community is ...
2
votes
2answers
34 views

Based on census data and namm data, how many musicians are there?

There are $115,226,802$ households in the US. $58$% of households have at least $1$ musician. $43$% have $2$ or more musicians. How many musicians are there? Any help would be appreciated...
17
votes
12answers
5k views

MENSA IQ Test and rules of maths

In a Mensa calendar, A daily challenge - your daily brain workout. I got this and put a challenge up at work. The Challenge starts with.. ...
0
votes
3answers
52 views

Problem Solving

Here the question on my daughter's 4th grade homework assignment: Sarah is decorating a mosaic board it is 12 inches wide and 16 inches long. Sarah is using square tiles all the same size. What size ...
1
vote
3answers
43 views

Permutations of numbers

Given the five digits $1,3,4,6,$ and $7$. In the following question, it should be understood that repition of a digit is not allowed. (i) How many three-digit numbers can be formed from the ...
2
votes
1answer
64 views

Every point of the interval $(0,1)$ is an interior point of that interval. Thus $(0,1)^0 = (0,1)$.

This is a question I found here (on pg.2 example 1.2.2): http://web.pdx.edu/~erdman/PTAC/problemtext_pdf.pdf Definition of interior and interior point: Let $A \subseteq \mathbb{R}$. The point $a$ is ...
1
vote
1answer
148 views

How to learn problem solving (IMO and IPhO)

I'm not interested in IMO and IPhO actually, but one of the most prestigious universities in my country admits students using a test which is composed by 5 IMO and IPhO questions (or slighly lower). ...
0
votes
1answer
30 views

Problem solving question with average

Johnny had to take a test a day late. His 96 raised the class average from 71 to 72. How many students, including Johnny, took the test? I tried to do trial and error to see how many students there ...
1
vote
1answer
98 views

How many ordered triples $(x,y,z)$ of positive integers satisfy $xyz=4000$

How would I find this out? Is there an equation or summation?
-1
votes
3answers
56 views

no positive roots for $(y+1)^{7}-2(y+1)^{5}+10(y+1)^{2}-1$

Hint for showing that $(y+1)^{7}-2(y+1)^{5}+10(y+1)^{2}-1$ has no positive roots thanks