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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1answer
16 views

For probabilities in sets, why multiply together for the complement but not for the normal probability?

For the birthday problem, the probability that a set of n birthdays (where n=1) contains your birthday is 1/365. The complement is that there is a 364/365 chance that it does not contain your ...
0
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1answer
13 views

Find caluclation to equal this value?

How can I find the calculation needed to reach the given value? This is related to programming but I don't see how I can do this myself. ...
0
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0answers
17 views

Ratio and rate using of SI units

When you have been given the ratio and rate of 4kg:500g do you change the values both to grams making it (8g:1g) or do you keep them in the SI units that they are placed in (1kg:125g) and for what ...
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1answer
35 views

Problem Analysis - Answer but no procedure - Differential Eq.

I stumbled with this problem in a notebook that has been bothering me...The answer is written but there's no explanation nor a steb-by-step procedure or anything. If you know how to analyse the ...
0
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1answer
27 views

What is the name for an ODE with an integral as a side condition?

My question: I have to find a function $y: \mathbb R \rightarrow \mathbb R$ fulfilling $$y^\prime(t) = f(t, y(t)),\ \int_{-\infty}^\infty y(t) dt = c$$ with a given $c \in \mathbb R$. What is the ...
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3answers
42 views

If |G|>1 is not prime, there exists a subgroup of G which is not G or {e}

Question: Prove the following: if|G|>1 is not prime, then $G$ has a subgroup other than $G$ and {e} We know that $\langle g \rangle$ is a subgroup of $G$ by previous part of the question and $G$ is ...
3
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2answers
53 views

Property of the solution for a specific system of non-linear equations.

We are stuck on a proof, and would appreciate any help: Let $\gamma >1$ be a known scalar and let $g,h=1,...,G$ and $s=1,...,S$. Let $\pi _{gs}$, $\beta _{s}$ and $y_{g}$ be known variables with ...
0
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1answer
42 views

Problem Analysis - Answer but no procedure - Finding Trajectories.

I stumbled with this problem in a notebook that has been bothering for the whole day(actually 3)...The answer is written but there's no explanation nor a steb-by-step procedure or anything. If you ...
0
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3answers
47 views

Problem Analysis - Answer but no procedure

I stumbled with this problem in a notebook that has been bothering for the whole day(actually 3)...The answer is written but there's no explanation nor a steb-by-step procedure or anything. If you ...
0
votes
0answers
48 views

Where does the problem statement say sides are *equal*?

In the book How To Solve It, Part I, chapter/section 19, Pólya's hypothetical teacher poses the following problem to prove to the hypothetical student: Two angles are in different planes but each ...
0
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2answers
19 views

The additive inverse for negative values only (otherwise zero)

I want to create a formula that only applies the additive inverse for negative values because I am trying to come up with a simple formula whereby two numbers are entered and if the second is larger ...
0
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1answer
37 views

What is a Single Objective Optimization problem?

I can't find any definition of this problem on the Internet. Could you help me by providing some definition?
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2answers
21 views

The Monthly Cost of the Third House Given the Total Rent Receipts of 186,390 in a Year.

This is how I solved this problem but I have some reservations regarding my answer. 1st house = x ; 2nd house = 3x ; 3rd house = [3x + x] - 2610 12(x) + 12(3x) + 12(4x - 2610) = 186,390 96x = ...
0
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1answer
70 views

Age Word Problem with 4 Variables

Simon is nine years older than Jairus. Simon is four times as old as Joter was three years ago. Joter is eighteen years younger than Marshall. How old is Jairus? The choices are as follow: 10 / ...
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2answers
24 views

Determining the Number of Adult Tickets from a Ratio of 4 is to 5

The ratio of adult tickets to student tickets for the play was 4:5. If the sum of the adult tickets and one half of the student tickets is 260, how many adult tickets were sold? The choices are as ...
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2answers
50 views

Show if $0 \le a <b$ implies $0 \le a^{\frac{1}{n}}<b^{\frac{1}{n}}$

Given that $0\le a<b$ show that $0\leq a^{1/n}<b^{1/n}$ Is this proof by induction? Show it's correct for $n=1$ Assume true for $n=k$, then $0\leq a^{1/k}<b^{1/k}$ holds for some $k$, ...
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2answers
65 views

How do you calculate P(A/B), when event B occurred after event A?

There's really only one question I can't begin to handle when it comes to probability, literally. It's not the only type of question I struggle with, though it's the type of question where I can't ...
0
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1answer
29 views

Isolate points of a metric space with some properties?

Suppose that all dense subspace of a metric space $(X,d)$ is open. Prove that the set of the isolate points of $X$ is dense in $X$. My Idea: all isolate points of $X$ are in any dense subspace, ...
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2answers
41 views

Is there a method or algorithm to solve “in what base is the equation true” questions?

I have been given some exercises in which I'm given some equation that doesn't hold in base ten, and I need to figure out in which base the equation does hold. For example: $\sqrt{41} = 5$ which I ...
1
vote
1answer
184 views

Does there exist continuously differentiable function $f:\mathbb{R}\longrightarrow\mathbb{R}$?

Does there exist continuously differentiable function $f:\mathbb{R}\longrightarrow\mathbb{R}$ such that for all $x\in \mathbb{R},\,\,f(x)>0$ and, $f'(x)=(f\circ f)(x)$? I see this question in ...
2
votes
1answer
76 views

What is the answer of this problem solving question?

You need to order 4 plastic cups for each of the 800 runners. Plastic cups are sold in 2 different pack sizes and you must choose one type of pack only. A pack of 500 costs £12.50 or a pack of 800 ...
0
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1answer
51 views

Wrong ILP solution with LPSolve (simple example)

I added the following example into LPSolve and found a strange issue. I don't want S1 and S2 to overlap within certain margins. ...
0
votes
1answer
112 views

Math Exercises, Highschool Student

I really want to improve my problem solving skills.. However I have found that most of the exercise books (lots of problems) are above my curent level (e.g. Olympiad and College) I am currently in ...
0
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1answer
53 views

Finding subgroups of a group from specific order

Given the following group: $$ \left<\left\{ \begin{bmatrix}a & b \\0 & c \end{bmatrix} \mid a,b,c\in \Bbb Z_{5},a,c \neq 0 \right\} ,\:\: * \right> $$ where ∗ is multiplication. ...
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2answers
69 views

List of N items, randomly putting them in order, showing the procedure ends.

On a bookshelf, there are N tomes of the encyclopedia in random order. Every hour, a librarian takes a tome which is not in place and puts it in its place, and we must show this process will stop ...
3
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3answers
146 views

Examples of open problems solved through short proof

Are there good examples of reasonable open problems in mathematics that had an 'obvious' solution via application of a theorem already known/not yet found in mathematics but could have been found with ...
1
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0answers
32 views

Techniques for computing (approximate or exact) partial sums for functions

Clearly there are several ways of computing the partial sum formulas of many summations, but is there a technique that can compute any partial sum. For example with $\sum_{x=0}^{n} \frac{1}{x}$, ...
3
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4answers
46 views

Prove $F^2_{n+1} - F_nF_{n+2} = (-1)^n$

This is a question about Fibonacci sequences, a sequence in which the previous terms build up upon the current term (e.g. $F_1 + F_2 = F_3$ where $F_1 = F_2 = 1$). How would I go about proving ...
0
votes
1answer
82 views

Finding the Compound Interest on 7500 Dollars at 4% per annum for 2 Years

Find compound interest on 7500 dollars at 4% per annum for 2 years, compounded annually. The choices are as follow: $512 $552 $612 $622 I tried to solve this problem by: C.I. = 7,500(.02) = ...
1
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1answer
22 views

Experiments with random selection: when to respect order?

I have a hard time imagining experiments of this nature without noting the arrangements (I draw that ball with my left hand, the other with my right. I draw that ball first, the other second) so I'm ...
0
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1answer
37 views

Help establishing restrictions for consistency on a linear system.

I'm having trouble wrapping my head around this problems, and others similar to it. I can typically solve systems of linear equations, but some give me trouble, especially dealing with unknown ...
0
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1answer
66 views

The Profit Gained by a Shopkeeper who Uses an 800gm Weight Rather than a Kilogram weight

A shopkeeper professes to sell his goods at $200 but uses a weight of 800gm instead of kilogram weight. Thus, he makes a profit of The choices are as follow: 20% 22% 25% None of these The ...
7
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2answers
79 views

For which $n, k$ is $S_{n,k}$ a basis? Fun algebra problem

Here it is a nice algebra problem I had some fun with Let $V$ be a vector space over $\mathbb R$ of finite dimension $\dim V = n$. Let $v = \{ v_1, \dots, v_n\}$ be a basis for $V$. Let $$S_{n,k} = ...
1
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1answer
103 views

What's the Total Number of Candidates who Applied for the Exam?

In an examination, 5% of the applicants were found ineligible and 85% of the eligible candidates belonged to the general category. If 4275 eligible candidates belonged to other categories, then how ...
1
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1answer
57 views

Solving equation with exponentials

How to solve $ {z = x^y, x = y^z, y = z^x }$ for $ x, y $ and $ z? $ Is some sort of triple Lambert W to be introduced? Done so far: Taking logs, $$ \log z = y \log x , \log x = z \log y , \log ...
1
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1answer
50 views

How to best approach a problem of this kind (problem solving and simple linear equations)

This is a common type of problem that appear on algebra tests to test problem solving abilities (this is not from a real test or homework). I am curious on how to best approach these kind of problems ...
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2answers
116 views

Trouble with Vakil's FOAG exercise 11.3.C

I'm having trouble with the exercise in the title, even with part (a), which asks to prove that if $X$ is a closed subset of $\mathbb{P}^n_k$ of dimension at least 1 and $H$ is a non-empty ...
1
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1answer
41 views

One hundred indistinguishable ants are dropped on a hoop of diameter 1

I have this question which I am not sure how to solve: One hundred indistinguishable ants are dropped on a hoop of diameter 1. Each ant is traveling either clockwise or counterclockwise with a ...
2
votes
1answer
40 views

Finding the best fit of 3 categories ( restaurants/meal/person analogy problem )

I have this problem that sounds tedious and long and I'm not sure if there exist an intuitive way to solve it. The problem is related to image recognition but I will try to give an analogy to it You ...
1
vote
1answer
105 views

Time & Distance : Pokemon Hunter and the Rogue Brook

I was working my way through some Puzzles in Discrete Maths by Rosen, when I came across the following question: A Pokemon Hunter is rowing upstream a brook As he passes under the ...
62
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23answers
9k views

An example of a problem which is difficult but is made easier when a diagram is drawn

I am writing a blog post related to problem solving and one of the main techniques used in problem solving is drawing a diagram. Essentially, I want to illustrate that some hard problems (for example, ...
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0answers
30 views

problem solving on work rate

please tell me this problem has insufficient data.. 5 men and 2 boys working together can do four times as much work as a man and a boy. working capacities of a woman and a boy are in the ratio ... ...
0
votes
1answer
28 views

Find the probability for … [duplicate]

Suppose we uniformly and randomly select permutations from the 20! Permutations of 1, 2, 3,..., 20. What is the probability that 2 appears at an earlier position than any other even number in ...
1
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1answer
57 views

Defining addition of vectors of different dimensions

While doing real data analysis I came up with a problem. I have given lots of efforts to solve it and could not succeed. Here is the problem: Suppose, we have a set of vectors ...
0
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1answer
40 views

how to reduce a fraction?

I solved expression and saw this solving, but I didn't see the way to reduce one. $$\begin{align}\frac{a+2\sqrt{ab}-3b}{ab(a - \sqrt{ab} - 3\sqrt{ab -3b})}=\frac{1}{ab}\end{align}$$ Can you show me ...
2
votes
1answer
42 views

Sequence pattern question

I have the following question. Let $S_1$ be the sequence of positive integers $1,2,3,4,5 , \ldots$ and define sequence $S_{n+1}$ in terms of $S_n$ by adding $1$ to the integers of $S_n$ which are ...
1
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2answers
46 views

Making up groups of Coins [duplicate]

In how many ways can a group of 100 coins be made up from 50,20,10,5,2 or 1 coin(s) respectively? An alternative way of phrasing this would be how many ways can a group of 100 coins be made from ...
0
votes
1answer
53 views

Polar coordinate system : Is radial coordinate is a function of angular coordinate?

In polar coordinate system: The polar coordinates $r$ is called the radial coordinate and $\theta$ is called the angular coordinate, often called the polar angle. I am confused when answering the ...
0
votes
1answer
51 views

How do you compare carsharing plans to calculate the cheapest?

Call hourly rate = HR. Assume that I can guess my monthly usage in hours, which I call $g$. Beware that the fixed fees are presented in different units of time, so first convert everything into ...
0
votes
1answer
79 views

Different ways to write $n$

What is a general formula $n(n)$ for this? We know that starting from below, we can see how many numbers a certain $n$ generates by counting the number of numbers contained in the column $n$ is in, ...