# Questions tagged [ratio]

For questions concerning the ratio of a certain quantity to another.

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### Ratio and Proportion Concept clarity.

The milk and water in two vessels $A$ and $B$ are in ratio of $4:3$ and $2:3$ respectively. In what ratio should the liquids in both vessels be mixed to obtain a new mixture in vessel $C$ consisting ...
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### Is the limiting ratio of the Dirichlet inverse of the Euler totient function on average equal to $1$ for all values of $h$?

Let $\varphi(n)$ be the Dirichlet inverse of the Euler totient function which is defined as: $$\varphi(n) = \sum\limits_{d|n} d \cdot \mu(d)$$ where $\mu(d)$ is the Möbius function. Is it true ...
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### Vector ratios on parallelogram

There is a parallelogram ABCD. On length CD there is point E with statement |CE|=2|ED| On length AD there is point F with statement |AF|=1/4|AD| Point S is intersection of length BE and CF. In ...
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### Geometric progression first term and common ratio of progression

Do I simplify? Trying to find first term and common ratio of the progression aswell as the sum of all the terms in the progression for homework please help trying to know what I’m doing wrong so I can ...
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### Formula to adjust two numbers from ratio to another

I have databases of people in countries, with sex, but the sex ratio of the databases don't always correspond with the actual sex ratio of the country. I am looking for a formula to be able to ...
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### $\frac{y}{x-z}=\frac{x+y}{z}=\frac{x}{y}$

If for three distinct positive numbers $x$, $y$, and $z$, $$\frac{y}{x-z}=\frac{x+y}{z}=\frac{x}{y}$$ then find the value of $\frac{x}{y}$ I have tried all types of manipulations, even quadratics ...
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### The origin of the Fibonacci sequence and the metallic means or silver means (also ratios or constants)

Is this equation the origin of the metallic means or silver means? (also ratios or constants) $2^2=(x+1/x)^2−(x−1/x)^2$ As discussed in my previous question, we can link this equation with ...
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### Scale a number but ensure it is greater than a value

I have a grid with a Y-axis with a minimum of 25, and a maximum of 50 but the scale begins at 25 (25-50) and a X-axis with a minimum of 0, and a maximum of 4 that begins at 0 (0-4) I have a set of ...
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### Prove that it cannot be proven that “The United States had more fallow acreage than planted acreage”

Followup question to Prove "If, in a country, there are $x$ fallow acres for every planted acre, yield per planted acre is $1+x$ times the yield per total acre." Given: A ten year ...
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### Converting Ratios

In a community of M men and W women, m men and w women smoke (m ≤ M,w ≤ W). If a person is selected at random and A and B are the events that the person is a man and smokes, respectively, under what ...
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### Show a relationship involving proportions

A ten year comparison between the United States and the Soviet Union in terms of crop yields per acre revealed that when only planted acreage is compared, Soviet yields were equal to 68 percent of ...
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### Combined variation with four variables: Is this even possible to solve?

I have this problem, and I'm quite confused on how to solve it. Mr. Plaridel owned a newspaper publication called Diaryong Tagalog Inc. He observed that when he used 3 printing presses, he can ...
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### Find the ratio of the lengths of chord AB to arc AB

The chord AB of a circle subtends an angle of 60 degrees at the centre. Find the ratio of the lengths of chord AB to arc AB. I tried $sin60 = AB/r = √3/2$ Therefore $r = 2$ and $chordAB = √3$ ...
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### Finding the ratio of 2 sides, and expressing OP in terms of a, b, c

I got a bit confused about this problem, and its something that my country's academic curriculum does not really delve into or practice as much. The Problem: Let $A,B,C$ be three points on a plane ...
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### Find the ratio of the area $EDPQ$ to the area of ABC

In triangle $ABC$,points $E$ and $D$ are on side $AC$ and point $F$ is on side $BC$ such that AE=ED=DC and $BF:FC$ =2:3. $AF$ intersects $BD$ and $BE$ at points $P$ and $Q$, respectively. Find the ...
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### Which is faster between the tiger and the leopard given the relation between the number of paces they take and length of their paces?

$I.$ For every $4$ paces taken by the tiger, the leopard takes $5$ paces. $II.$ The total length of $10$ paces of the tiger is less than the total length of $9$ paces of the leopard. The answer can ...
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### Inverting a ratio distribution

I have a ratio distribution $Z = X/Y$ of two random variables $X, Y$ with the same unknown distribution $f(x), f(y)$. The ratio distribution comes out as $\tilde{f}(z) = \frac{1}{z (\log{z})^2}$ in a ...
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### Time and work problem found to be hard

First pipe passes 4 liters of water per minute less then second pipe. How many liters of water per minute passes through the first pipe if it fills a 480 liter basin 8 minutes longer than the second ...
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### Apples, Bananas and Oranges [closed]

I am having a very slow Friday and cannot think of how to describe my problem in mathematical terms... I have 10 children who each must get an apple, a banana and an orange. Apples come in bags of 3, ...
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### If $\sin{\alpha}=\frac{8}{17}$ and $\sin{\beta}=\frac{15}{17}$, for acute $\alpha$ and $\beta$, then $\alpha+\beta=\pi/2$

Prove that $\alpha+\beta=\frac{\pi}{2}$, if $\sin{\alpha}=\frac{8}{17}$ and $\sin{\beta}=\frac{15}{17}$, where $0<\alpha<\frac{\pi}{2}$ and $0<\beta<\frac{\pi}{2}$. This is what I did ...
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### Ratio between two groups

I want to know among what is the ratio of insured people with disease $x$ to uninsured people with disease $x$. Here are my numbers. Insured, disease $x = 3600$ Uninsured, disease $x = 950$ Insured, ...
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### Trigonometric Ratios and Converse of Pythagoras Theorem Lemma

I am not quite sure what the question is asking here really. I understand the Lemma. Do I prove that $a^2+b^2=1$, using the given expressions for $a$ and $b$? Thank you!
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### How to determine mixing ratio to get desired percentage?

Let's say I have two types of chocolate. Chocolate A contains 70% cocoa and 30% sugar. Chocolate B contains 100% cocoa and no sugar. How can I figure out the exact mixing ratio I need to use to ...
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### I was wondering how I can solve this question as I'm a bit stuck. [closed]

$P, Q$, and $R$ are each mixtures of red and white paint. The percentage by volume of red paint in $P$ is $30\%$. The percentage by volume of red paint in $Q$ is $20\%$. The mixtures $P, Q$, and $R$ ...
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### Determining convergence of series when terms are decreasing by factor less than 1 [duplicate]

Suppose that $a_n > 0$ and that, for n sufficiently large, $$\frac{a_{n+1}}{a_n}\leq 1- \frac{c}{n}$$ for $c>1$ Prove that the series $\displaystyle \sum_{n=1}^{\infty}a_n$ converges. Hint ...
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### Difficult circle geometry question, proof sum of 2 sides ratio equals 1

I have been working on this question for hours on end but not even come close to solving. I have found 2 pairs of similar triangles and an isosceles triangle, and tried to equate the ratio of sides, ...
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### A machine produces B unit goods in A hours… [closed]

A machine produces $b$ unit goods in $a$ hours. How many hours does this machine need to produce $b\cdot c$ unit goods?
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### Value of B in this ratio problem? [closed]

a,b,c integers $a+b+c=45$ $\frac{a}{b}=\frac{3}{2}$ $\frac{b}{c}=\frac{4}{5}$ b=?
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### The ratio between positive/negative numbers

I am creating a model that compares multiple data points of two attributes and compares them vs one another as a percentage of 100. So for instance, comparing the values A=1.24 v B=0.44 would be: ...
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### What formula would I use to scale multiple images to fit in a canvas?

I’m trying to tile random square images with a fixed width and height on a rectangular canvas. The number of images that need to be tiled is a variable. All of the images need to show on the canvas. ...
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### How to find points on a graph from ratios

A bag of 75 balls has a ratio of red balls to green balls is 2:7. If y, which is the number of red balls is graphed as a function of x, which is the number of green balls, which set of points will the ...
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### ratio calculation problem, can someone help?

the problem is like this : an online recipe calls for 2 liter of 3% bleach to 50 liter of water. so, how many liter of 11% bleach to 50 liter of water ? anybody able to teach me ? thanks andrew
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### I Don't understand what is The Relation between Infinite series and limits [closed]

**I Don't understand what's The Relation or difference between Infinite series and limits **
So I was working on this problem $$\sum\limits_{n=2}^\infty \frac{2^n}{n^{100}}$$ After all of my work performing the ratio test, I ended up with a $$\frac{2}{n+1} = 0$$ Therefore, I assumed it ...