Questions tagged [ratio]

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

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1answer
19 views

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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40 views

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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1answer
16 views

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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1answer
22 views

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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1answer
27 views

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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1answer
34 views

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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3answers
417 views

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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0answers
15 views

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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1answer
19 views

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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3answers
54 views

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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5answers
72 views

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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2answers
23 views

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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3answers
52 views

If the AM and GM between two numbers are in the ratio $m:n$, then what is the ratio between the two numbers?

If the AM and GM between two numbers are in the ratio $m:n$, then what is the ratio between the two numbers? I have tried many approach like Let's two number be $a$ and $b$ Then their AM will be $\...
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3answers
34 views

Problem understanding proof of ratio test

The ratio test states that for an infinite series $$\sum_{n=1}^{\infty} a_n $$ if $\lim_{n\rightarrow \infty} \frac{|a_{n+1}|}{|a_n|} <1$, the series is convergent and if $\lim_{n\rightarrow \infty}...
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1answer
33 views

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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2answers
50 views

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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3answers
61 views

How to add up two percentages

I have two fraction: first one: $\frac{a}{b} $, where $0<\frac{a}{b}<1$ second one: $\frac{c}{d}$,where $0<\frac{c}{d}<1$ I apply this two percentages on two positive numbers: $q>0,k&...
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22 views

Absolute Value of Vector with only 2 values and one Angle?

How do I calculate the absolute Value of a Vector when I only know the Values of two Vectors and the angle between them? The Vector I wanna find is the resulting Vector after you add the other 2. ...
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1answer
29 views

How can I calculate the ratio required to line up these rectangles?

I have two rectangles of different sizes which need to slide horizontally, left and right. The left side of each rectangle needs to line up above P1 when the rectangles are fully right (diagram A). ...
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1answer
25 views

What are some examples of statement-reason format for ratios of segments?

I'm wondering what some examples might be for a proof (statement/reason format) that required you to find the length of two segments if you know that their ratio is $x:y$ and that the total length is $...
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2answers
35 views

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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19 views

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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1answer
45 views

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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2answers
25 views

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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2answers
25 views

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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2answers
35 views

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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0answers
23 views

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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1answer
19 views

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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2answers
31 views

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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1answer
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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 **
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1answer
31 views

Ratio of Means of two numbers 10 and 100

Table I was reading a book on computer architecture for my exam and came across this table. I understand all the columns except for the ratio of means. How is the ratio of means of 10 and 100 become ...
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3answers
47 views

Why does this series diverge using Ratio Test?

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 ...
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2answers
97 views

Equation Involving Ratios

In some of my research, I found multiple equations of this form: $$\frac{ax+b}{cx+d}=k$$ where $a,b,c,d$ are all non-zero integers. Is there a way (that doesn't include factoring or checking within a ...
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1answer
15 views

Proportionality of Products

If A is directly proportional to the product of B and C where B and C are not constants, can we always say that A is directly proportional to B and also that A is directly proportional to C?
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16 views

Is any line inside similar triangles is scaled with same similarity ratio like median, height, bisector?

In two similar triangles their median, height, angle bisector and perpendicular bisector (upon middle of a side) are all scaled like perimeters (with same similarity ratio). But can I say so for any ...
4
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2answers
178 views

Does the sign matter for proportionality?

This question arose from Physics, where the force on an object attached on a spring is proportional to the displacement to the equilibrium (that is, the rest position). Also, if the displacement to ...
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2answers
38 views

Can one combine proportions like so?

If $$y \propto x$$ and $$y \propto \frac1z$$ does this imply $$y \propto \frac{x}{z}$$ is true? I've tried a few cases and it has worked every time, however I can't find any information on the ...
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1answer
63 views

Finding integer coordinates for a pentagon, hexagon, heptagon, octagon, and nonagon, etc.

Wondering what the formula is for finding integer coordinates for an arbitrary "regular" polygon. By regular I mean symmetrical polygons like pentagon, hexagon, etc. In particular, I would like to ...
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2answers
32 views

Two parts of first ratio and one part of second ratio

I was preparing for Quantitative aptitude exams and I came across this question of ratios An alloy contains copper and zinc in ratio 5:2 and another alloy contains zinc and tin in the ratio 3:2. ...
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0answers
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Calculating probabilities from sigmoids

The problem is that I would like a user to rate a genre on a scale from 1 to 100. This input would go into the function as $x and return a number from the sigmoid function. The reason for the sigmoid ...
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0answers
10 views

Ratio of project costs to interviewer costs

I am not sure should I add up all the supplier cost but I still can't find the answer. Any ideas
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0answers
42 views

what does it mean that plane XY divides the line joining (2,4,5) & (3,5,-4) with a negative ratio

What does it mean that plane $XY$ divides the line joining $(2,4,5) \text{ and } (3,5,-4)$ with a negative ratio? It's an old question I saw when I was in high school. Search results didn't help. I ...
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1answer
50 views

Geometric problem about ratios of line segments: How to transform the limiting case method to a rigorous answer?

In $\triangle ABC$, $D, E, F, G$ are points on the sides of the triangle such that $BD:DE:EC=1:2:3$, $AF:CF=1:1$, and $AG:BG=2:3$. Find the ratio $FH:DH$. My classmate has come up with a brilliant ...
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1answer
11 views

Simple question about averages and proportions/ratios

I'd like to get the global average of 2 numbers in their proportions. How's that possible? Here is the example of what I want: ...
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2answers
41 views

Problem-solving with ratios and similar triangles.

The following question is designed to test problem-solving and reasoning skills with ratios and similar triangles. Without using Pythagoras Theorem or Trigonometry this question is supposed to be ...
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1answer
25 views

Dividing two equations to find a ratio [closed]

The question is: In the moon, the acceleration due to gravity is $1.6 m/s^2$. Calculate the difference in the period (the ratio) of two identical pendulums if one were on Earth and one on the Moon....
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0answers
24 views

Scaling rectangle and keeping ratio when height and/or width exceed container

I have a 2D box with a Height of 206 and a Width of 202. Inside of this box is a Rectangle. ...
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0answers
22 views

I want to find a ratio between $\displaystyle T_{2}$ and $\displaystyle T_{1}$

I have the following variables: $$ T_{2}, T_{1}, a_{2}, a_{1}, b_{2}, b_{1}, w, x, y, z$$ These are the following relations that I've found: \begin{align} T_2 &= a_2 + b_2 \\[1ex] T_1 &= ...
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0answers
79 views

Are my calculations of the pregnancy ratio of the population correct?

So this question is a math question having to do with me calculating the rate of population growth starting from a population of 100,000. I have already gotten the first 3 steps done(sex ratio, ratio ...
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1answer
49 views

Ratio question help: are my answers correct?

From the question given below, I am trying to, firstly, find the proportion of iPhone users from the information provided in the Business Scenario. Secondly, I am trying to find the share of Android ...