Questions tagged [ratio]

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

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23 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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4answers
53 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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0answers
16 views

what is the selling rate at which all five people earn same amount of money, [on hold]

Five people have oranges in ratio of 1:2:3:4:5 they have to sell the oranges , what is the selling rate at which all five people earn same amount of money, the selling price must be same for all ...
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2answers
1k views

How many servings of cereal in 450-gram box?

I am helping my brother with his math again - I need a way to explain this to him!I am ages past this and don't have the time to find an explanation and figured that asking here would be quicker. The ...
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2answers
22 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
48 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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2answers
850 views

Ratios of combination

A glass contains vinegar and water in the ratio 1:3. Another glass twice the capacity of the first has vinegar and water in the ratio 1:4. If the contents of both glasses were mixed together in ...
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3answers
32 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
48 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
60 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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98 views

Simple ratio problem

I am currently working through some tests for graduate schemes and I am finding the maths tests relatively okay despite the time restrictions. However, I have come across one basic ratio question that ...
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0answers
19 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
1k views

Calculating relative difference between two data sets which include negative numbers

I need to determine the relative difference between each element in vector 'A' and its corresponding element in 'B'. The vectors are: ...
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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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2answers
941 views

Excel function to divide a whole number into whole parts, according to a multi-part ratio

Suppose I have a number of objects N, and I want to separate them into three or more buckets according to a known ratio, let's say x : y : z. The value N does not necessarily divide perfectly along ...
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0answers
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
44 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
1k views

If $ \frac{y}{x-z} = \frac{x+y}{z} = \frac{x}{y} $ find the ratio of $x$, $y$ and $ z$

I have this question from higher algebra by Hall and Knight: if $ \frac{y}{x-z} = \frac{x+y}{z} = \frac{x}{y} $ then find the ratio of x,y and z? There are two answers given for this question, the ...
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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
24 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
33 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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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
38 views

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
30 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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1answer
1k views

Proving Ratios And Proportions

Help me solve this problem! I have tried it many times but nothing appeared. This is the question: If a:b=c:d=e:f, prove that each is equal to (a+c-e):(b+d-f).
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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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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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1answer
14 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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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 ...
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2answers
176 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
37 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
54 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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0answers
15 views

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
9 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
41 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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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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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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2answers
1k views

Solving a Ratio Problem with Three Variables

A question that just popped in my head after reading an article: If the radius of Planet X is 16% larger than that of Earth, and Planet X has 40% the radius of Planet Y, then what is the radius of ...
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1answer
834 views

Ratio Calculation in Linear Programming?

i struggle a bit with ratio and fraction calculations, so im just looking for some explanation for dummies of this one. in linear programming, i have a ratio constraint of 6:5, of product A to ...
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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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1answer
3k views

Convert odds ratio based on unit change to several unit changes

Imagine to have two groups of people, the first one more strongly exposed to a pollutant than the second one, and the first one developing a certain disease more often. Having measurements of the ...
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1answer
23 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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2answers
40 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
699 views

Fuel and Oil Ratio Problem

Joel mixes petrol and oil in the ratio 40:1 to make fuel for his leaf blower. (i) He pours 5 litres of petrol into an empty container to make fuel for his leaf blower. How much oil should be added to ...
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2answers
403 views

Calculating Percentage Error in the Ratio when there is an Error in Numerator or Denominator or both ?

I have serached google a bit, but Since Google searches for keywords and also I find it hard to put in a statement for which It can give me useful searches, I am asking it here. So, This is Question ...