Questions tagged [ratio]

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

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Change in Overall Ratio is Opposite of Change in Groupwise Ratios

The table below displays group-wise success rates of Asian, black and white students as well as their totals in 2020 and 2021. How is it possible that all three groups became less successful from 2021 ...
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19 views

Variance of a ratio of two Poissons

My question is related to Ratio of two binomial distributions. Assume $X\sim \text{Poisson}(p\lambda)$ and $Y\sim\text{Poisson}(q\lambda)$ where $p,q>0$ are constants. I have interest in the ...
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90 views

Mistake in Maths Cambridge Course Book Problem. [closed]

I have seen a problem. However, I am not certain that it is correct. Please try to help me in this. Regards.
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28 views

The Limit of a Ratio given the asymptotics

In my calculations I have had a limit appear and I wish to know its limit and the only information I have are the functions asymptotics. Suppose that, $ T(n) \sim C \frac{\alpha^{-n}}{\sqrt {n^5}}$ as ...
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Proportionality Equation

I’ve been scratching my head with this one. I think I have worked out one part but can’t seem to figure out the second part. “ The volume of wood in a tree varies directly with the tree's height and ...
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33 views

How to Infer Absolute Changes from Percentage Changes?

I have a set of financial "positionbook" data that shows the percentage of traders who are holding "long positions" versus "short positions" in a financial instrument at ...
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1answer
50 views

How can I correctly calculate a percentage of a number

I'm sending a transfer from the Stripe payout service API. I'd like to calculate out the Stripe payout fees ($0.25$%) from each transfer to a bank account? Problem - I need to collect/recoup fees from ...
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1answer
28 views

Which of the following CANNOT be the possible number of boys and girls in the class?

The ratio boys to girls is 5/4. If a few boys leave the class, the ratio boys to would become the reciprocal of the earlier ratio. Which of the following CANNOT be the possible number of boys and ...
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79 views

Why do Trigonometric functions _need_ to be negative?

The Trigonometric Unit Circle is a pretty common thing taught in High-School, yet it doesn't cover some questions I had. There have been questions in the past about why trigonometric functions can be ...
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15 views

Closest Number to two other numbers while maintaing ratio

I wanted to essentially compute the scaling factor of 2 numbers, based on two other numbers (I am unable to describe it well). Eg: Lets say I have an image of size 200x300 (aspect is 2:3) and I need ...
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12 views

proper dilution for different types of dog medication

I have a concentrated liquid supplement I'm supposed to give my dog that was originally meant to be diluted at 1ml / 24ml of water. Now that liquid is not available but I have the same supplement in ...
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How to understand why the alligation technique works well here?

Question: "The ratio of expenditure and savings is 3:2. If the income increases by 15 % and the savings increases by 6 %, then by how much per cent should his expenditure increases?" Doubt: ...
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1answer
43 views

Probability that the (rounded up or down) ratio of two random chosen numbers between 0 and 1 is ODD.

I thought i'd do a simple calculation to calculate that the probability of two random chosen numbers between 0 and 1 is 50%. At least I expect it to be 50%. However, I keep getting that the ...
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31 views

Need to check the logic of this theorem related approximation ratio among A, B,C

I am a student outside the mathematics major. I need a help to check the logic and formulation of this theorem. Let A= 2B =2C is best-case, where A and B are Known values. C is unknown value. Given ...
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2answers
58 views

Ratio estimation to find the total with 95% confidence interval

A survey has been conducted to see how many people in a town of $40,000$ people used Ebay to purchase a product last year. A simple random sample of $230$ is taken and from this sample $52$ people had ...
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26 views

How to solve this problem on alligations using successive technique?

Question : "The diluted wine contains only 8 litres of wine and the rest is water. A new mixture whose concentration is 30 % is to be formed by replacing wine. How many litres of mixture shall be ...
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73 views

Proving inequalities with ratios [closed]

Prove that $(a^2 + b^2)(x^2 + y^2) \geq (ax + by)^2$, with equality if and only if $a: b = x: y$. I have tried proof by induction but am stuck as I am confused on how to use ratios. I have also ...
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1answer
19 views

Transitive relation in proportionality

We know that if A=B and B=C, then A=C [Law of transitivity]. The same thing should be applicable for proportions right? i.e. if A is proportional to B, and B is proportional to C, then A should be ...
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2answers
51 views

How to calculate (a physical) ratio of colors to achieve a target color?

Sorry in advance about my way of expressing this - I am not really a math person to be fair. However, I have been pretty obsessed with an idea I got and that idea requires me to understand something ...
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58 views

What is the proper name for the "second ratio" of a prime number (meaning the second difference / second sum)?

I became interested in the second differences of prime numbers, and as part of my amateur investigations, I wanted simple metric that would allow me to directly compare prime number sequences across ...
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Is there a definition of the words: Quotient, Fractions and Ratio?

I'm curious, do we have a definition of quotient, fraction and ratio? The Wikipedia page is very unclear. To be honest I've used those words interchangeably to mean any expression of the form $$\frac{...
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40 views

In what proportion should water be mixed with spirit to gain 12.5% by selling it at cost price?

How to solve this problem by using laws of proportions analytically? In what proportion should water be mixed with spirit to gain 12.5% by selling it at cost price? Doubt: I feel that the problem is ...
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1answer
37 views

Dividing Rs.69 among 115 students, each girl gets 50 paise less than a boy; each boy gets twice the paise as each girl. How many girls in the class?

Question: Rs.69 were divided among 115 students so that each girl gets 50 paise less than a boy. Thus each boy received twice the paise as each girl received. The number of girls in the class is? ...
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26 views

Log-Ratio of IID RVs

Suppose $X,Y \in [0,\infty)$ are i.i.d. random variables with atomless CDF $F$ and PDF $f$. Their (log-)ratio is denoted $R=X/Y$ and $S=\log{R}$. The CDFs of $R$ and $S$ are $G$ and $H$, respectively, ...
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1answer
83 views

Mysterious ratio

I need some help or hints with a problem I can't seem to fully understand. I tried to experiment with Geogebra and I think I discovered the solution. My problem is that I don't know the reason why it ...
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2answers
22 views

Testing for convergence of expression with variable denominator raised to some constant 'a'

I am practicing some convergence test problems for an exam and encountered a problem I am not sure how to approach: $$\sum_{n=1}^{\infty}\frac{1}{n^{\ln3}}$$ My approach was the following: I used the ...
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22 views

Ratio between two numbers whose value is changed in a fixed proportion

I am sure this is obvious but I am trying to figure it out bottom-up and have hit a wall. $A$ is a fixed part of $B$ where $\frac{A}{B} = 0.25$. A is reduced by $20\%$ so that $B$ is reduced by $5\%$. ...
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4answers
247 views

Can a ratio of sinusoidal functions with the same frequency always be written as a tangent function?

In general, two sinusoidal functions $y_1$ and $y_2$ with angular frequency $\omega$ can be written as $y_1 = A\sin(\omega x) + B \cos(\omega x)$, $y_2 = C\sin(\omega x) + D \cos(\omega x)$. Where $...
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Ratios question related to mixtures

Milkman A adds some quantity of water to a milk-water solution, and thereby the ratio of milk to water in the resulting solution gets inverted. Milkman B realizes this and adds some amount of pure ...
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1answer
22 views

How to devise a formula for lower to higher?

I have to calculate a combined score based on other scores i.e. s1, s2, s3, and s4. For s1 and s2 the higher the number the better. But for s3, it could be 0,1,2,3,4,5. But for s3 the higher the ...
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2answers
35 views

Percentage and Set theory related question

So I have come across a question Where it says that among 500 students from a school, 35% play football, 25% play cricket and 20% play neither. So how many students play both the sports? The answer ...
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Calculating COV(X/Y,Y/Z)

Suppose you have 3 independent random variables with known normal distributions: X, Y, and Z. You then construct the ratios: $\frac{X}{Y}$, $\frac{Y}{Z}$, $\frac{Z}{X}$ where the variance of each ...
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Reduction Ratio Problem

I am trying to work out the relation between a $\mu$step and the distance moved by the moveable mirror in the Michaelson Interferometer: The mirror on the stage is moved by a stepper motor. Inside ...
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26 views

How to find optimal weighting of two ratios with non-zero covariance

Say you had 3 independent variables - A, B, and C with mean values and associated variances (the actual quantities are just an example): $\mu_A=1$; $\sigma^2_A=0.01$ $\mu_B=2$; $\sigma^2_B=0.02$ $\...
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1answer
69 views

$xy=10$ vs $xy\geq 10$

What I understand: $$xy=10\tag{1}$$ Let $x,y$ be two variables. Now, if we increase the value of $x$, then the value of $y$ must decrease, to preserve the validity of $(1)$, and vice versa. What I don'...
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22 views

Is it possible to build a firm connection between compound ratio and chain rule?

I am teaching the chain rule to a student in high school and was thinking about the possibility to justify the chain rule using (but not just by means of them) the cancellation process (which I am ...
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4answers
272 views

If $\frac{x^2-yz}{a^2-bc}=\frac{y^2-zx}{b^2-ca}=\frac{z^2-xy}{c^2-ab}$, prove that $\frac{x}{a}=\frac{y}{b}=\frac{z}{c}$.

Problem: Let $a, b, c, x, y, z$ be real numbers such that $abc \ne 0$, $ ~ a + b + c \ne 0$, $~ (a^2 - bc)(b^2 - ca)(c^2 - ab)\ne 0$, $xyz\ne0$, $x+y+z\ne0$, $(x-y)^2+(y-z)^2+(z-x)^2\ne0$ and $$\frac{...
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3answers
92 views

Ratio between two numbers allowing positive and negative values

I'm working on a project analyzing how many research projects every EU region has been involved in in 2020. My lists show (1) the number of projects each region joined as coordinator, and (2) how many ...
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How does the definition of ratios in book 5 of the Elements allow for dealing with the ratio of incommensurable numbers

Definition in Book 5 of the Elements "Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth, when, if any equimultiples whatever are taken of the first ...
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37 views

Understanding the significance of incommensurable numbers

I am currently reading "The History of Mathematics" by Uta C. Merzbach. I'm confused on the significance and the disruption caused by the discovery of incommensurable numbers. I get that all ...
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20 views

Lacking introspection in a certain category of questions.

Question: "The principal and amount ratio is 4:5 at a certain rate of Simple Interest in a certain time interval. After 3 years the principal and amount ratio becomes 5:7. Then find out the rate ...
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1answer
20 views

How do I interpret the scale factor as a quantity that needs to be divided?

The quantities which are often required to be multiplied to get a fractions of the original value lie between 0 to 1.The operation seems very intuitive to me. However while I need to divide a quantity ...
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1answer
26 views

Algebraically manipulating equations give a different answer than the true answer

I know the title isn’t that specific but honestly, I can’t think of a specific title that isn’t the whole problem. Anyways. Force is directly proportional to mass. Force is directly proportional to ...
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1answer
60 views

How to calculate the width and heights of three rectangles for a given frame

Three rectangles all of different sizes, two aligned left and one right Considering the image above, where: rectangles A, B and C must preserve their aspect ratio ...
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1k views

In time t, a dog does 3 jumps whereas a fox does 5. If distance covered in a jump by a dog is thrice that of the fox, find ratio of speed of dog : fox

This looks (and I think it is) a pretty simple problem. My reasoning is as follows : ...
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1answer
83 views

Ratio of shaded area to that of one of the 5 congruent triangles [closed]

Picture is attached. I want to use similarity to find the ratio but am not sure where to start. Hints are appreciated.
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1answer
35 views

How is it the possible to find the ratio of the sides in the picture

I am trying to calculate the ratio of CE(green) to BE(blue). Given that FC:FM = 3:1 and it's an equlateral triangle. I have tried drawing triangles to get an approximation, and I have drawn it in the ...
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37 views

Got myself in a head spin over defining ratios.

I was just wondering if anyone would be able to confirm a few quick questions I have in relation to making statements about ratios / rates. My understanding is that a ratio is a comparison of 2 or ...
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1answer
46 views

What proportion of the volume of Gabriel's horn could be filled by its surface area?

Space filling curves imply that lower dimensional objects can fill a proportion of higher dimensional objects. Eg. in the case of the Hilbert curve and the 2D space it fills, this proportion is 1. ...
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1answer
111 views

Find the ratio of the shaded areas in a square and circle.

In both pictures, the circle has radius 𝑟. Find the ratio of the shaded area in (i) to the shaded area in (ii). Answer in the form 1 : 𝑥, where 𝑥 is a decimal to 3 significant figures. (i) Area of ...

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