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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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 ...