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Questions tagged [ratio]

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

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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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185 views

Ratio of Radius of Circle $B$ to Radius Of Circle $A$ in the form $a + b\sqrt{c}$

The full question is as follows: Suppose $X, Y, Z$ are three different, circles of equal radius which are mutually tangent. Let circle $A$ be the circle tangent to $X, Y$, and $Z$ inside the gap ...
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65 views

Fitting the ratio of skew normal distributions

I have two probality functions that are following a skew normal distribution. I compute the ratio between these functions. Can I approximate this ratio with a skew normal distribution also? Do you ...
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21 views

What does a confidence interval tell you about the relationship between two things?

So I have found a 95% confidence interval for the odds ratio of developing cancer with vitamin A intake. My sample odds ratio was 1.1667 with a 95% confidence interval of (0.5394, 2.5227). I am then ...
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What is the ratio between answers equal to $0$ and answers not equal to $0$?

I was looking at A Conjecture About Prime Numbers and I went into the topic a little bit further. Say you are given the equation: $$\mathcal{N} = \{p_n - p_{n + 1} - p_{n + 2} + p_{n + 3} : p_n = \...
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Confusion regarding direct and indirect propotion.

If $x\ \propto \ y$ and $y\ \propto \ \dfrac{1}{z}$, then which of the following is correct $\color{green}{a.)\ x\ \propto \ z} \\ b.)\ x\ \propto \ \dfrac{1}{z}$ I did $x=k_{1}y,\ y=\dfrac{k_{2}}{...
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93 views

Is there a difference?

Problem: You have a choice of climbing one of three geometrically shaped mountains. One of the mountains is a perfect cylinder, another is in the shape of a cone, and the third looks like the top half ...
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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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25 views

Can anyone explain to me the math behind this code ? Calculating a bullet's trajectory in 2D

following the book Beggining c++ game programming by John Horton on Chapter 9 the author explains us how our character can shoot a bullet, the thing is that there is very little explanations on what ...
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141 views

Sorting on non-additive ratios

We are trying to aggregate and sort records by ratios (CTR = clicks/impressions). For some obscure reasons the technology we are using does not allow us to do this. We can group and sort on additive ...
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280 views

Upper bound for a ratio of gamma functions

I'm trying to find an upper bound for $$\left|\frac{\Gamma(z_1+n)}{\Gamma(z_2+n)}\right|$$ with $n\in\mathbb{N}$ and $z_1,z_2\in\mathbb{C}$. It's equivalent to find an upper and lower bound for $\...
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112 views

Ratio distribution of two specific random variables

Let $Z$ be a random variable with cumulative distribution function: \begin{equation} F_Z(x) = \frac{1}{4 \delta^2}\left( \arccos\left( \frac{2-x^2}{2} \right) - (\pi-2\delta)\right)^2, \end{equation} ...
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131 views

Prove six cross ratio values

I have to prove that the cross ratio of all permutations of 4 collinear points on a line can at most be one of the following values: $$ \left\{ \tau, \frac{1}{\tau}, 1-\tau, \frac{1}{1-\tau}, \frac{\...
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How to do this ratios problem without algebra?

Dinesh had some fiction and nonfiction books. The number of fiction was $4/9$ of the total number of books. After he had donated $80$ fiction books and $25$ nonfiction books, there were $20\%$ as many ...
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25 views

Relationship between a circle inscribed in a square and a sphere inscribed in a cylinder

The ratio of the area of a circle to the area of the square it is inscribed in is equal to ${\pi\over 4}$ and the ratio of the volume of a sphere to the volume of the cylinder it is inscribed in is $2\...
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59 views

Expected value of Rayleigh quotient

I want to compute the expectation of a generalized Rayleigh quotient, i.e., $$\mathbb{E}_{\mathbf{x}} \bigg[ \frac{\mathbf{x}^{\mathrm{H}} \mathbf{A} \mathbf{x}}{\mathbf{x}^{\mathrm{H}} \mathbf{B} \...
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36 views

Reason for ratio function for comparing predicted and actual values produced by Weighted Moving Average?

I am reading a paper that describes an approach towards detecting abnormal flows within a network. From what I understand, the way they do so is by keeping a list of $n$ most recent metrics and then ...
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Splitting expenses in a group

There are three friends A,B,C in a shared room. For a period of 30 days, A and B contributed amounts of 137.5 and 79.62 during the whole month whereas C's contribution is 158 during 12 days only. How ...
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32 views

How to bridge operational efficiency ratio between two periods?

I am looking at operational efficiency as a ratio of indirect production costs to gross profit 1 (GP 1 does not include these indirect costs) (Ind Prod/GP). I have been asked to bridge the difference ...
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48 views

Unexpected number appears

I am working on estimating norms of solutions of the simplified version of the Fokker-Planck equation$$ u_t=\text{div}(b(x)u)+\text{div}(a(x)\nabla u) $$ with $\text{div}\in L^q(\mathbb{R}^d)$ using ...
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Is : $\frac{dx}{\partial{x}}=1$ and what does it mean :$\displaystyle\frac{{\partial}}{d}$ or $\displaystyle \frac{d}{\partial} $?

let $d$ be a total derivative and $\partial$ be the partial derivative with respect to $ x$ , Here i want to know more about these operators and the relationship between them in the context of ratio ,...
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35 views

Given: $ \frac{xm_2 + yn_2}{xm_1 + yn_1} < k $ etc., show: $ \frac{xm_2^g + yn_2^g}{xm_1^g+yn_1^g} < k. $

Given: Strictly positive numbers, $$ m_1, m_2, n_1, n_2, x, y, g, k $$ which satisfy the following properties: $$ m_1 + m_2 = n_1 + n_2 $$ $$ \frac{m_2}{m_1} \le k \le \frac{n_2}{n_1} \le 1 $$ $$ \...
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391 views

Aspect ratio sides calculation

I am working on Android project, where the user needs to take picture of some card (credit card, insurance card, etc). The user needs to align their card in the rectangle shape, that I have drawn on ...
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343 views

Show that monotone likelihood ratio property implies increasing ratio of moments

Suppose that random variables $X_1$ and $X_2$ only take values on the non-negative integers, and they satisfy the monotone likelihood ratio property, i.e. $\forall x>y$, $\frac{f_1(x)}{f_2(x)}\geq \...
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94 views

Selecting rational numbers with maximum ratio of (sum of nummerator)/(sum of denominators)

I have n rational numbers. Out of that I have to select m numbers such that sum of numerators of m numbers /sum denominators of m numbers is maximum. e.g. ...
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413 views

Average K/D of online FPS game

In online FPS games, you can get kills, and you can be killed. You are commonly scored by the ratio of your kills to deaths, simply known as "K/D". It is commonly accepted that the average K/D is $1....
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26 views

Show that a certain ratio of diagonal entries dominates a certain ratio of singular values.

Let $D=[d_{ij}]_{i,j=1,\ldots,4}$ be a $4 \times 4$ “density matrix”, that is, a Hermitian (possibly symmetric) positive definite matrix having trace 1—that is, the (nonnegative) diagonal entries sum ...
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83 views

Ratio of numbers when both can be positive or negative

Suppose I have two series: A and B. Both series are mean 0, and have similar (unknown) volatility. I want to show the 'difference' between the series (i.e. how big one of them is than the other). ...
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291 views

What is the difference between a fraction, ratio, quotient, rational number?

They are mixed everywhere and I can't find a single article that treats them right and with the required rigor they should get. Can someone explain them?
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Mixing pait with ratios

I was wondering if any of you could solve the following equation, Green paint and yellow paint can be mixed in the ratio 4:7 to make a certain lime colored shade. If a painter has 500 ml of green and ...
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213 views

Proof of Menelaus using areas

I've tried to proof Menelaus' theorem using areas, but I've didn't figure out how. Some suggestions would be appreciated. Menelaus' Theorem states : Given a triangle ABC and a transversal ...
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Do all algebraic numbers have a sequence of integers where the ratio of consecutive terms tends to that number?

The most famous example of this is the Fibonacci sequence and the golden ratio. I feel like this should be obvious. But, if I have an algebraic number say: $\tan \left(\frac{15π}{16} \right) \...
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What function describes the frequency for each unique ratio for all possible expansions n over d where n<d?

I am hoping to solve the following problem for a scientific investigation, which relies on the probabilites of all possible expansions. What function $f(r)$ describes the frequency for each ratio for ...
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197 views

Width and height ratio of object in image

I hope I ask this in the correct place. How do I get the width and height ratio of for example a sheet of paper (or some other rectangular thing) from a image. I have built a program that that ...
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535 views

How do I calculate the aspect ratio of a width and height?

I am creating an image upload form. I want to restrict users from uploading images that are not of the aspect ratio of 16:9. What is the formula for calculating an aspect ratio such as this? If w = ...
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34 views

Dividing contents with ratios

I'm taking a mock test and there is a relatively straight forward question that I am not sure about. ...
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27 views

Variance of ratios of correlated values

I want to estimate a scaling factor $s$ between two vectors of scalars $a$ and $b$. In the ideal case it would be constant for all components, so $a = s \cdot b$, however there is some noise in the ...
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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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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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15 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 ...
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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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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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22 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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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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10 views

Turning line around the point but independent of that point

I need to ask you for help. I can't figure it out how to rotate the line around the point which is point of cross with other line BUT at the same time I want my line to be INDEPENDENT of that point. ...
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22 views

Is there an upper bound for the mean of a ratio between two random variables?

Is there an upper bound for the mean of a ratio between two random variables ?
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17 views

bounding min-entropy gain in differential privacy

In privacy-related computer science literature, we say that a randomized algorithm $\mathcal{K}$ that produces a model $\theta$ from a sample $X=(x_1,...,x_n)$ is $\epsilon$-differentially private iff ...
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28 views

Does convergence by the ratio test for sequences implies that the sequence is monotonic?

I wonder, Let's say $(a_n)_n$ is a sequence. If $ \frac{a_{n+1}}{a_n} \to L $ and $ L<1$. Then $ a_n \to 0 $. But, does it mean that $a_n$ is monotonically decreasing? (For every $n$, $a_n > ...
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15 views

Ratios and rounding figures to nearest thousand

I'm using the WHO Suicide Statistics to try and ascertain the rate of suicide per 100,000 of the population. I'm afraid I'm not from a maths background and this is the first time using Stack ...
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24 views

Mixing two different essential oils to their maximum safe dilutions in one carrier oil

I want to mix cinnamon bark essential oil (safe at a maximum 0.5% dilution) with tea tree essential oil (safe at a maximum 15% dilution) in shea butter. Shea butter is safe undiluted. The above ...