Questions tagged [ratio]
For questions concerning the ratio of a certain quantity to another.
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Find the ratio of the area of the triangle $PRQ$ ¸and the area of the triangle $ETA$
the problem
On the side $BC$ of the triangle $ABC$, the points $D$ and $E$ are considered such that $BD = DE = EC$. Let $M$
the middle of the segment $AD$, $BM ∩ AE = {P}, CM ∩ AE = {Q}$. $RM$ ¸and $...
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Finding the general convolution of probability function with hypergeometric PDFs.
I am trying to find the generalized convolution of this PDF distribution.
$$f(n, \sigma; v)= \frac{2^{\frac{3}{2}-\frac{n}{2}} \sigma ^{-n-1} v^\frac{n - 1}{2} K_{\frac{ n - 1}{2}}\left(\frac{v}{\...
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Reference for the lemma that, given $0<A<180^\circ$, function $f(x)=\frac{\sin x}{\sin(A-x)}$ is injective for $0\leq x\leq A$
There is a geometry lemma used in my mathematical community which states:
Given an angle $A$, $0 < A < 180^\circ$, the function $$f(x) = \dfrac{\sin(x)}{\sin(A-x)}$$ is injective, for $0 \leq x ...
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Understanding this ratio trick
Two numbers are in the ratio $3:5.$ If $9$ is subtracted from each, they become in the ratio $12:23.$ Find the smaller number.
Solution
Let's denote the two numbers as $3x$ and $5x$.
According to the ...
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What would be the best position in pick order when picking a card out of a bowl with one bad card? [duplicate]
Let's say there are 10 people, and each person has to pick a random card out of a bowl consisting of 10 cards; 9 good ones and 1 bad one. I was wondering what position to pick a card from the bowl ...
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Efficiency of ratios
Suppose we have a computer application and we want to calculate the influence of the frequency in the final runtime.
If this application is executed at 2 GHz this takes 1000s, whereas if the ...
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Linear coupled recursive relations and finding the limit of the ratio
Let $a_0,b_0$ be any two positive integers. Define $a_n,b_n$ using the relations:
$$a_n=a_{n-1}+2b_{n-1}, b_n=a_{n-1}+b_{n-1} \forall n \in N$$
Find: $$\lim_{n \to ∞} \dfrac{a_n}{b_n}$$
My attempt:
I'...
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Converting ratio with range [0<x<inf] to range [-inf<x<inf]
I am creating some statistics, one of them is a ratio of positive integers, each in range [0<x<inf]; the ratio takes on the same range. I am interested in using a formula to convert such a ratio ...
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Proof for $\frac{x}{a} = \frac{y}{b} = \frac{z}{c} = \frac{\sqrt{x^2 + y^2 + z^2}}{\sqrt{a^2 + b^2 + c^2}} $ [closed]
My teacher used this relation to prove another result, but I can not seem to wrap my head around it.
$\frac{x}{a} = \frac{y}{b} = \frac{z}{c} = \frac{\sqrt{x^2 + y^2 + z^2}}{\sqrt{a^2 + b^2 + c^2}} $
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Why is a resolution of portrait mode 480 x 640 described as 4 : 3 instead of 3 : 4?
As I've read that:
The aspect ratio of an image is the ratio of its width to its height.
For instance, if a rectangle has an aspect ratio of 2:1, then it is twice ...
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Sharing of profit in a partnership
I have two theories and I was pondering on what basis we are choosing one over the other. Let me take specific example and describe the two theories and any discussion in this regard would be helpful ...
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Given the direction cosines of two mutually perpendicular lines, show the direction cosines of the lines perpendicular to the above two lines are:
I just want to ask that if it is written two equations of relations of l, l1, m, etc. How did he write it in that ratio or fractional form like l upon something and m upon something etc and made it ...
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Mean and variance when sampling temporal rates
I having some trouble understanding how mean and variance are be used in sampling rates and temporal rates (per unit of time).
Example
If I eg. wanted to evaluate car crashes per hours driven I would ...
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Adjusted nominator for a more reflective ratio change
Two variables change every year, e.g. $a_1=500$, $a_2=600$ and $b_1=1000$ and $b_2=800$. Their ratio change is
$$YoY=a_2/b_2-a_1/b_1=600/800-500/1000=0.25$$
The negative change in the denominator is a ...
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Ratio Scale transformation
I am in a pickle, and I would genuinely appreciate it if you could guide me.
I spent 2 years to find a way to develop a ratio scale, and I did it; however, it cannot be used the way it is.
The scale ...
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