Questions tagged [ratio]

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

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-3
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0answers
26 views

Ratios of Areas [closed]

The question I wanted to know about some ratio in a circle and with its certain rectangle I posted a link which has the question with a picture
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2answers
42 views

GCSE vectors question [closed]

click here for question I have this question and I know the answer - $(1:1)$ but don't understand how to get this? the only thing I tried was to first set $C\rightarrow X$ to y and $X\rightarrow F$ as ...
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3answers
42 views

Let's assume 1 kilogram is equal to 2.2 pounds. But I got: 1 : 2.2 = lb : kg

Let's assume 1 kilogram is equal to 2.2 pounds. $1 kg = 2.2 lb$ So we get: $1/2.2 = lb/kg$ Which means: $1 : 2.2 = lb : kg$ So if we convert 5 kg to lb and y stands for the pound number, we get: ...
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2answers
68 views

What is a Rate in this Wikipedia sentence?

"In mathematics, a rate is the ratio between two related quantities in different units. If the denominator of the ratio is expressed as a single unit of one of these quantities, and if it is ...
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1answer
22 views

Does $\frac{\text{clockrate}(P_2)}{\text{clockrate}(P_1)}=1.37$ say that $P_2$ is $37\%$ faster than $P_1$, or the opposite?

Sorry for the trivial question, but ... Does this ratio say $P_2$ is $37\%$ faster than $P_1$, or the opposite? $$\require{cancel} \frac{ClockRate(P_2)}{ClockRate(P_1)} = \left(\frac{(1.2 \times 10^...
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1answer
38 views

What should I do to get how much juice is to be added?

A certain brand of beverage contains $60\%$ orange and $40\%$ mango juice. How much mango juice must be added to $2.4$ liters of the beverage in order to get a mixture which is $30\%$ orange and $70\%$...
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0answers
33 views

Increasing and Decreasing a Number by a Given Ratio

In my Grade 9 textbook, it was asked of me to increase 40 by a ratio of 5:4. I can solve the problem, but I don't conceptually understand it. $$ 40 \times \frac{5}{4} = 50 $$
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1answer
35 views

Mass of an element in an Alloy [closed]

An alloy is prepared by mixing metals A, B, C in the proportion 3 : 4 : 7 by volume. Weights of the same volume of metals A, B, C are in the ratio 5 : 2 : 6. In 130 kg of the alloy, the weight, in kg, ...
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1answer
23 views

How to calculate the range [0,1] of a line section in ratio to the total line length?

(Disclaimer: I am a programmer, not great in maths, so sorry if I don't explain my question in proper mathematical terms. Moreover English is not my first language, which makes it even harder for me ...
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26 views

More details on ratio of means vs. mean of ratios

I have seen some other posts related to using the ratio of means vs. the mean of ratios, but I'm still confused about some things and hoping to get a little more clarity. First, from what I've read, I'...
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2answers
38 views

Why can't I use ratio in this ??

The Question: Average salary of 60 employees is 12000 per month. Number of executives is twice the no of non-executives. If average salary of non-executives be 2/5th of the average salary of ...
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0answers
27 views

Why don't gear ratios in manual transmission gearboxes always follow a discrete exponential curve?

This question is going to go a bit into the automotive industry, but I've always wondered how and with what methodology car manufacturers choose the specific gear ratios for their car transmissions. ...
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1answer
31 views

Determining the number of times a rectangular object must be tossed.

Suppose the four faces of a regular rectangular object are marked with letters A, B, C, and D, respectively. How can we determine the number of times this object must be tossed so that the probability ...
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1answer
19 views

Proper notation when converting ratios to fractions

When converting ratios to fractions which is the correct way of doing it? I've seen conflicting information that says the the denominator should be the total while other sources say the denominator ...
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2answers
54 views

Are ratios preserved when multiplied infinitely? [duplicate]

If I offered to give you \$10 but steal $5 from you, you should take that deal. You should take it once, and again, and again. You will always gain money no matter how many times you take it and the ...
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1answer
31 views

Equivalent of absolute value when referring to reciprocals

I'm currently unaware of terminology or notation that refers to "some function" of a rational number similarly to how "absolute value" relates to a number. Let me explain. If one ...
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1answer
11 views

Question relating to inverse proportionality.

I just came across a question I can't seem to understand, perhaps it it worded wrong that I do not know. The question is: $y$ is inversely proportional to $x^3y=44$, when $x=a$. Find $y$ when $x=2a$
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1answer
25 views

Getting from $A$ to $B$ (both constants) given $n$ iterations of $A*=x$. What's the ratio of $n/x$? How to express algorithmically?

For context, I created code of the form: A = 0.125 n = 20 x = 1.1 for (int i = 0; i < 20; i++) { A = A * x } B = A But I don't necessarily always want to get ...
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2answers
96 views

Does the ratio of the $x-$values of two continuous functions $f(x), g(x) \in \mathbb{R^+}$ tell you anything about the ratio between their $y-$values?

Does the ratio of the $x-$values of two continuous functions $f(x), g(x) \in \mathbb{R^+}$ tell you anything about the ratio between their $y-$values? In general, obviously not. But suppose the ...
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2answers
32 views

Normalise rest of list

I have an list of fractions as such: sum(3/10, 1/2, 1/5) = 1 and I multiply some element (the second in this case) by some known factor (...
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1answer
23 views

Get the ratio of a products uses and price per use.

Not sure I am going to ask this well or even if the title is correct. say you have a dataset like: 59 uses - price per use £0.09p 43 uses - price per use £0.06p 59 uses - price per use £0.04p 66 uses ...
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1answer
16 views

Maximizing Pieces of fabric cut out of a roll

I have a problem I am trying to solve in google sheets. I have a roll of fabric that is 120 yards long of that I need to cut into 1 yard, 2 yard, 3 yard, 4 yard, and 5 yard pieces. We have varying ...
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1answer
31 views

Ratio problem solving- ten machines use 200 kW

Ten machines use 200 kilowatts to operate for 5 days, 10 hours per day. Determine the number of kilowatts used if they work for 3 days, 8 hours per day? and the answer has to be in kW updated would it ...
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3answers
39 views

Ratio in triangle $\Delta ABC$. Find ratio $|CF|:|FP|$.

Let $\Delta ABC$ be triangle and $P$ and $Q$ points on $AB$ and $AC$ such that $|AP|:|PB|=1:5$ and $|AQ|:|QC|=2:1$. Lines $BQ$ and $CP$ intersect in point $F$. Find ratio $|CF|:|FP|$. I want to solve ...
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1answer
28 views

Find the meaning of this proportionality

I'm having understanding the maths part of a certain chemistry concept. There's a formula that states: $$\frac{A}{B}\sim v^{-3}$$ From this I can say that as v gets bigger the numerical value of the ...
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1answer
44 views

Finding the Covariance of a portfolio given the weights of two assets, with their probability and return % for each asset.

I am given the details below: The following Table reflects data relating to two assets X and Y, which are present in a portfolio in the ratio 60:40 ...
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1answer
20 views

prove the ratio of the line in the question

the book's solution uses $(a+b)/a= a/b$. I got my answer using b and c but want to understand the book's method.
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0answers
34 views

Been trying to convert absolute co-ordinate alterations to relative ones based on current Euler angles. Can anyone give me a good method? Thanks

I've spent weeks searching the internet and experimenting to find a method for changing the position of XYZ co-ordinates that are relative to an object's Euler angles (Yaw, Pitch, Roll), but in an ...
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1answer
65 views

Find the limit of the sequence $ \frac{x^n}{n^k}$ as $n \to \infty$ for all values of$ x > $0 and $k = 1, 2,\cdots$ [duplicate]

I have tried using the ratio lemma to tackle this question and also the fact $(n+1)^k \geq 1 + nk$ and I haven't reached an answer. How should I go about solving this problem?
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21 views

How does Proportion and Proportionality co-relate?

Is there any co-relation between Proportion and Proportionality? How do you think about it?
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0answers
61 views

Is it ever true that the identity $E(\frac{1}{X^2}) = \frac{1}{E(X^2)}$ holds for a nontrivial random variable X?

Is it ever true that the identity $E(\frac{1}{X^2}) = \frac{1}{E(X^2)}$ holds for a nontrivial random variable X? I see that it would work if $X$ is a constant $1$ because $\frac{1}{1^2} = \frac{1}{1^...
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1answer
32 views

Vectors in triangle

The triangle ABC is given. You get B' by mirroring point B over point A. Let point M lie on the side BC such that | BM | : | BC | = k, where k∈(0,1). Let N be the intersection of the line MB' and the ...
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2answers
137 views

If ratios like 4:0 and 2:0 are defined, then how can we determine if they are equivalent?

According to answer in this post ratios with zero on either side of them are defined: Are ratios with zero defined? But it raises another problem. How can we know if ratios 4:0 and 2:0 are equivalent? ...
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1answer
16 views

Ratio & Proposition: Question on mixtures

Ratio of milk to water in a jar is 5:1. If 10 litres of this mixture is removed and 4 litres of milk and 2 litres of water are added, then quantity of milk becomes 300% more than that of water in the ...
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2answers
34 views

$ABC$ is a triangle with $a,b$ and $c$ are the opposite sides of the angles. Let $(a^2+b^2):c^2=2019:1$, find $(\cot A+\cot B+\cot C:\cot A +\cot B)$

$ABC$ is a triangle with $a,b$ and $c$ are the opposite sides of the angles. Let $(a^2+b^2):c^2=2019:1$, find $(\cot A+\cot B+\cot C:\cot A +\cot B)$ My attempt: \begin{align*} a^2+b^2-2ab\cos C&=...
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1answer
31 views

Ratio & Proportion - Splitting the ratio

A picture is made up of just two colours, red and green. They are used in the ratio 4:3. In the picture, if the ratio of red and green in the lower half of the picture is 2:3, then what is the ratio ...
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0answers
29 views

Is there geometric meaning to the fact that $\alpha=\frac1{2(\sqrt2+1)}$ minimizes $\|\sqrt{1+x^2}-x-\alpha\|_{L^\infty[1,\infty)}$?

Question: Is there any geometric meaning to the fact that $\alpha=\frac{1}{2(\sqrt 2+1)}$ is the minimizer of $$\left\|\sqrt{1+x^2} - x-\alpha\right\|_{L^\infty[1,\infty)}?$$ My calculus student came ...
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1answer
26 views

Is there a term for this form of equation or ratio?

I am referencing and explaining the use of the Normalized Difference Vegetation Index (NDVI) in my work and am lost for a term that describes the form of the equation. It takes the form $$ NDVI = \...
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4answers
56 views

Best way to evaluate $\lim_{n \rightarrow \infty} |\frac{(3(n+1)+4)(4^{n+1}+5)(5^n+3)}{(5^{n+1}+3)(3n+4)(4^n+5)}|$

Best way to evaluate $\lim_{n \rightarrow \infty} |\frac{(3(n+1)+4)(4^{n+1}+5)(5^n+3)}{(5^{n+1}+3)(3n+4)(4^n+5)}|$ Can you all show me some different ways to evaluate this limit? I was thinking of ...
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0answers
35 views

Can this ratio of weight vectors be simplified to one line?

$$\frac{\boldsymbol w' \boldsymbol\sigma}{\boldsymbol{w' \Sigma w}}$$ Can the ratio above be simplified to one line, given that the weights could cancel somehow? $\boldsymbol{w}\in \mathbb{R}^{N\times ...
3
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2answers
48 views

Combining two ratios of the same mass to create a new ratio

This was stuck on this question wondering if you could help? Two solutions, each of mass 1L, has a ratio of liquid A to liquid B as 1:6 and 1:8 respectively. Both solutions are mixed together to ...
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5answers
104 views

Prove that $\frac{AB}{AE} + \frac{AD}{AG} = \frac{AC}{AF}$ in parallelogram $ABCD$, where $E$, $F$, $G$ are points on a line intersecting the sides

Let $ABCD$ be a parallelogram. A line meets segments $AB$, $AC$, $AD$ at points $E$, $F$, $G$, respectively. Prove that $\frac{AB}{AE} + \frac{AD}{AG} = \frac{AC}{AF}$. So recently I've been assigned ...
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1answer
31 views

How to rate the similarity of aspect ratio of rectangles

Given two rectangles, and a maximum difference score, tell me whether the aspect ratio of these rectangles are considered similar or not? For example a $2\times4$ rectangle [ratio $0.5$] and a $2\...
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1answer
31 views

Is ratio of members of two progression increases?

I have two progressions: $$\begin{align}P_1&: xy, xy + (x+2)(y+2), xy + (x+2)(y+2) + (x+4)(y+4),\dots, \sum_1^i (x+2(j-1))(y+2(j-1))\end{align}$$ $$\begin{align}P_2&: (x+2)(y+2), (x+4)(y+4),\...
2
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1answer
38 views

In triangle ABC a point X is taken on AC and a point Y is taken on BC if AY and BX meet at O

This question is from pre collage mathematics. The question goes on like this: In $\triangle ABC$ a point $X$ is taken on $\overline{AC}$ and a point $Y$ is taken on $\overline{BC}$. If $\overline{AY}...
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3answers
71 views

Convert US Dollar / lb to Canadian Dollar / kg

I can find exchange rate conversions and lbs to kgs. How can I convert USD/LB to CAD/KG? What is the formula? Specifically, I have $1.61 / lb and I need to know what that is in CAD/KG. Thanks!
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0answers
51 views

Prove that either $a+b+c=0$ or $a=b=c$ for the given conditions. (INMO 2000)

If $a,b,c,x$ are real numbers, such that $abc\ne 0$ and : $$\dfrac{xb+(1-x)c}{a}=\dfrac{xc+(1-x)a}{b}=\dfrac{xa+(1-x)b}{c}$$ then prove that either $a+b+c=0$ or $a=b=c$ My Approach: $$\dfrac{xb+(1-x)...
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2answers
41 views

Find $x+y+z$, where $x, y, z$ are edges of a parallelepiped

A parallelepiped has its edges represented by $x$, $y$ and $z$, these are directly proportional to the numbers $3$, $4$ and $5$ respectively. It is also known that they are, in this order, in ...
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2answers
29 views

Getting the ratio of X and Y with different powers

I am given a relation that $3X^3 = 2Y^2$ I then have to find the ratio of $X : Y$ To me, the first steps would be the following: Divide by two: ${3X^3\over2} = {2Y^2\over2}$ ${3\over2}X^3 = Y^2$ Then ...
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0answers
24 views

Analytical geometry proof of the invariance of cross ratio under a projective transformation

I was reading about the cross ratio and wanted to go through its proof but I was not able to find appropriate proofs on internet and most proofs required knowledge of abstract algebra and determinants....

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