Questions tagged [ratio]

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

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3
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3answers
35 views

Ratio and Proportion Concept clarity.

The milk and water in two vessels $A$ and $B$ are in ratio of $4:3$ and $2:3 $ respectively. In what ratio should the liquids in both vessels be mixed to obtain a new mixture in vessel $C$ consisting ...
-2
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2answers
25 views

Help me solving this please [closed]

Two mixtures of milk and water contain $20\%$ and $30\%$ water. In what ratio should the two mixtures be mixed so that the resulting mixture contains $26\%$ water? A) $2:1$ B) $1:3$ C) $3:2$ D) $2:...
2
votes
2answers
29 views

Solving for a ratio of intervals

How is it possible to solve for the possible values of $x$ given the following information? $\frac{a}{b}=\frac{2}{3},$ where $a \in [x, x+1)$ and $b \in [x,x+\frac{1}{2})$. I can see that a valid ...
0
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2answers
35 views

Finding length of clothes

There are three types of clothes: A- Rs. 1 for 5mtrs B- Rs. 5 for 1mtr C- Rs. 1 for 1.5mtrs How much cloth is required for each type in mtrs, So that total for ...
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0answers
21 views

How much does each person owe?

A group of friends are sharing accommodation for a house they are renting. The accommodation is £100 per day altogether The total duration of the stay is £1700 for 17 days Person A - 23/12/19 - 30/...
0
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1answer
12 views

Percentage or Ratio using two values in nano seconds

I am running two different python code, one using a for loop and the other numpy library in python and I have timed it using %timeit function, yet I don't ...
1
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1answer
33 views

Conversion between in$^2$oz$^{-1}$ and cm$^2$g$^{-1}$?

I want to convert $~16~$in$^2$oz$^{-1}$ into cm$^2$ and grams. This is my attempt: I just want to check that my answer is correct, as my book says it should be $~3.686~$cm$^2$g$^{-1}$, but I got $~3....
0
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0answers
18 views

Is the limiting ratio of the Dirichlet inverse of the Euler totient function on average equal to $1$ for all values of $h$?

Let $\varphi(n)$ be the Dirichlet inverse of the Euler totient function which is defined as: $$\varphi(n) = \sum\limits_{d|n} d \cdot \mu(d)$$ where $\mu(d)$ is the Möbius function. Is it true ...
0
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2answers
30 views

Vector ratios on parallelogram

There is a parallelogram ABCD. On length CD there is point E with statement |CE|=2|ED| On length AD there is point F with statement |AF|=1/4|AD| Point S is intersection of length BE and CF. In ...
1
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2answers
52 views

Geometric progression first term and common ratio of progression

Do I simplify? Trying to find first term and common ratio of the progression aswell as the sum of all the terms in the progression for homework please help trying to know what I’m doing wrong so I can ...
1
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4answers
52 views

Let $a_1,a_2,a_3…$ be an arithmetic progression.

Question is Let $a_1,a_2,a_3....$ be an arithmetic progression. If $\frac{a_1+a_2+a_3+...+a_p}{a_1+a_2+a_3+...+a_q}=\frac{p^2}{q^2},p\not=q$, then find $\frac{a_6}{a_{21}}$ Answer: $\frac{...
19
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4answers
461 views

How is $\sin 90° = 1$ possible?

How can two angles of a triangle be equal to $90°$? If two angles were $90°$, this would mean that the two sides would be parallel and the angle of the third side would be equal to 0. Thus, there ...
1
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1answer
54 views

A.M. is two times G.M.

If the A.M. between $a$ and $b$ is twice as great as their G.M., show that $a:b=(2+\sqrt3):(2-\sqrt3)$. My attempt: $$\frac{a+b}{2}=2\sqrt{ab}$$ $$\sqrt\frac{a}{b}+\sqrt\frac{b}{a}=4$$ Let $\sqrt\...
-1
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1answer
23 views

Formula to adjust two numbers from ratio to another

I have databases of people in countries, with sex, but the sex ratio of the databases don't always correspond with the actual sex ratio of the country. I am looking for a formula to be able to ...
1
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5answers
52 views

$\frac{y}{x-z}=\frac{x+y}{z}=\frac{x}{y}$

If for three distinct positive numbers $x$, $y$, and $z$, $$\frac{y}{x-z}=\frac{x+y}{z}=\frac{x}{y}$$ then find the value of $\frac{x}{y}$ I have tried all types of manipulations, even quadratics ...
1
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0answers
79 views

The origin of the Fibonacci sequence and the metallic means or silver means (also ratios or constants)

Is this equation the origin of the metallic means or silver means? (also ratios or constants) $ 2^2=(x+1/x)^2−(x−1/x)^2 $ As discussed in my previous question, we can link this equation with ...
1
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1answer
25 views

Scale a number but ensure it is greater than a value

I have a grid with a Y-axis with a minimum of 25, and a maximum of 50 but the scale begins at 25 (25-50) and a X-axis with a minimum of 0, and a maximum of 4 that begins at 0 (0-4) I have a set of ...
4
votes
1answer
88 views

Prove that it cannot be proven that “The United States had more fallow acreage than planted acreage”

Followup question to Prove "If, in a country, there are $x$ fallow acres for every planted acre, yield per planted acre is $1+x$ times the yield per total acre." Given: A ten year ...
2
votes
1answer
21 views

Converting Ratios

In a community of M men and W women, m men and w women smoke (m ≤ M,w ≤ W). If a person is selected at random and A and B are the events that the person is a man and smokes, respectively, under what ...
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0answers
251 views

Show a relationship involving proportions

A ten year comparison between the United States and the Soviet Union in terms of crop yields per acre revealed that when only planted acreage is compared, Soviet yields were equal to 68 percent of ...
0
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1answer
18 views

Combined variation with four variables: Is this even possible to solve?

I have this problem, and I'm quite confused on how to solve it. Mr. Plaridel owned a newspaper publication called Diaryong Tagalog Inc. He observed that when he used 3 printing presses, he can ...
0
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1answer
34 views

Find the ratio of the lengths of chord AB to arc AB

The chord AB of a circle subtends an angle of 60 degrees at the centre. Find the ratio of the lengths of chord AB to arc AB. I tried $sin60 = AB/r = √3/2$ Therefore $r = 2$ and $chordAB = √3$ ...
0
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1answer
31 views

Finding the ratio of 2 sides, and expressing OP in terms of a, b, c

I got a bit confused about this problem, and its something that my country's academic curriculum does not really delve into or practice as much. The Problem: Let $A,B,C$ be three points on a plane ...
1
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1answer
45 views

Find the ratio of the area $EDPQ$ to the area of ABC

In triangle $ABC$,points $E$ and $D$ are on side $AC$ and point $F$ is on side $BC$ such that AE=ED=DC and $BF:FC$ =2:3. $AF$ intersects $BD$ and $BE$ at points $P$ and $Q$, respectively. Find the ...
4
votes
3answers
421 views

Which is faster between the tiger and the leopard given the relation between the number of paces they take and length of their paces?

$I.$ For every $4$ paces taken by the tiger, the leopard takes $5$ paces. $II.$ The total length of $10$ paces of the tiger is less than the total length of $9$ paces of the leopard. The answer can ...
0
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0answers
16 views

Inverting a ratio distribution

I have a ratio distribution $Z = X/Y$ of two random variables $X, Y$ with the same unknown distribution $f(x), f(y)$. The ratio distribution comes out as $\tilde{f}(z) = \frac{1}{z (\log{z})^2}$ in a ...
0
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1answer
20 views

Time and work problem found to be hard

First pipe passes 4 liters of water per minute less then second pipe. How many liters of water per minute passes through the first pipe if it fills a 480 liter basin 8 minutes longer than the second ...
0
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3answers
61 views

Apples, Bananas and Oranges [closed]

I am having a very slow Friday and cannot think of how to describe my problem in mathematical terms... I have 10 children who each must get an apple, a banana and an orange. Apples come in bags of 3, ...
0
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5answers
81 views

If $\sin{\alpha}=\frac{8}{17}$ and $\sin{\beta}=\frac{15}{17}$, for acute $\alpha$ and $\beta$, then $\alpha+\beta=\pi/2$

Prove that $\alpha+\beta=\frac{\pi}{2}$, if $\sin{\alpha}=\frac{8}{17}$ and $\sin{\beta}=\frac{15}{17}$, where $0<\alpha<\frac{\pi}{2}$ and $0<\beta<\frac{\pi}{2}$. This is what I did ...
1
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2answers
24 views

Ratio between two groups

I want to know among what is the ratio of insured people with disease $x$ to uninsured people with disease $x$. Here are my numbers. Insured, disease $x = 3600$ Uninsured, disease $x = 950$ Insured, ...
0
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3answers
68 views

If the AM and GM between two numbers are in the ratio $m:n$, then what is the ratio between the two numbers?

If the AM and GM between two numbers are in the ratio $m:n$, then what is the ratio between the two numbers? I have tried many approach like Let's two number be $a$ and $b$ Then their AM will be $\...
1
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3answers
36 views

Problem understanding proof of ratio test

The ratio test states that for an infinite series $$\sum_{n=1}^{\infty} a_n $$ if $\lim_{n\rightarrow \infty} \frac{|a_{n+1}|}{|a_n|} <1$, the series is convergent and if $\lim_{n\rightarrow \infty}...
0
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1answer
40 views

Trigonometric Ratios and Converse of Pythagoras Theorem Lemma

I am not quite sure what the question is asking here really. I understand the Lemma. Do I prove that $a^2+b^2=1$, using the given expressions for $a$ and $b$? Thank you!
3
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2answers
55 views

How to determine mixing ratio to get desired percentage?

Let's say I have two types of chocolate. Chocolate A contains 70% cocoa and 30% sugar. Chocolate B contains 100% cocoa and no sugar. How can I figure out the exact mixing ratio I need to use to ...
1
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3answers
61 views

How to add up two percentages

I have two fraction: first one: $\frac{a}{b} $, where $0<\frac{a}{b}<1$ second one: $\frac{c}{d}$,where $0<\frac{c}{d}<1$ I apply this two percentages on two positive numbers: $q>0,k&...
0
votes
0answers
30 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. ...
0
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1answer
29 views

How can I calculate the ratio required to line up these rectangles?

I have two rectangles of different sizes which need to slide horizontally, left and right. The left side of each rectangle needs to line up above P1 when the rectangles are fully right (diagram A). ...
0
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1answer
25 views

What are some examples of statement-reason format for ratios of segments?

I'm wondering what some examples might be for a proof (statement/reason format) that required you to find the length of two segments if you know that their ratio is $x:y$ and that the total length is $...
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2answers
37 views

I was wondering how I can solve this question as I'm a bit stuck. [closed]

$P, Q$, and $R$ are each mixtures of red and white paint. The percentage by volume of red paint in $P$ is $30\%$. The percentage by volume of red paint in $Q$ is $20\%$. The mixtures $P, Q$, and $R$ ...
0
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0answers
19 views

Determining convergence of series when terms are decreasing by factor less than 1 [duplicate]

Suppose that $a_n > 0$ and that, for n sufficiently large, $$\frac{a_{n+1}}{a_n}\leq 1- \frac{c}{n}$$ for $c>1$ Prove that the series $\displaystyle \sum_{n=1}^{\infty}a_n$ converges. Hint ...
0
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1answer
46 views

Difficult circle geometry question, proof sum of 2 sides ratio equals 1

I have been working on this question for hours on end but not even come close to solving. I have found 2 pairs of similar triangles and an isosceles triangle, and tried to equate the ratio of sides, ...
-2
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2answers
26 views

A machine produces B unit goods in A hours… [closed]

A machine produces $b$ unit goods in $a$ hours. How many hours does this machine need to produce $b\cdot c$ unit goods?
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votes
2answers
25 views

Value of B in this ratio problem? [closed]

a,b,c integers $a+b+c=45$ $\frac{a}{b}=\frac{3}{2}$ $\frac{b}{c}=\frac{4}{5}$ b=?
-1
votes
2answers
41 views

The ratio between positive/negative numbers

I am creating a model that compares multiple data points of two attributes and compares them vs one another as a percentage of 100. So for instance, comparing the values A=1.24 v B=0.44 would be: ...
0
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0answers
24 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. ...
0
votes
1answer
19 views

How to find points on a graph from ratios

A bag of 75 balls has a ratio of red balls to green balls is 2:7. If y, which is the number of red balls is graphed as a function of x, which is the number of green balls, which set of points will the ...
0
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2answers
31 views

ratio calculation problem, can someone help?

the problem is like this : an online recipe calls for 2 liter of 3% bleach to 50 liter of water. so, how many liter of 11% bleach to 50 liter of water ? anybody able to teach me ? thanks andrew
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1answer
43 views

I Don't understand what is The Relation between Infinite series and limits [closed]

**I Don't understand what's The Relation or difference between Infinite series and limits **
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1answer
31 views

Ratio of Means of two numbers 10 and 100

Table I was reading a book on computer architecture for my exam and came across this table. I understand all the columns except for the ratio of means. How is the ratio of means of 10 and 100 become ...
0
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3answers
48 views

Why does this series diverge using Ratio Test?

So I was working on this problem $$\sum\limits_{n=2}^\infty \frac{2^n}{n^{100}}$$ After all of my work performing the ratio test, I ended up with a $$\frac{2}{n+1} = 0$$ Therefore, I assumed it ...