Questions tagged [ratio]
For questions concerning the ratio of a certain quantity to another.
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Odds of winning a competition show with 10 contestants and 1 person eliminated each round
Say there are 10 contestants in a competition reality show. 1 contestant loses each episode and is removed from the show. Then in episode 2 there would be 9 contestants and so on with each episode.
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Divided Diamonds : a proportionality & ratio problem
Problem
For stones of the same quality (e.g. the same colour), the monetary value of a diamond is proportional to the square of its mass (i.e. $C\propto M^2$). Find the monetary loss ($\Delta C$) ...
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Constant area and ratio peculiarities regarding equilateral triangles.
I'm just writing this problem out of curiosity, so let me know whether I make any mistakes. FYI this problem was inspired by the 1998 AIME problem 12. Also, if you have a better name for this question,...
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relationship between proportions
consider some variables $x_1,x_2,y_1,y_2$ that are positive and for which $\frac{x_1}{y_1}=\frac{x_2}{y_2}=p$. Is it true that $\frac{x_1+x_2}{y_1+y_2}=p$?
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Absolute Convergence of a Series (maybe use ratio test) [closed]
Let
$p:=\lim_{{k \to \infty}} k(1-|\frac{a_{k+1}}{a_k}|)$
Prove
$p>1$ or $p=\infty \implies \sum_{n=1}^\infty a_n $ converge absolutely
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Is Basic Proportionality theorem applicable to trapezium? [closed]
I was studying vectors and came up with this question
Show that the line joining the midpoints of two non parallel sides of a trapezium is parallel to the parallel sides and is equal to half of their ...
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Turning division by zero to zero with basic math operators
I need to compute $\frac{const}{y}$, where $y$ may equal $0$ to present PC state in a human-readable format from exposed internal registers. Is it possible to build an expression of basic math ...
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Contribution of a single value in a Division of Sums
I need to isolate contribution of a single entity in a Division of Sums as shown below. For example, find the contribution of variable a in the following:
(a 1 + b ...
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Determine point from one aspect ratio to an equivlent aspect ratio
I am working on a code program and get the X and Y coordinates of my cursor. My aspect ratio is 1280x720 and a point I am using for an example is (710, 300) however my x and y values must be 0.0-1.0, ...
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Converting a ratio into percentage.
As per many websites and text books, 3:4 converted into % is 75%.
But as per my understanding, its not.
If 3:4 is the ratio of boys and girls in a class, then it means that 3 out 7 are boys and 4 out ...
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Ratio of two Jensen's Inequality
I have these pair of numbers
$ (a, b) = (\frac{4}{9}, \frac{1}{9}) $ and $(c, d) = (\frac{1}{2}, \frac{1}{6}) $. (Number mean nothing, just for illustration and simplification)
Note that - (a, b) are ...
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formula for reducing (as little as possible) one or both sides of a rectangle to match a given aspect ratio
I am writing a small program (for personal use). In the program, I need to be able to give a base ratio (such as 16:9), take a rectangle (such as 2048 x 1536), and reduce one or both sides of the ...
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Algorithm for allocating whole gold bars amongst thieves by % share of the booty
I have N big gold bars and 1 small gold bar equivalent in weight to some fraction x of a large bar. E.g N = 10 and x = 0.5 then I have 10.5 large bars worth of gold, in 10 large bars and 1 small bar
I ...
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Find the ratio of recursive integrals
Given $ I_n = \int_0^{\pi/2} \sin^n\theta d\theta $, the recursive formula can be found as
$$ I_n = \frac{n-1}{n}I_{n-2} $$
The lecture notes later state that
$$ \frac{I_{2n-1}}{I_{2n+1}} = 1 + \frac{...
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Find the ratio of the perimeter of a square and of a triangle.
Problem:
Let the square $ABCD$ be on the side $l$ and the points $E$ and $F$ on the sides $BC$ and $CD$ respectively so that $\angle EAF= 45$. Find the ratio between the perimeter of the square and ...
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TV aspect ratio
I am working through "Geometry" by McDougal Littell. Doing self study. There is a problem that has me stumped:
A standard 27 inch analog television screen has an aspect ratio of 4:3. Use ...
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If you need 3:2:1 ratio of X,Y,Z to make a something, doesn't that mean you need 6 units:4 units:2 units to make two units of that thing?
Oil, vinegar, and water are mixed in a 3 to 2 to 1 ratio to make salad dressing.
If Larry has 8 cups of oil, 7 cups of vinegar, and access to any amount of water, what is the maximum number of cups of ...
user1208473
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Algorithm to make every number in a set positive but keep the ratios between them?
I don't know what tags to use for this question so if I am using the wrong ones, please suggest others.
I have a set of numbers (ex: -20, -3, 5, 8, 30). I need to ...
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Finding the fraction for a given segment by only knowing its ratio.
I'm studying analytic geometry in Khan Academy and I'm struggling at dividing segments when given ratios like 1:3, 5:6, 2:1 and finding their fractions.
According to what I read and learned from them ...
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Jigsaw puzzle ratio question.
I was doing a puzzle when this question popped into my head:
Assuming a puzzle had an equal amount of pieces in each row, and an equal amount of pieces in each column, what would be the least amount ...
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Finding $x:y:z$ when $\frac{y}{x-z}=\frac{y+x}{z}=\frac{x}{y}$. What is the reason for this peculiar behaviour in the equations?
I am solving this old book and this question is really interesting.
Suppose $$\frac{y}{x-z}=\frac{y+x}{z}=\frac{x}{y}$$
We are asked to find $x:y:z$
Now here is what I've done.
Suppose all of this ...
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Expressing ratios verbally
$\frac{1}{3}$ of angels are demons, and $\frac{2}{3}$ are good angels.
Does this mean there are:
$2$ good angels for every $1$ bad angel(∵ $2+1=3$ total angels, but this ratio seems to be $1:2$ not $...
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If I know the ratio of two variable differences, how to write it as a percentage increase?
I know that $ \dfrac{\delta x}{ \delta y} = 5.8,$ meaning that the change in $x$ is $5.8$ times the change in $y.$
Is there a way to write this as a percentage increase? For example, there is a '$p$' ...
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How to prove that $\lim_{x \to \infty} (\sqrt{x + \gamma} / x) = \lim_{x \to \infty} 1 / \sqrt{x} = 0$? [closed]
As the title specifies:
How do I (rigorously) prove that
$$\lim_{x \to \infty} \frac{\sqrt{x + \gamma}}{x} = \lim_{x \to \infty} \frac{1}{\sqrt{x}} = 0?$$
($\gamma \in \mathbb{R}.$)
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How to make logical sense of following problem with ratios/percentages
I have the following variables
L
M
T
L1
M1
T1
L2
M2
T2
L3
M3
T3
L4
M4
T4
where $L+M=T$
I want to calculate an approximate value for the 4s using the ratio between the 2s and 1s, and then ...
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expectation of a ratio vs ratio of the expectations
Consider a stochastic vector $\mathbf{x}(t)$, that I know is ergodic and stationnary.
Are they conditions on the distribution of $\mathbf{x}(t)$, that allow me to approximate $E\left(\frac{\mathbf{x}(...
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Ratios of Big O
Consider two functions $f(n) = C_1 + O(1/n)$ and $g(n) = C_2 + O(1/n)$ where $C_1$ and $C_2$ are two non-zero constants.
Is is true that
$$\frac{f(n)}{g(n)} = \frac{C_1 + O(1/n)}{C_2 + O(1/n)} = (?) \...
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Compute the ratio : $\frac{\int_{0}^{\pi/2}\sin^{√2+1}xdx}{\int_{0}^{\pi/2}\sin^{√2-1}xdx}$ [duplicate]
I want to find the ratio of the following :
$$
\frac{\int_{0}^{\pi/2}\sin^{√2+1}xdx}{\int_{0}^{\pi/2}\sin^{√2-1}xdx}
$$
I have tried a lot but can't solve it. Please help. Thanks.
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Least Angle Regression for Complex Rational Models
Background
I am doing a project and need to fit the following rational model, where the terms $\Psi$s are real but $y$, $p$, and $q$ are complex:
$$
y_{i} = \frac{\sum_{j=1}^{n_{p}}\Psi_{ij}p_{j}}{1+\...
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How does dividing for a rate gives you a whole remainder?
Calvin cleans $\frac{3}5$ of his bathroom with $\frac{1}3$ of a bottle.
At this rate, what fraction of the bottle of will Calvin use to clean his entire bathroom?
Khan Academy solve this via $\frac {\...
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Does it make sense to calculate relative ratios of items from different scales when I need to normalize the result?
Let's say I have two different scales for size, where the first (A) is 0-10 and the other (B) is 0-1000. Then I will use each to measure (relative) sizes of products for which I know the number of ...
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Intersection of two Bessel functions
I am trying to find an analytical expression (exact or approximate) for the following expression:
$$
J_{n_1}(\alpha_1 x)= J_{n_2}(\alpha_2 x)
$$
where $J_{n}(x)$ denotes a Bessel function, $n_1,n_2\...
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According to what rule is $\frac{a+b}{a} = \frac{b}{a+b} = \frac {a+b-b}{a-a-b}=-\frac {a}{b}$ true and why?
I want to prove that $a$ and $b$ that satisfy
$$\frac{a+b}{a} = \frac{b}{a+b}$$
cannot both be real.
Here is the natural solution.
$$(a+b)\times (a+b)=ab$$
$$a^2+2ab+b^2=ab$$
$$a^2+ab+b^2=0$$
$a=0$ ...
user1166899
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Find LRT and rejection
enter image description here
For each of the n independent individuals, there are two measures of interest:xi which is some known value, and Yi which is a random variable distributed as N(α+βdo,σ^2)
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How much would the diamter of a pipe increase after some pressure?
A pipe of mild steel with a wall 0.4 cm thick and a diameter of 50 cm
contains a liquid at a pressure of 2 X 10^4 N/m2. How much will the diameter of the pipe expand due to this pressure?
I was trying:...
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Sort including ratio between values and best of list
I have following values for each object:
100,50,50
30,100,20
100,80,20
120,50,70
120,60,60
300,100,20
350,50,100
30,300,300
120,10,100
I want to find an function how to calculate optimal ratio (...
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Temperature at which a copper cable brakes up
A power cable of copper is stretched straight between two fixed towers.
If the temperature decreases, the cable tends to contract . The amount of contraction for a free copper cable or rod is
0.0017% ...
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Limit of the ratios of consecutive central binomial coefficient integers
When looking at the central binomial coefficients (A000984), I found that if you took the ratio of consecutive numbers in the sequence it approached 1/4.
the sequence being; 1, 2, 6, 20, 70, etc.
the ...
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HELP Let ABC an isosceles right triangle with ABC = 90°. Consider the point P on AB such that $\frac{PA}{PB}=2$. Show that $PA\cdot BP=BQ\cdot BG$.
Let ABC be an isosceles right triangle with ABC = 90°, M and N the midpoints of sides BC and AC, and G is BN intersected by AM. Consider the point P on AB such that $\frac{BM}{BP}=2$. If BN intersects ...
user1104319
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Wallis Product and Rectangles
The Question
We construct rectangles as follows. Start with a square of area 1 and attach rectangles of area 1 alternately beside or on top of the previous rectangle (see the figure). Find the limit ...
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Ratio of lengths $QD/QC$ where $Q$ belongs to the side $CD$ of a square
Let ABCD be a square, M the middle of (AB), N the middle
of (AD), {P} = CN ∩ DM and {Q} = AP ∩ CD. Calculate $QD/QC$.
You can see down my idea and the drawing::
Okey! So first of all i thought of the ...
user1104319
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Questions about ratio and overlapping figures
As I am helping my younger brother on his math papers (bought on external sources), I came across a question that seems unsolvable.
I feel that the question is not complete as they did not state the ...
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Ratios and Mixtures - Arithmetic (Need help in understanding the solution presented in textbook)
A milkman has 500 litres of milk with him. He also has 2 helpers H1 and H2. All three of them decide to cheat customer by mixing water. Each one of them first removes 100 L of the solution and add ...
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Ratio definition
My teacher gave me the definition of ratios as "the comparison between two like quantities"
And one of the example he gave for a popular ratio was that of Body mass index (BMI).
My question ...
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Mixing two components at a $7.5:1$ ratio to make a solution of $200$ grams total
I am mixing two components at a $7.5:1$ ratio to make a solution of $200$ grams total.
So, I tried algebra: $$200 = 7.5A + 1B\\
200 - 1B = 7.5A\\\frac{200 - 1B}{7.5} = A.$$
How to continue from here?
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Time and Work question - Case when people leave in between
Mr. X can do a job in 10 days, Mr. Y in 15 days and Mr. Z in 20 days. They work together for 2 days. Then Mr. X leaves the job. Mr. Y leaves the job a day earlier to the completion of the work. ...
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Dishonest shopkeeper at the time of buying as well as selling
James is a dishonest shopkeeper, and at the time of selling and purchasing, weighs 20% less and 10% more per kilogram respectively. Find the percentage profit earned by treachery. (Assume he sells ...
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Confusion with the meaning of percentage higher, percentage increase
Question:- Had the rate of simple interest been higher by 2.5%, $£50,000$ would have amounted to $£82,750$ in 3 years. What did the sum of money amount to at the existing rate of interest ?
I have ...
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Question on Discount, Marked Price, Selling price
Question :- A shopkeeper gives a discount of 10% on marked price of every shirt and when he sells 12 shirts he gives one shirt free. What is the approximate real rate of discount offered by ...
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Profit Loss - Faulty weights even at the time of buying
Question :- A shopkeeper claims he sells at 10% profit but his 1 kg weight actually measures 800 gram when selling and buying. Find his Profit/Loss %
Author's solution :- $800 * 1000 * SP$ = $(11/10) ...
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