In mathematics, a ratio indicates how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8∶6, which is equivalent to the ratio 4∶3). Similarly, the ratio of lemons to oranges is 6∶8 (or 3∶4) and the ratio of oranges to the total amount of fruit is 8∶14 (or 4∶7).
The numbers in a ratio may be quantities of any kind, such as counts of people or objects, or such as measurements of lengths, weights, time, etc. In most contexts, both numbers are restricted to be positive.
A ratio may be specified either by giving both constituting numbers, written as "a to b" or "a∶b", or by giving just the value of their quotient a/b. Equal quotients correspond to equal ratios.
Consequently, a ratio may be considered as an ordered pair of numbers, a fraction with the first number in the numerator and the second in the denominator, or as the value denoted by this fraction. Ratios of counts, given by (non-zero) natural numbers, are rational numbers, and may sometimes be natural numbers. When two quantities are measured with the same unit, as is often the case, their ratio is a dimensionless number. A quotient of two quantities that are measured with different units is called a rate.
A shop sells small chocolate bars and large chocolate bars
The small bars are sold in packs of 4
The large bars are sold in packs of 9
On one day;
packs of small sold ; packs of large sold = 5:2
A total of 95 bars were sold
How many small bars were sold?
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My question; Is this an example...
my doubt is that let's say we have a ratio 5:10 now the equivalent ratio for this would be 1:2 but what I am not able to understand is - let's say we have a situation in which it is given that the ratio of girls to boys is 5:10 which means for every 5 girls we have 10 boys but if we see the...
I have the solution:
## \dfrac{2x-3y}{3z+y} = \dfrac{z-y}{z-x} = \dfrac {x+3z}{2y-3x} ## (1)
## \dfrac{2x-3y}{3z+y} = \dfrac{3(z-y)}{3(z-x)} = \dfrac {x+3z}{2y-3x} ## (2)
##= \dfrac{(2x-3y)-3(z-y)+x+3z}{(3z+y)-3(z-x)+(2y-3x)} ## (3)
##=\dfrac{x}{y}##
My question is how is it possible to go...
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In competitive rowing, the more people in a boat, the faster it goes, but what is the ratio of additional human to speed, and what is the theoretical limit?
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Hi everyone!
I am studying Higgs phenomenology, in particular its BRs
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Hello guys
I have a motorcycle engine in which I know the ratios of the transmission. and given the diagram of Power and rpm I made a function of P(ω) which is a polynomial of 6 order.
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a) In the rough approximation that the density of the Earth is uniform throughout its interior, the gravitational field strength (force per unit mass) inside the Earth at a distance r from the center is gr/R, where R is the radius of the Earth. (In actual fact, the outer layers of rock have...
Amal, Geoffrey, and Julia each have some fireworks. If Amal gives half of his fireworks to Geoffrey, then Amal and Geoffrey will have in a 2:3 ratio. If Julia has 1/5th as many as Geoffrey (after Amal gives half his fireworks to Geoffrey), then what is the ratio of the number of fireworks Amal...
Lets say we got a larger cylinder-piston combo and a smaller one.
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Here, we clearly have exp ratio > P_atm/P_final
We then compress the larger...
Hello,
I am confused about something. I will take the time to work it out, but right now, I am using it to remember. And I am now confused.
Go here:
https://www.smlease.com/entries/mechanism/gear-train-gear-ratio-torque-and-speed-calculation/
Scroll down to the section on...
I used the two equations i listed by using B1=B2 and by doing that i ended up finding that N1/N2=λ.
However i am not sure if that's the correct answer as λ is just a variable and not an actual number. Do you think it has to be an actual number or is it not really necessary?
As a 'non-mathematician' (somebody who sucks at maths) I've been enjoying reading up on a lot of the stuff that flew over my head in maths class many years ago. I've encountered some examples of weighted averages and I've been puzzling over how one might derive the weights in the following...
I understand that In general, the branching ratio for a particular decay mode is defined as the ratio of the number of atoms decaying by that decay mode to the number decaying in total. But I can’t get this specific branching ratio.
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I already know the fact that angles are physical quantities, but sin, cos of some angles are quantities?
Quantities are those things, which can be quantified, are sin, cos, tan be quantified through measurement, if yes then other mathematical functions should also be categorised as physical...
The concept of naturalness as dimensionless ratios of parameters of order unity has recently come under criticism, most obviously because Sabine Hossenfelder wrote a book (Lost In Math) criticizing it.
Very recently however, Peter Shor and Lee Smolin had a discussion about this over at Peter...
Homework Statement
A vector r has length 21 and direction ratio's 2,-3,6. The direction cosines of r, given that r makes an obtuse angle with x-axis is given by?
Homework Equations
l/a = m/b =n/c ...(1) (l,m,n are direction cosines, a,b,c are direction ratios
l^2 + m^2 + n^2=1...(2)
The...
In square ABCD point M is the midpoint of side CD. Find the ratios of the areas of the four regions (∆MPC, ∆BPC, ∆APB, and quadrilateral APMD) that are formed. Justify your result.
Homework Statement
Triangle ABC is shown in the diagram below.
A C
AC = 3AB
<BAC = 120° Respectively
<BCA =
Show that angle BCA can be written in the form...
Hello,
I often hear the phrase "Well, since you are taking a ratio bin-by-bin, you don't have to care about the luminosity syst. uncertainty and the trigger efficiency syst. uncertainty".
I think I understand qualitatively why this is the case (It cancels out in the ratio, since both...
This may not be the proper forum but i need to find a way to calculate how much effort it will take to move a cylinder using a manual helm pump.
The hydraulic cylinder i intend on using is a 32mm bore with a 16mm diameter. Stroke of 178mm. Volume of 107 cc
The helm pump (attaches to a steering...
So I've found the following formula for calculating the gear ratio of a planetary gear.
Tr Turns of the ring gear
Ts Turns of the sun gear
Ty Turns of the planetary gear carrier
R Ring gear teeth
S Sun gear teeth
P Planet gear teeth
( R + S ) ×Ty = R × Tr + Ts × S
The example I saw on the same...
This is from labwork experiments. I have no background in mathematics.
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Here is a setup that only uses fixed detectors.
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For this question instead of the coincidence counter, 3 simple counters are needed.
Also the detectors D1 and D2 need some lenses...
Hello,
I was doing some research on enthalpy of water-ethanol mixtures at different ratios, and when looking at all the information graphed, I don't understand why it produces the trend line it does. Why doesn't it produce a 'quadratic' trend line? Shouldn't having a 10:90 water-ethanol exert...
Hi, I'm undergraduate researcher and my professor is interested in the answer to this question. He's kind of left me in the dark on why this is important to us, but that is another matter.
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Sun produces neutrinos by sundry reactions:
p+p→d+e++νe - called "pp"
p+p+e→d+νe - called "pep"
3He+p→α+e++νe - called "hep"
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What is the intensity of heep line...
It is commonly known that the solution to the brachistochrone problem is a cycloid.
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Hi guys.
We're on a new topic in math now which has to do with ratios and proportions but with scaling.
A few questions I have are
How can I express the following scales in ratio?
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1/8" = 1'0"
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I'm trying to calculate the required gear sizes for the system shown below:
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I want to calculate the most efficient sizing of...
In a recent election, the ratio of the number of voters for the Purple Party to the
number of voters for the Pink Party was 15:16 and the Pink Party won the
election. Had 300 more people voted for the Purple Party and 200 fewer people
voted for the Pink Party, the ratio would have been 11:10 and...
Homework Statement
A person has come to a world full of pets. He notices right away that dogs are the most prevalent of all pets. But that's not all. He notices these 8 ratios:
Dog:Cat = 5:1
Dog:Rodent = 1:5
Dog:Lizard = 1:3
Dog:Snake = 2:1
Dog:Turtle = 1:3
Dog:Alligator = 3:1
Dog:Crocodile =...
Homework Statement
The number density of 1H nuclei in the body is roughly 600 times greater than that of 13C
nuclei. By what factor is the magnetisation M0 of 1H greater than 13C in the same external magnetic
field?
Homework Equations
3. The Attempt at a Solution
[/B]
Surely it can't be as...
Homework Statement
The question states to find the primary trig ratios for (7π)/4
Homework EquationsThe Attempt at a Solution
I got
sin= (-√2)/2
cos=(√2)/2
tan= -1
csc= 2/(-√2)
sec= 2/(√2)
cot= -1
I got all of them correct except for csc and sec, and I am unsure why the solutions are telling...
Homework Statement
The vx(t) curves for two carts, A and B, that collide on a low-friction track are shown below:
What is the ratio of their inertias?
Homework Equations
the ratio i am looking for is mB/mA
The Attempt at a Solution
I believed that the ration was 1/2 however that is not...
Homework Statement
A triangle with a hypotenuse of 13.5 and height of 11.8. Find the measure of angle P.
Angle p is on the same line as the 90 degree angle and I found out that it must be sine.
Homework Equations
sine = opposite/hypotenuse
The Attempt at a Solution
sin p = 11.8/13.5
sin p =...
Homework Statement
A telescope has a focal ratio of f/7.5. You wish to use it with a spectrometer that requires a f/10 beam as its input. Compute the focal length of a 50mm diameter lens that, when inserted into the beam 150mm in front of the unmodified focal plane, produces the required beam...
Hello!
I'm having some trouble understanding stress and strain rations in sheet metal forming. I understand that they're constants, but how do you calculate them? Or are they usually given?
Thank you!
Homework Statement
Branching ratios of tau lepton decay:
hadrons 66%
muon 17%
electron 17%
Use your knowledge of the decay of W bosons to justify these rates.
Homework EquationsThe Attempt at a Solution
[/B]
The W+ boson can decay to any combination of quarks with +1 charge, but the CKM...
The gear ratio is the ratio of angular displacement, angular velocity, angular acceleration, torque etc of the input with respect to output. However, I would like to know that which of these variables will be scaled exactly to the gear ratio in reality, as there might be some friction in the...
Homework Statement
Hi, I need to get an estimate of the branching ratios of the processes [/B]
t ---> b + W ---> b + c anti-s
t ---> b + W ---> b + anti-tau nu(tau)
without doing the calculations, just a qualitative estimation.
I know I have to take into account the way W decays...