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3 years ago

Please explain how to get the answer.

Mathematics

2 answers:

katen-ka-za [31]3 years ago

7 0

Alrighty..

Volume of sphere = 4/3 x (pi)x r^3 .where r is the radius of a circle ..in this case the radius for the smaller circle. and the Volume of the larger one would be 4/3 x (pi)x R^3 .
so when they say the volume if the larger one is Twice the smaller one they're bascially telling you that (4/3x(pi)xR^3 = 2 x (4/3x(pi)xr^3)

When you multiply the formula by two you'd get 4/3x(pi)xR^3= 8/3 x (pi)x r^3

Now solve accordingly by taking 4/3 to the other side.. you'll get sth like this

(pi)R^3 = 2(pi)r^3
Cancel the pi out

now you have R^3 = 2r^3 divide the equation now by r^3
R^3/r^3 =2
you can also write this as (R/r)^3 = 2
take the power cube to the other side to get cube root of 2!!!
therefore R/r= cube root of 2

Hope this helped! :)

Maru [420]3 years ago

3 0

2r=R

Because 2 of "r" make 1 R

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a) P=0.091

b) If there are half of each taste, picking 3 vainilla in a row has a rather improbable chance (9%), but it is still possible that there are 6 of each taste.

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Step-by-step explanation:

We can model this problem with the variable x: number of picked vainilla in a row, following a hypergeometric distribution:

$P(x=k)=\dfrac{\binom{K}{k}\cdot \binom{N-K}{n-k}}{\binom{N}{n}}$

being:

N is the population size (12 candies),

K is the number of success states in the population (6 vainilla candies),

n is the number of draws (3 in point a, 4 in point c),

k is the number of observed successes (3 in point a, 4 in point c),

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$P(x=3)=\dfrac{\binom{6}{3}\cdot \binom{12-6}{3-3}}{\binom{12}{3}}=\dfrac{\binom{6}{3}\cdot \binom{6}{0}}{\binom{12}{3}}=\dfrac{20\cdot 1}{220}=0.091$

b) If there are half of each taste, picking 3 vainilla in a row has a rather improbable chance (9%), but is possible.

c) In the case k=4, we have:

$P(x=3)=\dfrac{\binom{6}{4}\cdot \binom{6}{0}}{\binom{12}{4}}=\dfrac{15\cdot 1}{495}=0.030$

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