sphere a has radius 4 and a hemisphere b has a radius 8. fin the ratio of the volume of A to the volume of b

Mathematics

1 answer:

salantis [7]2 years ago

4 0

Answer:

A/B = 0.125

Step-by-step explanation:

Givens

r for Sphere A = 4

r for Sphere B = 8

Solution

Volume A = 4/3 pi r^3

r = 4

Volume A = 4/3 pi 4^3

Volume A = 4/3 pi 64

Note: there is no point in expanding the result. 4/3 and pi are going to cancel out when you set up the volume formula

Volume B = 4/3 pi * r^3

r = 8

Volume B = 4/3 pi * 8^3

Volume B = 4/3 pi * 512

Ratio A to B = 4/3 pi * 64 / 4/3 * pi * 512 Cancel 4/3 pi

Ratio A to B = 64/512

Ratio A to B = 1/8

Ratio A to B = 0.125

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A coin, having probability p of landing heads, is continually flipped until at least one head and one tail have been flipped. (a

Natali [406]

Answer:

(a)

The probability that you stop at the fifth flip would be

$p^4 (1-p) + (1-p)^4 p$

(b)

The expected numbers of flips needed would be

$\sum\limits_{n=1}^{\infty} n p(1-p)^{n-1} = 1/p$

Therefore, suppose that $p = 0.5$ , then the expected number of flips needed would be 1/0.5 = 2.

Step-by-step explanation:

(a)

Case 1

Imagine that you throw your coin and you get only heads, then you would stop when you get the first tail. So the probability that you stop at the fifth flip would be

$p^4 (1-p)$

Case 2

Imagine that you throw your coin and you get only tails, then you would stop when you get the first head. So the probability that you stop at the fifth flip would be

$(1-p)^4p$