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3 years ago

Michael has a ball that has a radius of 3 inches and Patrick has a ball that has a radius

Mathematics

1 answer:

Diano4ka-milaya [45]3 years ago

7 0

Answer:

27 times bigger

Step-by-step explanation:

V(sphere) = 4/3πr³

Michael: 4/3π3³ = 4/3×27π or 36π

Patrick: 4/3πr³ = 4/3πx9³ or 4/3x729π or 972π

36π to 972π is 1 : 27

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3 years ago

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3 years ago

A research team conducted a study showing that approximately 15% of all businessmen who wear ties wear them so tightly that they

Helen [10]

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a) 0.913

b) 0.397

c) 0.087

Step-by-step explanation:

We are given the following information:

We treat wearing tie too tight as a success.

P(Tight tie) = 15% = 0.15

Then the number of businessmen follows a binomial distribution, where

$P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}$

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 15

We have to evaluate:

a) at least one tie is too tight

$P(x \geq 1) = P(x = 1) +....+ P(x = 15)\\=1 - P(x = 0)\\= 1 - \binom{15}{0}(0.15)^0(1-0.15)^{15}\\=1 - 0.087\\= 0.913$

b) more than two ties are too tight

$P(x > 2) = P(x = 3) +....+ P(x = 15)\\=1 - P(x = 0) - P(x=1) - P(x=2)\\= 1 - \binom{15}{0}(0.15)^0(1-0.15)^{15}-\binom{15}{1}(0.15)^1(1-0.15)^{14}-\binom{15}{0}(0.15)^2(1-0.15)^{13}\\=1 - 0.087 - 0.231 - 0.285\\= 0.397$

c) no tie is too tight

$P(x = 0)\\=\binom{15}{0}(0.15)^0(1-0.15)^{15}\\=0.087$

d) at least 18 ties are not too tight

This probability cannot be evaluated as the number of success or the failures exceeds the number of trials given which is 15.

The probability is asked for 18 failures which cannot be evaluated.

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