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3 years ago

A cone has a volume of 12 cubic inches. What is the volume of a cylinder that the cone fits exactly inside of?

Mathematics

1 answer:

Nastasia [14]3 years ago

8 0

Volume of a cone = 1/3 r² π h
Volume of a cylinder = r² π h = 3 · V ( cone ) = 3 · 12 = 36 in³

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$P(X \geq 6) = P(X=6) +P(X=7) +P(X=8) +P(X=9) +P(X=10)$

And using the probability mass function we got:

$P(X=6)=(10C6)(0.5)^6 (1-0.5)^{10-6}=0.205$

$P(X=7)=(10C7)(0.5)^7 (1-0.5)^{10-7}=0.117$

$P(X=8)=(10C8)(0.5)^8 (1-0.5)^{10-8}=0.0439$

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And adding the values we got:

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The best answer would be:

D. 0.377

Step-by-step explanation:

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=10, p=0.5)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

For this case in order to pass he needs to answer at leat 6 questions and we can rewrite this:

$P(X \geq 6) = P(X=6) +P(X=7) +P(X=8) +P(X=9) +P(X=10)$

And using the probability mass function we got:

$P(X=6)=(10C6)(0.5)^6 (1-0.5)^{10-6}=0.205$

$P(X=7)=(10C7)(0.5)^7 (1-0.5)^{10-7}=0.117$

$P(X=8)=(10C8)(0.5)^8 (1-0.5)^{10-8}=0.0439$

$P(X=9)=(10C9)(0.5)^9 (1-0.5)^{10-9}=0.0098$

$P(X=10)=(10C10)(0.5)^{10} (1-0.5)^{10-10}=0.000977$

And adding the values we got:

$P(X\geq 6) = 0.377$

The best answer would be:

D. 0.377

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3 years ago