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Gwar [14]
3 years ago
13

A hollow sphere sits snugly in a foam cube so that the sphere touches each side of the cube. Find the volume of the foam.

Mathematics
1 answer:
ExtremeBDS [4]3 years ago
5 0

Answer:

                             π

V-foam = 4r³( 2 - ----- )

                             3

Step-by-step explanation:

Let the radius of the sphere be r.  Then the volume of the sphere is

V = (4/3)(π)(r³).  

Next, recognize that the side length of the cube is 2r, and that the volume of the cube is thus

V = (2r)³, or 8r³.

Then the volume of the foam is equal to the volume of the cube less the volume of the sphere:

V-foam = 8r³ - (4/3)(π)(r³).  This could be factored into

                             π

V-foam = 4r³( 2 - ----- )

                             3

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Answer:

H0 : μd = 0

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Test statistic = 0.6687 ;

Pvalue = 0.7482 ;

Fail to reject H0.

Step-by-step explanation:

H0 : μd = 0

H1 : μd ≠ 0

Given the data:

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After: 16 24 42 80 78 73

Difference = -1 2 24 35 -18 -9

Mean difference, d ; Σd / n

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d = Σx / n = 33 / 6 = 5.5

Test statistic = (d / std / sqrt(n))

std = sample standard deviation = 20.146

Test statistic = 5.5 ÷ (20.146/sqrt(6))

Test statistic = 0.6687

The Pvalue :

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At α = 0.05

Pvalue > α ; Hence we fail to reject H0

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3 years ago
Can Fractions and ratios cannot have zero in the denominator?
labwork [276]
True , is the answer ! :)
4 0
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The variables x and y vary inversely. When y is 725, x is 20. What is x when y is 50?
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Black_prince [1.1K]

Probabilities are used to determine the likelihood of events

The value of the probability P(thinking of a song)P(turn on the radio and hear the song) is 0.056

<h3>How to estimate the probability</h3>

To calculate the probability, we make use of the following representations:

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So, we have:

P(thinking of a song)P(turn on the radio and hear the song) = P(A) * P(B)

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P(thinking of a song)P(turn on the radio and hear the song) = 0.12* 0.47

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