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gulaghasi [49]
3 years ago
5

A sculpture is shaped like a sphere with 4 cones attached to it. Several dimensions of the sculpture, in feet, are shown in the

diagram below. The total height of the sculpture from top to bottom is 12 feet. What is the volume of the sculpture, to the nearest cubic foot? 

Mathematics
1 answer:
suter [353]3 years ago
5 0

volume of the center sphere = 4/3*PI*r^3

r = 3 ( given in the picture)

 so 4/3 * 3.14 *3^3 = 113.04 cubic feet

 volume of 1 cone: pi *r^2 *h/3

r = 3 and h=3 ( given in the picture)

so 3.14 * 3^2 * 3/3 = 28.26 cubic feet

 there are 4 cones so 28.26* 4 = 113.04 cubic feet


113.04 + 113.04 = 226.08 cubic feet

 rounded to nearest cubic foot = 226 cubic feet

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Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

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For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

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What is the probability that a sample of 72 gas stations taken that same week will have a sample mean within $0.15 of the population mean?

This is the pvalue of Z when X = 2.77 + 0.15 = 2.92 subtracted by the pvalue of Z when X = 2.77 - 0.15 = 2.62. So

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By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{2.92 - 2.77}{0.0667}

Z = 2.25

Z = 2.25 has a pvalue of 0.9878

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Z = \frac{2.62 - 2.77}{0.0667}

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8 0
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