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3 years ago

7

A homeowner is building a circular fire pit in his backyard. He plans to outline the pit with bricks and cover the space inside

the pit with sand. The homeowner has decided to build the pit with a diameter of 3 feet. In order to know how many bricks to buy, the homeowner must know the distance around the outside of the pit. Calculate both the exact distance and the approximate distance. In order to know how much sand to buy, the homeowner must know how much space needs to be covered inside the pit. Calculate both the exact area and the approximate area.

1 answer:

sergiy2304 [10]3 years ago

8 0

Answer:

Exact Circumference = 3π feet

Approximate Circumference = 9.42 feet

Exact Area = 2.25 π ft²

Approximate Area = 7.07 ft²

Step-by-step explanation:

Diameter = d = 3 feet

Radius = r = 1.5 feet

<u><em>Circumference:</em></u>

Outline of the pit is the circumference.

=> Circumference = $\pi d$

Where d = 3 feet

=> <u>Exact Circumference = 3π feet</u>

=> <u>Approximate Circumference = 9.42 feet</u>

<u><em>Area:</em></u>

Area of Circle = πr²

Area = π(1.5)²

<u>Exact Area = 2.25 π ft²</u>

<u>Approximate Area = 7.07 ft²</u>

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Answer:

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Step-by-step explanation:

This can be solved by the the z-score formula:

On a normaly distributed set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a value X is given by:

$Z = \frac{X - \mu}{\sigma}$

Each z-score value has an equivalent p-value, that represents the percentile that the value X is:

The problem states that:

Mean = 35, so $\mu = 35$

Variance = 81. The standard deviation is the square root of the variance, so $\sigma = \sqrt{81} = 9$ .

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Looking at the z-score table, $z = -0.44$ has a pvalue of 0.333. So what is the value of X when $z = -0.44$ .

$Z = \frac{X - \mu}{\sigma}$

$-0.44 = \frac{X - 35}{9}$

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$X = 31.04$

The 33rd percentile of the time it takes Finn to get to work on any given day is 31.04 minutes.

Over the next 2 days, find the probability that Finn took more than 40.5 minutes to get to work on the first day or more than 38.5 minutes to get to work on the second day.

$P = P_{1} + P_{2}$

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$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{40.5 - 35}{9}$

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$X = 38.5$

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$Z = \frac{38.5 - 35}{9}$

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$Z = 0.39$ has a pvalue of 0.6517. This means that the probability that it took LESS than 38.5 minutes for Finn to get to work is 65.17%. The probability that it took more than 38 minutes if $P_{1} = 100% - 65.17% = 34.83% = 0.3483$

So:

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