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Nadusha1986 [10]
3 years ago
10

A Parks and Recreation official surveyed 200 people at random who have used one of the city's parks. The survey revealed that 26

resided outside the city limits. If she had to arrive at one single value to estimate the true proportion of park users who are residents outside of the city, it would be 0.13. Group of answer choices True False
Mathematics
1 answer:
emmasim [6.3K]3 years ago
5 0

Answer:

True

Step-by-step explanation:

The estimate of the true proportion of park users who are residents outside of the city is the number of park users in the sample who are residents outside of the city divided by the size of the sample.

In this problem:

26 park users resided outside the city, in a sample of 200 park users.

So

p = 26/200 = 0.13

So the answer is True

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Answer:

The volume of pyramid B is 81 cubic units

Step-by-step explanation:

Given

<u>Pyramid A</u>

s = 4 -- base sides

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<u>Pyramid B</u>

s = 6 --- base sides

Required

Determine the volume of pyramid B <em>[Missing from the question]</em>

From the question, we understand that both pyramids are equilateral triangular pyramids.

The volume is calculated as:

V = \frac{1}{3} * B * h

Where B represents the area of the base equilateral triangle, and it is calculated as:

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Where s represents the side lengths

First, we calculate the height of pyramid A

For Pyramid A, the base area is:

B = \frac{1}{2} * s^2 * sin(60)

B = \frac{1}{2} * 4^2 * \frac{\sqrt 3}{2}

B = \frac{1}{2} * 16 * \frac{\sqrt 3}{2}

B = 4\sqrt 3

The height is calculated from:

V = \frac{1}{3} * B * h

This gives:

36 = \frac{1}{3} * 4\sqrt 3 * h

Make h the subject

h = \frac{3 * 36}{4\sqrt 3}

h = \frac{3 * 9}{\sqrt 3}

h = \frac{27}{\sqrt 3}

To calculate the volume of pyramid B, we make use of:

V = \frac{1}{3} * B * h

Since the heights of both pyramids are the same, we can make use of:

h = \frac{27}{\sqrt 3}

The base area B, is then calculated as:

B = \frac{1}{2} * s^2 * sin(60)

Where

s = 6

So:

B = \frac{1}{2} * 6^2 * sin(60)

B = \frac{1}{2} * 36 * \frac{\sqrt 3}{2}

B = 9\sqrt 3

So:

V = \frac{1}{3} * B * h

Where

B = 9\sqrt 3 and h = \frac{27}{\sqrt 3}

V = \frac{1}{3} * 9\sqrt 3 * \frac{27}{\sqrt 3}

V = \frac{1}{3} * 9 * 27

V = 81

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Answer:

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