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Since this cylinder has a radius of 2.5 centimeters, its height is approximately equal to 8.3 meters.
<h3>How to calculate the height of this cylinder?</h3>
Mathematically, the volume of a cylinder is calculated by using this formula:
V = πr²h
<u>Where:</u>
<u>Given the following data:</u>
- Radius of cylinder = 2.5 cm.
- Volume of cylinder = 163 cubic centimeters.
Substituting the given parameters into the formula, we have;
163 = 3.142 × 2.5² × h
163 = 19.6375h
h = 163/19.6375
Height, h = 8.3 meters.
Read more on cylinder here: brainly.com/question/21367171
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To solve this problem, first we have to determine the z statistic. The formula is

where x is the test point which is 8.019, the mean is 8 mph, s is the standard deviation which is 3.813 and n is the number of data which is 1114. Then,

Next, we find the p-value for the particular z. p-value is used in hypothetical test. Using a wind turbine would be the null hypothesis. From the standard normal table found in any statistics book, the p-value for z<0.17 is 0.5675. If the p-value is greater than 0.05, then you do not reject the null hypothesis.
Therefore, the landowner could use a small turbine at the site.
The width of the rectangle using synthetic division is; 5x² + 4x - 6
<h3>Synthetic division of Polynomials</h3>
We are given;
Area of rectangle = 5x³ + 19x² + 6x - 18
Length of rectangle = x + 3
We know that;
Width of rectangle = Area/length.
Using synthetic division, we have;
<u>5x² + 4x - 6 </u>
(x + 3) | 5x³ + 19x² + 6x - 18
- <u>5x³ + 15x²</u>
4x² + 6x
- <u>4x² + 12x</u>
-6x - 18
<u> -6x - 18</u>
0
Thus, the width of the rectangle is 5x² + 4x - 6
Read more about polynomial synthetic division at; brainly.com/question/24323423