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ExtremeBDS [4]
3 years ago
15

The length of a rectangle it twice it's within. If the perimeter of the rectangle is 30 cm, find its area.

Mathematics
1 answer:
Xelga [282]3 years ago
6 0

w - width

2w - length (l)

30 cm - perimeter

w + w + 2w + 2w = 6w - perimeter

The equation:

6w = 30    <em>divide both sides by 6</em>

w = 5 cm

2w = 2(5) = 10

l = 10 cm

The area of a rectangle: A = lw.

Substitute:

A = (5)(10) = 50

<h3>Answer: The area is 50cm²</h3>
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Heights of men have a bell-shaped distribution, with a mean of 176 cm and a standard deviation of 7 cm. Using the Empirical Rule
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Answer:

a) 68% of the men fall between 169 cm and 183 cm of height.

b) 95% of the men will fall between 162 cm and 190 cm.

c) It is unusual for a man to be more than 197 cm tall.

Step-by-step explanation:

The 68-95-99.5 empirical rule can be used to solve this problem.

This values correspond to the percentage of data that falls within in a band around the mean with two, four and six standard deviations of width.

<em>a) What is the approximate percentage of men between 169 and 183 cm? </em>

To calculate this in an empirical way, we compare the values of this interval with the mean and the standard deviation and can be seen that this interval is one-standard deviation around the mean:

\mu-\sigma=176-7=169\\\mu+\sigma=176+7=183

Empirically, for bell-shaped distributions and approximately normal, it can be said that 68% of the men fall between 169 cm and 183 cm of height.

<em>b) Between which 2 heights would 95% of men fall?</em>

This corresponds to ±2 standard deviations off the mean.

\mu-2\sigma=176-2*7=162\\\\\mu+2\sigma=176+2*7=190

95% of the men will fall between 162 cm and 190 cm.

<em>c) Is it unusual for a man to be more than 197 cm tall?</em>

The number of standard deviations of distance from the mean is

n=(197-176)/7=3

The percentage that lies outside 3 sigmas is 0.5%, so only 0.25% is expected to be 197 cm.

It can be said that is unusual for a man to be more than 197 cm tall.

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Step-by-step explanation:

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6/14 : 14/14

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