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3 years ago

Assume the following triangles are similar. Find the scale factor and the lengths of the missing sides.

Mathematics

1 answer:

Elanso [62]3 years ago

5 0

Answer:

If two figures are similar, then the correspondent sides are related by a constant factor.

For example, if the base of one side of one of the figures has a length L, then the correspondent side of the other figure has a length k*L where k is the scale factor.

Let's start with the two left triangles.

In the smaller one the base is 5, and the base of the other triangle is 15.

Then we will have:

15 = k*5

15/5 = k = 3

The scale factor is 3.

Then we will have that:

a = scale factor times the correspondent side in the smaller triangle:

a = k*3 = 3*3 = 9

a = 9

For the other two triangles, the base of the smaller triangle is 12, while the base of the larger triangle is 20.

Then we will have the relation:

12*k = 20

k = (20/12) = 10/6 = 5/3

The scale factor is 5/3

This means that the unknown side b is given by:

b*(5/3) = 15

b = (3/5)*15 = 3*3 = 9

b = 9.

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A survey found that women's heights are normally distributed with mean 62.7 in, and standard deviation 2.8 in. The survey also f

Viefleur [7K]

Using the normal distribution, we have that:

The percentage of men who meet the height requirement is 3.06%. This suggests that the majority of employees at the park are females.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean $\mu$ and standard deviation $\sigma$ is given by:

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

The z-score measures how many standard deviations the measure is above or below the mean.

Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

The mean and the standard deviation of men's heights are given as follows:

$\mu = 69.3, \sigma = 3.9$ .

The proportion of men who meet the height requirement is is the <u>p-value of Z when X = 62 subtracted by the p-value of Z when X = 55</u>, hence:

X = 62:

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

$Z = \frac{62 - 69.3}{3.9}$

Z = -1.87

Z = -1.87 has a p-value of 0.0307.

X = 55:

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

$Z = \frac{55 - 69.3}{3.9}$

Z = -3.67

Z = -3.67 has a p-value of 0.0001.

0.0307 - 0.0001 = 0.0306 = 3.06%.

The percentage of men who meet the height requirement is 3.06%. This suggests that the majority of employees at the park are females.

More can be learned about the normal distribution at brainly.com/question/4079902

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