1. The triangle inequality tells you the sum of any two sides of a triangle must exceed the length of the other side. (Some versions say, "must be not less than ..." rather than "must exceed.") In practice, this means two things:

the sum of the shortest two sides is greater than the length of the longest side
the length of any side lies between the sum and the difference of the other two sides

Here, we can use the latter fact to write the desired inequality. The difference of the given sides is 13 -4 = 9; their sum is 13 +4 = 17. The third side must lie between 9 and 17. If that side length is designated "s", then ...

9 < s < 17

(If you don't mind a "triangle" that looks like a line segment, you can use ≤ instead of <.)

2. Same as (1) using different numbers.

12 -7 < MN < 12 +7

5 < MN < 19

3. Side CD is congruent to itself, and side CA is shown congruent to side CB. This means the requirements of the Hinge Theorem are met. That theorem tells you the longer side is opposite the greater angle:

AD > BD

7 0

3 years ago

In 2014, the CDC estimated that the mean height for adult women in the U.S. was 64 inches with a standard deviation of 4 inches.

Vladimir79 [104]

Answer:

A. 16%

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 64, \sigma = 4$

Which of the following gives the probability that a randomly selected woman has a height of greater than 68 inches?

This is 1 subtracted by the pvalue of Z when X = 68. So

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

$Z = \frac{68 - 64}{4}$

$Z = 1$

$Z = 1$ has a pvalue of 0.84.

1 - 0.84 = 0.16

So the correct answer is:

A. 16%

6 0

3 years ago