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Alenkinab [10]
3 years ago
7

From her house, Haley could drive due north to get to her parents' house or she could drive due east to get to her grandparents'

house. It is 7 kilometers from Haley's house to her parents' house and a straight-line distance of 9 kilometers from her parents' house to her grandparents' house. How far is Haley from her grandparents' house? If necessary, round to the nearest tenth. Please help me with this phytagareon theorem question please. I would really appreciate it . Please asap
Mathematics
1 answer:
vivado [14]3 years ago
5 0

Answer:

5.7km

Step-by-step explanation:

-let the drive east be the base of our 'triangle' and the drive north be the height, h.

-The distance from the parents to the grandparents, 9km, forms the hypotenuse.

#Using Pythagorean Theorem, we can find the distance to her grandparents as:

H^2=h^2+b^2\\\\9^2=7^2+b^2\\\\b^2=81-49\\\\b=\sqrt{32}\\\\=5.657\approx5.7\ km

Hence, the distance fro Hayley's place to her grandparents is 5.7km

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The distribution of heights for adult men in a certain population is approximately normal with mean 70 inches and standard devia
KengaRu [80]

Answer:

The interval (meassured in Inches) that represent the middle 80% of the heights is [64.88, 75.12]

Step-by-step explanation:

I beleive those options corresponds to another question, i will ignore them. We want to know an interval in which the probability that a height falls there is 0.8.

In such interval, the probability that a value is higher than the right end of the interval is (1-0.8)/2 = 0.1

If X is the distribuition of heights, then we want z such that P(X > z) = 0.1. We will take W, the standarization of X, wth distribution N(0,1)

W = \frac{X-\mu}{\sigma} = \frac{X-70}{4}

The values of the cumulative distribution function of W, denoted by \phi , can be found in the attached file. Lets call y = \frac{z-70}{4} . We have

0.1 = P(X > z) = P(\frac{X-70}{4} > \frac{z-70}{4}) = P(W > y) = 1-\phi(y)

Thus

\phi(y) = 1-0.1 = 0.9

by looking at the table, we find that y = 1.28, therefore

\frac{z-70}{4} = 1.28\\z = 1.28*4+70 = 75.12

The other end of the interval is the symmetrical of 75.12 respect to 70, hence it is 70- (75.12-70) = 64.88.

The interval (meassured in Inches) that represent the middle 80% of the heights is [64.88, 75.12] .

Download pdf
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Step-by-step explanation:

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