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qwelly [4]
4 years ago
7

Blake is driving home from the water park. He drives for 60 miles and stops to rest before driving 20 more miles. Unfortunately,

Blake remembers he was supposed to pick up a present for his friend on the way home, so he turns around and drives 36 miles back towards the water park. Once he picks up the present, he drives the rest of the way home, which is 70 miles away. What is the distance from the water park to Blake's home?
Mathematics
1 answer:
Firlakuza [10]4 years ago
8 0

Answer:

The distance from the water park to Blake's home is 114 miles.

Step-by-step explanation:

Let's list out the steps!

1) Blake started at his home. (+0) (0)

2) Then he drove 60 miles towards his home. (+60) (60)

3) He stops and rests. (+0) (60)

4) He drives another 20 miles. (+ 20) (80)

5) He drives back, 36 miles, towards the water park. (-36) (44)

6) He drives home, which is 70 miles. (+70) (114)

The first number after each statement, is the miles added/subtracted, with each step. The second number in parenthesis, is what the total miles is, UP to that step.

Thus, from the water park, to Blake's home, it is 114 miles!

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Answer:

a) Mean = 382.3 psi

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b) 392.7 psi

c) P(X<400)=0.8026

Step-by-step explanation:

a) The population mean can be estimated as equal to the mean of the sample, and the population standard deviation can be estimated from the sample standard deviation:

M=\frac{1}{n}\sum x_i=\frac{1}{10}(389+405+409+367+358+415+376+375+367+362)\\\\M=\frac{1}{10}(3823)=382.3\\\\\mu\approx M=382.3

s=\sqrt{\frac{1}{n-1}\sum (x_i-M)^2}=\sqrt{\frac{1}{10-1}(389-382.3)^2+...+(362-383.2)^2}\\\\\\s=\sqrt{\frac{1}{9}(3906.1)}=\sqrt{434}=20.8\\\\\\\sigma\approx s=20.8

b) We start by searching for the z-value for the 95th percentile. This value is

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P(z

Then, the strength value below which 95% of all welds will have their strengths is:

X=\mu+z\cdot \sigma/\sqrt{n}=382.3+1.645*20.8/\sqrt{10}\\\\X=382.3+32.9/3.2=382.3+10.4\\\\X=392.7

c) We calculate the probability of X being equal or less than 400 as:

z=(X-\mu)/\sigma=(400-382.3)/20.8=17.7/20.8=0.851\\\\\\P(X\leq400)=P(z

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