Answer:
The midpoint is (2, -2) :)
Step-by-step explanation:
Midpoint formula time!
(3 + 1) / 2 + (0 - 4) / 2
=
(2, -2) :)
So Looks like it’s area so 2x1x500x300 =300000
This is a conditional probability question.
The conditional probability is given as follows: The probability of an event A given B is given by
![P(A|B)= \frac{P(A\cap B)}{P(B)}](https://tex.z-dn.net/?f=P%28A%7CB%29%3D%20%5Cfrac%7BP%28A%5Ccap%20B%29%7D%7BP%28B%29%7D%20)
Thus, given that the
fracture toughness of a particular steel alloy is known to be
normally distributed with a mean of 28.3 and a standard deviation of
0.77.
The probability that the fracture toughness will be between 29 and 40.3 given that the <span>fracture toughness is at least 27 is given by
![P(29 \leq X \leq 40.3 \, | \, X \geq 27)= \frac{P(29 \leq X \leq 40.3)\cap P(X \geq 27)}{P(X \geq 27)} \\ \\ =\frac{P(29 \leq X \leq 40.3)}{P(X \geq 27)}](https://tex.z-dn.net/?f=P%2829%20%5Cleq%20X%20%5Cleq%2040.3%20%5C%2C%20%7C%20%5C%2C%20X%20%5Cgeq%2027%29%3D%20%5Cfrac%7BP%2829%20%5Cleq%20X%20%5Cleq%2040.3%29%5Ccap%20P%28X%20%5Cgeq%2027%29%7D%7BP%28X%20%5Cgeq%2027%29%7D%20%20%5C%5C%20%20%5C%5C%20%3D%5Cfrac%7BP%2829%20%5Cleq%20X%20%5Cleq%2040.3%29%7D%7BP%28X%20%5Cgeq%2027%29%7D)
![P(29 \leq X \leq 40.3)=P\left(z \ \textless \ \frac{40.3-28.3}{0.77}\right)- P\left(z \ \textless \ \frac{29-28.3}{0.77}\right) \\ \\ =P(z\ \textless \ 15.58)-P(z\ \textless \ 0.91)=1-0.81835=0.18165](https://tex.z-dn.net/?f=P%2829%20%5Cleq%20X%20%5Cleq%2040.3%29%3DP%5Cleft%28z%20%5C%20%5Ctextless%20%5C%20%20%5Cfrac%7B40.3-28.3%7D%7B0.77%7D%5Cright%29-%20P%5Cleft%28z%20%5C%20%5Ctextless%20%5C%20%20%5Cfrac%7B29-28.3%7D%7B0.77%7D%5Cright%29%20%5C%5C%20%20%5C%5C%20%3DP%28z%5C%20%5Ctextless%20%5C%2015.58%29-P%28z%5C%20%5Ctextless%20%5C%200.91%29%3D1-0.81835%3D0.18165)
![P(X \geq 27)=1-P(x\ \textless \ 27) \\ \\ =1-P\left(z\ \textless \ \frac{27-28.3}{0.77}\right)=1-P(z\ \textless \ -1.688) \\ \\ =1-0.04568=0.95432](https://tex.z-dn.net/?f=P%28X%20%5Cgeq%2027%29%3D1-P%28x%5C%20%5Ctextless%20%5C%2027%29%20%5C%5C%20%20%5C%5C%20%3D1-P%5Cleft%28z%5C%20%5Ctextless%20%5C%20%5Cfrac%7B27-28.3%7D%7B0.77%7D%5Cright%29%3D1-P%28z%5C%20%5Ctextless%20%5C%20-1.688%29%20%5C%5C%20%20%5C%5C%20%3D1-0.04568%3D0.95432)
Thus, </span>the probability that the fracture toughness will be between 29 and 40.3 given that the <span>fracture toughness is at least 27 is given by</span>
Answer:
220
Step-by-step explanation:
660÷12=55 miles per hour
4×55=220
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5+2-3=7-3=4
Hope it helps
Good luck
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