Answer:
Step-by-step explanation:
Given that a teacher gives a test to a large group of students. The results are closely approximated by a normal curve
mu =74 and sigma =8
A grade starts from 100-8 = 92nd percentile
Z score for 92nd percentile = 1.405
X score = 74+8(1.405) = 85.24
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B cut off is to next 16%
Hence C would start for scores below 100-(8+16) = 76%
76th percentile = 0.705*8+74 =79.64
Answer:
x > 36 in
Step-by-step explanation:
Let x = the width of the picture frame.
Then x + 6 = the length of the frame.
The formula for the perimeter P of a rectangle is'
P = 2l + 2w.
So, the condition is
2l + 2w > 156
2(x + 6) + 2x > 156 Distribute the 2
2x + 12 + 2x > 156 Combine like terms
4x + 12 > 156 Subtract 12 from each side
4x > 144 Divide each side by 4
x > 36
The perimeter of the picture frame will be greater than 156 in if x > 36 in.
-13 and -14
They both are consecutive negative integers that multiply to 182.
Answer:
![g(x) = \sqrt[3]{x-1} - 2](https://tex.z-dn.net/?f=%20g%28x%29%20%3D%20%5Csqrt%5B3%5D%7Bx-1%7D%20-%202%20)
Step-by-step explanation:
We want to find h and k in:
![g(x) = \sqrt[3]{x-h} + k](https://tex.z-dn.net/?f=%20g%28x%29%20%3D%20%5Csqrt%5B3%5D%7Bx-h%7D%20%2B%20k%20)
At the inflection point, the second derivative is equal to zero, so:


Then x - h = 0.
Inflection point is located at (1, -2), replacing this x value we get:
1 - h = 0
h = 1
We know that the point (-2.5, -3.5) belongs to the function, so:
![-3.5 = \sqrt[3]{-2.5-1} + k](https://tex.z-dn.net/?f=%20-3.5%20%3D%20%5Csqrt%5B3%5D%7B-2.5-1%7D%20%2B%20k%20)
k ≈ -2
All data, used or not, are shown in the picture attached.