Answer:
62 .5 minutes or 1 hr, 2 min, and 24 sec.
Step-by-step explanation:
Answer:
The value that corresponds to the 75th percentile is 16.35.
Step-by-step explanation:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean
and standard deviation
, the zscore of a measure X is given by:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
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.
A normal distribution has a mean of 15 and a standard deviation of 2.
This means that ![\mu = 15, \sigma = 2](https://tex.z-dn.net/?f=%5Cmu%20%3D%2015%2C%20%5Csigma%20%3D%202)
Find the value that corresponds to the 75th percentile.
This is X when Z has a pvalue of 0.75. So X when ![Z = 0.675](https://tex.z-dn.net/?f=Z%20%3D%200.675)
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![0.675 = \frac{X - 15}{2}](https://tex.z-dn.net/?f=0.675%20%3D%20%5Cfrac%7BX%20-%2015%7D%7B2%7D)
![X - 15 = 2*0.675](https://tex.z-dn.net/?f=X%20-%2015%20%3D%202%2A0.675)
![X = 2*0.675 + 15](https://tex.z-dn.net/?f=X%20%3D%202%2A0.675%20%2B%2015)
![X = 16.35](https://tex.z-dn.net/?f=X%20%3D%2016.35)
The value that corresponds to the 75th percentile is 16.35.
Answer:
C
Step-by-step explanation:
The tops and sides are parallel to each other so there is two sets and there are 4 right angles.
In the region 0-2, the first derivative has a zero at x=1, and the second derivative (slope of the first derivative line) is positive. This means f(x) will have a minimum at x=1.
Likewise, in the region 4-6, the second derivative is negative and the first derivative is zero at x=5, indicating a maximum there.
These observations narrow the selection to choices A or C. The derivative curve is continuous at x=2 and x=4, so there will not be any discontinuities in f(x)--eliminating selection C.
The best choice is
A.
Answer:
x = 1
Step-by-step explanation:
3x + 1/2 (2x + 6) = 6x + 1
3x + x + 3 = 6x + 1
4x + 3 = 6x + 1
2 = 2x
x = 1