If the standard deviation for a set of data is 0, which of the following must be true?
a. all of the data values are negative.
b. all the data values equal 0.
c. all of the data values are identical.
d. none of the above must be true since the standard deviation cannot be equal to 0.

C. All of the data values are identical.

Step-by-step explanation:

If the standard deviation for a set of data is 0, then all of the data values are identical.

When a standard deviation is 0, then the variance is also 0 and the mean of the deviation that is squared is also 0, thereby making all the values identical to the mean, that is 0.

5

step-by-step explanation:

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)