Steel factory workers ages mean: 42 median: 38 range: 52 mean deviation: 11.23 shift 1 18 25 56 42 29 38 54 47 35 30 shift 2 23 19 50 49 67 34 30 59 40 33 shift 3 19 22 24 40 45 29 33 29 39 59 shift 4 21 23 25 40 35 19 70 40 22 23 the summary statistics for all of the workers at a steel factory are shown. four sample groups were taken from each of the four shifts. for which sample group is the mean closest to the population mean? a) shift 1 b) shift 2 c) shift 3 d) shift 4

Solution: We are given the population mean

Now, in order to find which shift's mean is closest to population mean, we will find the mean of each shift.

The mean of shift 1 is:

The mean of shift 2 is:

The mean of shift 3 is:

The mean of shift 4 is:

We clearly see the mean of shift 2 is close to the population mean. Hence the option B) Shift 2 is correct.

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)

solve systems of equations by graphing. a system of linear equations contains two or more equations e.g. y=0.5x+2 and y=x-2. the solution of such a system is the ordered pair that is a solution to both equations. to solve a system of linear equations graphically we graph both equations in the same coordinate system