The probability distribution of x, the number of imperfections per 10 meters of a synthetic fabric in con- tinuous rolls of uniform width, is given in exercise 3.13 on page 112 as x01234 f (x) 0.41 0.37 0.16 0.05 0.01 find the average number of imperfections per 10 meters of this fabric.

Suppose you want to transform the graph of the function y=tan(x+pi/4)-1 into the graph of the function y=-tan(x+pi/2)+1 which transformations should you perform. a) reflect the graph of the first function across the x-axis, translate it pi/4 units to the left, and translate it 2 units up. b) reflect the graph of the first function across the x-axis, translate it pi/4 units to the right, and translate it 2 units up. c) reflect the graph of the first function across the line y = -1, translate it pi/4 units to the left, and translate it 2 units up. d) reflect the graph of the first function across the line y = -1, translate it pi/4 units to the right, and translate it 2 units up.