Pieces of 2 by 4 by 72 lumber sold by a certain yard have been observed by a consumer watchdog to have 0, 1, 2, 3, 4, or 5 visible flaws (but rarely more). The probabilities for various numbers of flaws are provided by its cumulative distribution function Fr)Px: 0 4 Fox) .45 .67 .81 .89 96 a) As a customer, I find it unacceptable to buy such a piece of lumber if it has more than 3 flaws. What is the probability that a piece I buy will by accident be unacceptable? b) Find the average number of flaws in a piece of lumber chosen arbitrarily, E(X)

Circle a has a diameter of 7 inches, a circumference of 21.98 inches, and an area of 38.465 square inches. the diameter of circle b is 6 inches, the circumference is 18.84 inches, and the area is 28.26 square inches. part a: using the formula for circumference, solve for the value of pi for each circle. (4 points) part b: use the formula for area and solve for the value of pi for each circle. (4 points)

Use the method of cylindrical shells to find the volume v generated by rotating the region bounded by the curves about the given axis.y = 7ex, y = 7e^-x, x = 1; about the y-axis

Desmond wants to sell his car that he paid $8,000 for 2 years ago. the car depreciated, or decreased in value, at a constant rate each month over a 2-year period. if x represents the monthly depreciation amount, which expression shows how much desmond can sell his car for today? 8,000 + 24x 8,000 - 24x 8,000 + 2x 8,000 - 2xdesmond wants to sell his car that he paid $8,000 for 2 years ago. the car depreciated, or decreased in value, at a constant rate each month over a 2-year period. if x represents the monthly depreciation amount, which expression shows how much desmond can sell his car for today? 8,000 + 24x 8,000 - 24x 8,000 + 2x 8,000 - 2x