The height of a basketball thrown by a 6 foot tall man follows a path defined by the function h(x) = -0.5x^2 + 3x + 6 h(x) = −0.5x^2 + 3x + 6, where x is the horizontal distance from where it is thrown. How far away from the basket should the player stand in order for the ball to go in the basket (10 feet high) on its way down? Show all work.

Thompson and thompson is a steel bolts manufacturing company. their current steel bolts have a mean diameter of 127 millimeters, and a variance of 36. if a random sample of 35 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by greater than 0.5 millimeters? round your answer to four decimal places.