Suppose that z = f(x, y) and that both x and y are functions of a single variable t such that ∇f(x, y) = x 2 , y 2 i and dx dt = dy dt = t 2 − 4. For what values of t in the interval [0,[infinity]) is z increasing

Margie is practicing for an upcoming tennis tournament. her first serve is good 20 out of 30 times on average. margie wants to know the estimated probability that her first serve will be good at least four of the next six times she serves. how could she design a simulation for this scenario?