Calculate the circulation, f · dr, c in two ways, directly and using stokes' theorem. f = y i + z j + xk and c is the boundary of s, the paraboloid z = 4 − (x2 + y2), z ≥ 0 oriented upward. (hint: use polar coordinates.)

1. there are 25 students who started computer programming in elementary school and 25 students who started computer programming in middle school. the first group had a mean final project grade of 95% and the second group had a mean final project grade of 92%. the line plot shows the differences after 10 rerandomizations. determine whether the difference in the means of the two groups is significant based on the line plot. explain your answer.

Adaycare center charges a $75 enrollment fee plus $100 per week. which of the following represents the cost of sending a child to daycare for 14 weeks?

The radius of a sphere is 3 inches. which represents the volume of the sphere?