Let C be the closed, piecewise smooth curve formed by traveling in straight lines between the points (0,0,0), (2,0,4), (3,2,6), (1,2,2), and back to the origin, in that order. (Thus the surface S lying interior to C is contained in the plane z=2x.) Use Stokes' theorem to evaluate the integral: ∫C(zcosx)dx+(x2yz)dy+(yz)dz.

The graph shows the function f(x) = (2.5)x was horizontally translated left by a value of h to get the function g(x) = (2.5)x–h.

The number if marbles of different colors stored in a hat is listed below: 4 red marbles 10 green marbles 7 blue marbles. without looking in the hat, dan takes out a marble at random. he replaces the marble and then takes out another marble from the hat. what is the probability that dan takes out a blue marble in both draws?

Pyotr tchaikovsky sporting goods operates on a 45% overhead based on the selling price, which results in an overhead of $65.34 on the newest version of an air hockey game set. if the air hockey game set costs pyotr tchaikovsky sports $49.32, find the selling price, the markup, and the net profit.