if alpha and beta are zeroes of polynomial 4x^2-1 obtain a quadratic polynomial whose zeroes are 1/2 alpha+beta and 1/alpha+2 beta

Find the area of the surface obtained by rotating the curve z=4e^2y from y = 0 to y =1 about the y-axis. the area is square units

Fracisco's game involves 3 green, 2 yellow, 4 red, and 3 black marbles. if he randomly draws three marbles from the bag, without replacement, what is the probability that he will draw yellow, and then red, and then black? a)1/192 b)1/72 c)3/220 d)1/55

You work for a landscape company that just got a contract to re-mulch a park. the area that needs mulching is 30 feet by 60 feet. they want a 3 inch layer of much on the area. the company has bags of mulch that cover 2 cubic yards that cost $4.00 per bag. how much will it cost the consumer just in materials to re-mulch the area (round to the nearest dollar)?