Acompany dyes two sizes of rugs. a small rug requires 8 hours for dyeing and a medium-size rug requires 12 hours for dyeing. the dyers have to make at least 22 rugs, and they must do it in less than 240 hours. let x equal small rugs and y equal medium rugs. which of the following inequalities can be paired with x + y ≥ 22 to create a system that represents this situation? 8x + 12y > 240 12x + 8y > 240 8x + 12y < 240 12x + 8y < 240

The figures below are made out of circles, semicircles, quarter circles, and a square. find the area and the perimeter of each figure and give your answers as a completely simplified exact value in terms of π (no approximations).

The accompanying normal probability plot was constructed from a sample of 30 readings on tension for mesh screens behind the surface of video display tubes used in computer monitors. does it appear plausible that the tension distribution is normal? the given probability is has a significant downward curve, so it is plausible that the tension distribution is normal. the given probability is has a significant downward curve, so it is not plausible that the tension distribution is normal. the given probability is quite linear, so it is plausible that the tension distribution is normal. the given probability is has a significant upward curve, so it is not plausible that the tension distribution is normal. the given probability is quite linear, so it is not plausible that the tension distribution is normal.

The discrete random variables x and y take integer values with joint probability distribution given by f (x,y) = a(y−x+1) 0 ≤ x ≤ y ≤ 2 or =0 otherwise, where a is a constant. 1 tabulate the distribution and show that a = 0.1.2 find the marginal distributions of x and y. 3 calculate cov(x,y).4 state, giving a reason, whether x and y are independent. 5 calculate e(y|x = 1).