Consider a continuous-time LTI system with impulse response given by h(t) = u(t) u(t 2) where u(t) is the unit step function. (a) Is this system stable? Justify your answer. (b) Sketch the output of this system given the input x(t) = ?(t)(t1), where ?(t) is the unit impulse function. (c) Find the frequency response H(j!) for this system.

Afriend of mine is giving a dinner party. his current wine supply includes 10 bottles of zinfandel, 8 of merlot, and 11 of cabernet (he only drinks red wine), all from different wineries. (a) if he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this? ways (b) if 6 bottles of wine are to be randomly selected from the 29 for serving, how many ways are there to do this? ways (c) if 6 bottles are randomly selected, how many ways are there to obtain two bottles of each variety? ways (d) if 6 bottles are randomly selected, what is the probability that this results in two bottles of each variety being chosen? (round your answer to three decimal places.) (e) if 6 bottles are randomly selected, what is the probability that all of them are the same variety? (round your answer to three decimal places.)