All of the following can be the focus of an apprenticeship program except: a. athletics. b. construction. c. health care. d. culinary arts.

This is a bit of an odd question, but-- you can apprentince in construction, health care, and the culinary arts. The only I don't suppose you can apprentince in is athletics, as far as I know. I hope this helps somehow, but this really is an odd little question. 

The answer is    (d) 7/2======we have    we also  have an integral      notice how function f splits up at x = 0. there's a left piece and a right pieceso we'll need to do the same thing with our integral: split it at x = 0we use a property of integrals that allows us to split up and sum:     notice that for the piecewise function f, the function has the equationf(x) = x when x  ≤ 0. so for the integral  , f(x) = x so it changes into      for the piecewise function f, the function has the equationf(x) = x+1  when x  > 0. for the integral  , we have    therefore, back to our splitted integral: