Arandom sample of 50 university admissions officers were asked about expectations in application interviews. of these sample members, 28 agreed that the interviewer usually expects the interviewee to have volunteer experience doing community projects. test the null hypothesis that one-half of all interviewers have this expectation against the alternative that the population proportion is bigger than one-half.

Here is their argument. given the obtuse angle x, we make a quadrilateral abcd with ∠dab = x, and ∠abc = 90◦, and ad = bc. say the perpendicular bisector to dc meets the perpendicular bisector to ab at p. then pa = pb and pc = pd. so the triangles pad and pbc have equal sides and are congruent. thus ∠pad = ∠pbc. but pab is isosceles, hence ∠pab = ∠pba. subtracting, gives x = ∠pad−∠pab = ∠pbc −∠pba = 90◦. this is a preposterous conclusion – just where is the mistake in the "proof" and why does the argument break down there?

In trapezoid abcd, ac is a diagonal and ∠abc≅∠acd. find ac if the lengths of the bases bc and ad are 12m and 27m respectively.

(c) a vine called the mile-a-minute weed is known for growing at a very fast rate. it can grow up to 0.5 ft per day. how fast in inches per hour can the mile-a-minute weed grow up to? show your work using the correct conversion factors.