The distributions of heights of 1000 men and 1000 women selected at random from the population of a large metropolitan area are shown. Compare the heights of the
men and women by comparing the mean and the spread of the data sets.

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?

Julia is going for a walk through the neighborhood. what unit of measure is most appropriate to describe the distance she walks?

Zahra runs a 500-meter race at a constant speed. which graph shows her distance from the finish line during the race?