Chris bought some gum for $0.15 each and some candy $0.10 each. The amount of candy was 12 less than three times the amount of gum. He spent a total of $5.25. How much of each did he buy?

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?

Which data set has a greater spread? why? set a: {38, 12, 23, 48, 55, 16, 18} set b: {44, 13, 24, 12, 56} has a greater spread because .

Over the course of the school year, you keep track of how much snow falls on a given day and whether it was a snow day. your data indicates that of twenty-one days with less than three inches of snow, five were snow days, while of the eight days with more than three inches of snow, six were snow days. if all you know about a day is that it is snowing, what is the probability that it will be a snow day?