A draw is being held to win a prize. Bruce buys 17 tickets.
A total of 350 tickets are in the draw.
Find the probability that Bruce does not win the prize.

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 system of linear inequalities is represented by the graph?

Alex took his brother to a birthday party. the party was scheduled to last for 1 and 3/4 hours but they stayed for 4/5 of an hour more. how long did she stay at the party?