For a certain spinner, if we expect to win a prize five times in forty tries, what is the theoretical probability of winning a 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?

Based on the graph, what is the initial value of the linear relationship? a coordinate plane is shown. a line passes through the y-axis at -2 and the x-axis at 3.

Someone me! if you’re smart you can solve this!