Question 1: 155 people visit a Leisure Centre. 97 use the waterslide. 43 use the sauna. 43 people do not use
either the water slide or the sauna. If one person is chosen at random, find the probability that
this person uses both the waterslide and the sauna.

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?

2pointswhich of the following appear in the diagram below? check all that apply. d a. zcdeов. сеo c. aéo d. zdce

What is the point of inflection for the function f(x)=2cos4x on the interval (0, pi/2)