(a) Given the following information about three events A, B, and C. ( ) 0.69 ( ) 0.19 ( ) 0.70 ( ) 0.20 ( ) 0.71 ( ) 0.21 P A B P A B P A C P A C P B C P B C = = = = = = Find the values of P A P B ( ), ( ), and P C( ) .

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?

An equation of the line tangent to y=x^3+3x^2+2 at its point of inflection is

God's gym charges a sign-up fee of $100 plus $30 per month. write an expression to represent how much someone would pay for a membership.