a particular group of miniature poodles has a mean weight of 13 kg with a standard deviation of 2 kg. the weights are normally distributed, so 95% of the weights fall into a certain range of values around the mean.

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?

Find x to the nearest hundredth place

The hawaiian alphabet has 12 letters. how many permutations are posible for each number of letters?