In a class book order, 2/3 of the books are fantasy and 1/4 of the books are biography. if the order contains 60 books, how many books are either fantasy or bio?

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 statement is true 1.the pythagorean theorem can be used to find the missing side of any triangle 2.the pythagorean theorem can be used to find the missing side of any polygon 3. the pythagorean theorem can be used to find the missing side of any right triangle 4.the pythagorean theorem can be used to find the missing side of any isosceles triangle

A) if $50000 is invested in a bank account that pays 9.3% of interest compounded on a six-monthly basis, how much money will be in the account after 3 and 12 years? b) if matusalen's father had put $2.0 in the bank when he was born and there, how long would matusalen have had to his death (969 years later) if the interest was 7% per year composed each month and weekly?