You want to estimate the mean time college students spend watching online videos each day. the estimate must be within 2 minutes of the population mean. determine the required sample size to construct a 99% confidence interval for the population mean. assume the population standard deviation is 2.4 minutes.

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?

In the pendulum formula t=2pi. read the problem on the picture ! ; $; $; ! ; ! ; ! ; )$; ! ; ! ; ! ; $; $; $! ; ! ; ); $; $$

How many different three-digit numbers can be formed using the digits 1 comma 2 comma 9 comma 6 comma 4 comma 3 comma and 8 without repetition? for example, 664 is not allowed.