The population standard deviation for the number of corn kernels on an ear of corn is 94 kernels. if we want to be 90% confident that the sample mean is within 17 kernels of the true population mean, what is the minimum sample size that should be taken?

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?

How many triangles can be drawn with side lengths 4 centimeters, 4.5 centimeters, and 9 centimeters? explain

The points (1, 7) and (0, 2) fall on a particular line. what is its equation in slope-intercept form?