Matt has three pairs of dark socks and six pairs of white socks. if the socks are dark, Matt will choose an outfit that includes dress pants. If the socks are white, Matt will toss a coin. If he gets heads, he will wear jeans. If he gets tails, he will wear shorts. What is the probability that Matt will wear shorts to school? Just write the fraction only.

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?

If the speed of an electromagnetic wave is 100,000 cm/s and its wavelength is 100 cm, what is its frequency? a) 100,000 cycles per second (hz) b) 1 × 10-3 cycles per second (hz) c) 10,000,000 cycles per second (hz) d) 1,000 cycles per second (hz)

Find the slope and the y-intercept if there's one and the equation of the line given these two points( 3, 2) and( 3, -4)