What is the standard deviation of the data set given below?
4, 7, 8, 9, 12

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?

Hector and alex traded video games. alex gave hector one fourth of his video games in exchange for 6 video games. then he sold 3 video games and gave 2 video games to his brother. alex ended up with 16 video games. how many video games did alex have when he started?

Amy is plan her school's new basketball court. the west edge of the basketball court is located on the line y = 5x + 2. the east edge cannot intersect with the west edge. on which line could the east edge be located? −y − 5x = 100 y + 5x = 100 −5x − y = 50 5x − y = 50