A college prep program compared the practice SAT math scores given before and after a seven-week instruction for each student. The scores are given below. Student 1 2 3 4 5 6 7 8 9 Before 750 800 500 520 490 670 600 410 440 After 780 800 550 550 570 690 700 440 480 Test if the average score has been raised by more than 30 points and find the -value (round off to second decimal place). Assume normal population.

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12

B. because the 7 represents "seven times", x represents "a number", 12 represents "plus twelve", and -4 represents "minus four"

(-0, -7) is your answer