Bjork larsen was trying to decide whether to use a newracing wax for cross-country skis. he decided that the wax would beworth the price if he could average less than 55 seconds on acourse he knew well, so he planned to test the wax by racing on thecourse 8 times. a) suppose that he eventually decides not to buy the wax, butit really would lower his average time to below 55 seconds. whatkind of error would he have made? b) his 8 race times were 53.3, 65.9, 50.2, 52.4, 46.5, 57.8,52.2, and 43.2 seconds. should he buy the wax? explain.

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