The table shows the results of a survey of 400 random people on whether they like liquid soap, bar soap, or both. A 4-column table with 3 rows. The first column has no label with entries bar, not bar, total. The second column is labeled liquid with entries 200, 80, 280. The third column is labeled not liquid with entries 100, 20, 120. The fourth column is labeled total with entries 300, 100, 400. Which is the marginal relative frequency for the people who do not like bar soap? StartFraction 100 Over 400 EndFraction StartFraction 120 Over 400 EndFraction StartFraction 280 Over 400 EndFraction StartFraction 300 Over 400 EndFraction

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