In a game of chance, a contestant must choose a number from one of three categories. Correct number choices in Category A are worth $1500,
but there is a penalty of $1000 for each incorrect choice. Correct number
choices in Category B are worth $1000, with a $500 penalty for each
incorrect choice. Correct number choices in Category C are worth $500,
with no penalty for an incorrect choice. The probability of choosing
correctly is 0.05 for Category A, 0.15 for Category B, and 0.25 for Category
C. Which category has the highest expected value? Enter answer as
follows: Game A = , Game B =, Game C =, Game that has the highest
expected value. Don't put dollar signs in front of the amounts. *

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

3.64 deaths an hour.