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?

More challenges: 1) factor out the indicated quantity.8mn² + 7mn - m : factor out the quantity -m2) factor the polynomial by grouping.2vw + 7cv + 14cw + 49c²3) factor completely using the difference of squares along with factoring by grouping.25v³ - 25v² - 4v + 44) factor the sum of cubes. 125x³ + 645) q³ + 27r³6) factor completely. use difference of squares.729p^6 - 6^67) solve the equation(7x + 4)(9x - 1) = 08) a. find the values of x for which f (x) = 0b. find f (0)f (x) = x² + 2x - 489) find the x and y-intercepts for the function defined by y = f (x)f (x) = (x + 3)(x + 4)(x - 1)²10) factor the trinomial completely by using any method. remember to look for a common factor first. 3v² - 2v - 16