If an unfair coin is tossed into the air and drops without interruption, its probability of landing on heads is 0.51 whereas the probability of landing on tails is 0.49. if the payoff for landing on heads is $0.99 and the payoff for landing on tails is $1.01 and it costs $1 to play each game, should you play? 1)yes, because over the long run your expected value is greater than the lowest payoff 2)no, because over the long run your expected value is lower than the lowest payoff 3)yes, because over the long run your expected value is greater than the cost to play 4)no, because over the long run your expected value is less than the cost to play

Evaluate 8x2 + 9x − 1 2x3 + 3x2 − 2x dx. solution since the degree of the numerator is less than the degree of the denominator, we don't need to divide. we factor the denominator as 2x3 + 3x2 − 2x = x(2x2 + 3x − 2) = x(2x − 1)(x + 2). since the denominator has three distinct linear factors, the partial fraction decomposition of the integrand has the form† 8x2 + 9x − 1 x(2x − 1)(x + 2) = correct: your answer is correct. to determine the values of a, b, and c, we multiply both sides of this equation by the product of the denominators, x(2x − 1)(x + 2), obtaining 8x2 + 9x − 1 = a correct: your answer is correct. (x + 2) + bx(x + 2) + cx(2x − 1).