Sophia has a bag with 333 purple marbles and 444 blue marbles in it. She is going to randomly draw a marble from the bag 280280280 times, putting the marble back in the bag after each draw. 3 purple marbles and 4 blue marbles Complete the following statement with the best prediction. Sophia will draw a purple marble... Choose 1 Choose 1 (Choice A) A Exactly 120120120 times (Choice B) B Close to 120120120 times but probably not exactly 120120120 times (Choice C) C Exactly 160160160 times (Choice D) D Close to 160160160 times but probably not exactly 160160160 times

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).