A) a fair die has six sides labeled 1 through 6. what is the sample space (s) if the die is thrown once? b) list the possible outeomes for the following events) a = the event that the number thrown is even: b = the event that the number thrown is at least 2: c- an odd number greater than 3 a n b: auc: not a: a) determine the following probabilities i) p(a) ii) p(c) iv) use the general addition rule to find p(a ub) e) are a and b mutually exclusive? explain

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).