4. Two hockey players, Sid and Alex, each independently take a penalty shot. The odds of Sid scoring are 5:3 in favor. The odds of Alex scoring are 1:2
against
a
Determine the probability that Sid scores
5:3 = 5/8
b. Determine the probability that Alex scores
1:2 = 1/3 against Alex, so its
2/3
in favourof Alex
C. Draw a probability tree diagram and determine the probability that
i. Both score
ii. Both miss
iii. Only one scores
iv. At least one scores

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).