Vani signed up for a streaming music service that costs $12 per month. The service allows Vani to listen to unlimited music, but if she wants to download songs for offline listening, the service charges $1.25 per song. How much total money would Vani have to pay in a month in which she downloaded 30 songs? How much would she have to pay if she downloaded s songs?

Acommunity group sells 2,000 tickets for its raffle. the grand prize is a car. neil and 9 of his friends buy 10 tickets each. when the winning ticket number is announced, it is found to belong to neil's group. given this information, what is the probability that the ticket belongs to neil? a.1/5 b.1/10 c.1/200 d.1/4

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).

An isosceles trapezoid with a perimeter of 42 inches. each of the congruent non parallel sides is 5 inches long, and the trapezoid is 3 inches tall. how long are the two parallel sides? a. 10 in, 22 in b. 16 in, 16 in c. 10 in, 16 in d. 12 in, 20 in