Let x determine a random variable, and use your knowledge of probability to prepare a probability distribution. a family has four children and the number of boys is recorded. (assume an equal chance of a boy-or girl for each birth.) complete the probability distribution. 4 1 16 p(x) (type an integer or a simplified fraction.)

About 9% of th population is hopelessly romantic. if 2 people are randomly selected from the population, what is the probability that at least 1 person is hopelessly romantic?

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).

Find the measure of angle b in the following triangle