A bin contains 5 red and 3 green balls. 3 balls are chosen at random, with replacement. Let the random variable X be the number of green balls chosen. (a) Explain why X is a binomial random variable.

(b) Fill out the following probability distribution table. (Round your answers to four decimal places)

X
P(X)

(c) Find the expected value of X

(d) Interpret the expected value.

Mr. walker gave his class the function f(x) = (x + 3)(x + 5). four students made a claim about the function. each student’s claim is below. jeremiah: the y-intercept is at (15, 0). lindsay: the x-intercepts are at (–3, 0) and (5, 0). stephen: the vertex is at (–4, –1). alexis: the midpoint between the x-intercepts is at (4, 0). which student’s claim about the function is correct?

Find the length of the diagonal of the rectangle. round your answer to the nearest tenth. || | | 8 m | | | | 11 m

Write the sine and cosine values of a, b, respectively, in the figure for (1) and (2) + explanation.