Abox contain 3 plain pencils and 9 pens. a second box contains 5 color pencils and 3 crayons. one item from each box is chosen at random. what is the probability that a pen from the first box and a crayon from the second box are selected

Given: and prove: what is the missing reason in the proof? given transitive property alternate interior angles theorem converse alternate interior angles theorem

Does the function satisfy the hypotheses of the mean value theorem on the given interval? f(x) = 4x^2 + 3x + 4, [−1, 1] no, f is continuous on [−1, 1] but not differentiable on (−1, 1). no, f is not continuous on [−1, 1]. yes, f is continuous on [−1, 1] and differentiable on (−1, 1) since polynomials are continuous and differentiable on . there is not enough information to verify if this function satisfies the mean value theorem. yes, it does not matter if f is continuous or differentiable; every function satisfies the mean value theorem.

What is the product? a-3/15a × 5/a-3