One gear turns 33\frac{1}{3} times in a minute. another gear turns 45 times in a minute. initially, a mark on each gear is pointing due north. after how many seconds will the two gears next have both their marks pointing due north?

Sandy works at a clothing store. she makes $7 per hour plus earns 15% commission on her sales. she worked 75 hours over the last two weeks and had a total of $2,566 in sales before taxes. which of the following is closest to how much she will earn in hourly wages and commission for those two weeks?

Michael is training for a marathon. in his first week he plans to run 8miles. what path should he take

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.