You are offered one billion dollars cash and tax free . you may spend it however you like. the only condition i see that upon receipt, you count it 1 dollar at a time. you may count 7 days a week, 8 hours per day, at the rate of 1 dollar per second. will you accept this offer? about how long do you think it would take to count it? show your work and record your estimate

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.

If the probability of an event happening is 65% then the probability this event does not occur?

(25 ! ) what does it mean for an equation to have no solution or infinitely many solutions?