Which statement correctly explains how dana can solve the following system of linear equations for x using the elimination method? 4x+8y=20 -4x+2y= -30 add the two equations, solve for y, and then substitute –1 for y to find x. multiply the bottom equation by –4, solve for y, and then substitute –1 for y to find x. multiply the bottom equation by –1, combine the two equations, solve for y, and then substitute 1 for y to find x. multiply the two equations, solve for y, and then substitute 1 for y to find x.

Arestaurant gives out a scratch-off card to every customer. the probability that a customer will win a prize from a scratch-off card is 25%. design and conduct a simulation using random numbers to find the experimental probability that a customer will need more than 3 cards in order to win a prize. justify the model for your simulation, and conduct at least 10 trials.

Prove that the value of the expression 7^8–7^7+7^6 is divisible by 43.

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.