If total revenue received from the sale of x items is given by R(x)equals10 ln (3 x plus 1 ), while the total cost to produce x items is C(x)equalsStartFraction x Over 3 EndFraction , find the following. (a) The marginal revenue (b) The profit function P(x) (c) The marginal profit when xequals30 (d) Interpret the results of part (c).

Write two subtraction equations that are equivalent to 5 + 12 = 17.

If a line is defined by the equation y = 5x + 2, what is the slope?

Abottled water distributor wants to estimate the amount of water contained in 1-gallon bottles purchased from a nationally known water bottling company. the water bottling company’s specifications state that the standard deviation of the amount of water is equal to 0.02 gallon. a random sample of 50 bottles is selected, and the sample mean amount of water per 1-gallon bottle is 0.995 gallon a. construct a 99% confidence interval estimate for the popula-tion mean amount of water included in a 1-gallon bottle. b. on the basis of these results, do you think that the distributor has a right to complain to the water bottling company? why? c. must you assume that the population amount of water per bottle is normally distributed here? explain. d. construct a 95% confidence interval estimate. how does this change your answer to (b)?