statistics

If 30 lb of rice and 30 lb of potatoes cost $24.60, and 20 lb of rice and 12 lb of potatoes cost $13.04, how much will 10 lb of rice and 50 lb of potatoes cost? Let x be the cost of 1 lb of rice and y be the cost of 1 lb of potatoes. Set up two linear equations from the given information using x and y as the variables. = 24.60 = 13.04 2 A theater charges $8 for main-floor seats and $5 for balcony seats. If all seats are sold, the ticket income is $3300. At one show, 25% of the main-floor seats and 40% of the balcony seats were sold and ticket income was $1200. How many seats are on the main floor and how many are in the balcony? 3 A player scored 89 points in a single professional basketball game. He made a total of 56 baskets, consisting of field goals (worth two points) and foul shots (worth one point). Find the number of field goals and the number of foul shots that the player made. 9 A bank teller has a total of 66 bills in five-, ten-, and twenty-dollar denominations. The total value of the money is $750. (a) Find the total number of solutions. (b) Find the solution with the smallest number of five-dollar bills. (c) Find the solution with the largest number of five-dollar bills. 5 Suppose that the supply function for honey is p = S(q) = 0.4q + 2.8, where p is the price in dollars for an 8-oz container and q is the quantity in barrels. Suppose also that the equilibrium price is $4.80 and the demand is 4 barrels when the price is $6.50. Find an equation for the demand function, assuming it is linear. A firm produces a product that has the production cost function C(x) = 460x + 7820 and the revenue function R(x) = 575x. No more than 66 units can be sold. Find and analyze the break-even quantity, then find the profit function. Joanne sells silk-screened T-shirts at community festivals and craft fairs. Her marginal cost to produce one T-shirt is $4.50. Her total cost to produce 80 T-shirts is $440, and she sells them for $8 each. a. Find the linear cost function for Joanne's T-shirt production. b. How many T-shirts must she produce and sell in order to break even? c. How many T-shirts must she produce and sell to make a profit of $800? A person is the manager of a firm. He is considering manufacturing a new product, so he asks the accounting department for cost estimates and the sales department for sales estimates. After he receives the data, he must decide whether to go ahead with production of the new product. Analyze the following data (find a break-even quantity) and then decide what the manager would do in this case. Also, write the profit function. C(x) = 120x + 600 and R(x) = 105x