10, If the demand function for a commodity is given by the equation p^2 + 4q = 1400 and the supply function is given by the equation 300 - p2 + 10q = 0, find the equilibrium quantity and equilibrium price. (Round your answers to two decimal places.)

equilibrium quantity

equilibrium price

11) If the supply and demand functions for a commodity are given by 4p q = 66 and (p + 2)q = 1,550,respectively, find the price and quantity that will result in market equilibrium.

equilibrium price $

equilibrium quantity

17) If $1000 is invested for x years at 11%, compounded continuously, the future value that results is

S = 1000e0.11x.

What amount will result in 5 years? (Round your answer to the nearest cent.) $

18) If $5000 is invested at 9% annual simple interest, how long does it take to be worth $7250? yr

19) Consider an investment where $42,000 is invested for 15 years at 8% compounded continuously. How much will this investment be worth after 15 years? (Round your answer to the nearest cent.) $ What is the total amount earned in compound interest? (Round your answer to the nearest cent.) $

20) If $9,000 is invested at 9.5% compounded continuously, find the future value after 5 1/2 years. (Round your answer to the nearest cent.) $

21) A sinking fund is established to discharge a debt of $30,000 in 5 years. If deposits are made at the end of each 6-month period and interest is paid at the rate of 9%, compounded semiannually, what is the amount of each deposit? (Round your answer to the nearest cent.)

22) Find the future value of an annuity of $1300 paid at the end of each year for 5 years, if interest is earned at a rate of 8%, compounded annually. (Round your answer to the nearest cent.) $

23) Find the present value of an annuity of $6000 paid at the end of each 6-month period for 2 years if the interest rate is 5%, compounded semiannually. (Round your answer to the nearest cent.)

24) The problem describes a debt to be amortized. (Round your answers to the nearest cent.) A man buys a house for $320,000. He makes a $150,000 down payment and amortizes the rest of the purchase price with semiannual payments over the next 13 years. The interest rate on the debt is 11%, compounded semiannually.

(a) Find the size of each payment. $

(b) Find the total amount paid for the purchase. $

(c) Find the total interest paid over the life of the loan.

25) One ball is drawn from a bag containing 5 red balls numbered 1-5 and 9 white balls numbered 6-14. Find the following probabilities. (Enter your probabilities as fractions.)

(a) What is the probability that the ball is white and even-numbered?

(b) What is the probability that the ball is white or even-numbered?

(c) What is the probability that the ball not divisible by 7?

26) A red ball and 6 white balls are in a box. If two balls are drawn, without replacement, what is the probability of getting each of the following? (Enter your probabilities as fractions.)

(a) a red ball on the first draw and a white ball on the second

(b) 2 white balls

(c) 2 red balls

27) If 12 people are qualified for the next flight of a new space vehicle, how many different groups of 2 people can be chosen for the flight? groups

28) One ball is drawn at random from a bag containing 3 red balls and 6 white balls. (Enter your probabilities as fractions.)

(a) What is the probability that the ball is red?

(b) What is the probability that the ball is green?

(c) What is the probability that the ball is red or white?

30) If a box with a square cross section is to be sent by a delivery service, there are restrictions on its size such that its volume is given by V = x2(54 2x), where x is the length of each side of the cross section (in inches).

(b) If V = V(x),find V(6) and V(19). (If V is not a function of x, enter DNE.)

V(6) = in3

V(19) = in3

(c) What restrictions must be placed on x (the domain) so that the problem makes physical sense? (Enter your answer using interval notation. If V is not a function of x, enter DNE.)

31) A concert promoter needs to make $88,100 from the sale of 1940 tickets. The promoter charges $40 for some tickets and $55 for the others. Let x represent the number of $40 tickets and y represent the number of $55 tickets.

(a) Write an equation that states that the sum of the tickets sold is 1940.

(b) Write an expression for how much money is received from the sale of $40 tickets? $

(c) Write an expression for how much money is received from the sale of $55 tickets? $

(d) Write an equation that states that the total amount received from the sale is $88,100.

(e) Solve the equations simultaneously to find how many tickets of each type must be sold to yield the $88,100.

x =

y =

32) The table defines a discrete probability distribution. Find the expected value of the distribution. x 0 1 2 3

Pr(x)- 1/16 3/16 3/16 9/16

33) A nonprofit organization sells chances for a $78,000 classic Mustang at $100 per ticket. It sells 1500 tickets and offers four prizes, summarized in the table. What are the expected winnings (or loss) for each ticket? (Round your answer to the nearest cent.)

Prizes Amount

First $78,000

Second 8,400

Third 3,700

Fourth 700