Final Exam MATH1324 Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) A shoe company will make a new type of shoe. The fixed cost for the production will be $24,000. The variable cost will be $30 per pair of shoes. The shoes will sell for $100 for each pair. What is the profit if 600 pairs are sold? A) $42,000 B) $66,000 C) $54,000 D) $18,000 Find the matrix product, if possible. 2) 3 -1 0 -1 6 0 3 6 A) -6 0 45 -3 2) B) -3 -9 0 -6 C) 01 18 0 Use the Gauss-Jordan method to solve the system of equations. 3) x - y + 4z = -22 3x + z = -5 x + 5y + z = 5 A) (-5, 2, 0) B) (0, 2, -5) C) (-5, 0, 2) D) -9 -3 -6 0 3) D) No solution Use graphical methods to solve the linear programming problem. 4) Minimize z = 2x + 4y x + 2y 10 3x + y 10 x0 y0 subject to: y 10 -10 1) 10 x -10 A) Minimum of 20 when x = 10 and y = 0 B) Minimum of 20 when x = 2 and y = 4, as well as when x = 10 and y = 0, and all points in between C) Minimum of 20 when x = 2 and y = 4 D) Minimum of 0 when x = 0 and y = 0 Graph the feasible region for the system of inequalities. 1 4) 5) 2x + 5y 10 x - 3y 3 5) y 10 5 -10 -5 5 10 x -5 -10 A) B) y -10 y 10 10 5 5 -5 5 10 x -10 -5 -5 -5 -10 -10 C) 5 10 x 5 10 x D) y -10 y 10 10 5 5 -5 5 10 x -10 -5 -5 -5 -10 -10 Solve the problem. 6) A certain area of forest is populated by two species of animals, which scientists refer to as A and B for simplicity. The forest supplies two kinds of food, referred to as F1 and F2. For one year, species A requires 1.4 units of F1 and 1.1 units of F2 . Species B requires 2.4 units of F1 and 1.8 units of F2. The forest can normally supply at most 987 units of F1 and 495 units of F2 per year. What is the maximum total number of these animals that the forest can support? A) 198 animals B) 1058 animals C) 449 animals 2 D) 353 animals 6) Find the amount of compound interest earned. 7) $6000 at 7% compounded annually for 3 years A) $3,066,000.00 B) $13,260.00 7) C) $1373.26 D) $1350.26 Find the effective rate corresponding to the given nominal rate. Round to the nearest hundredth. 8) 7% compounded quarterly A) 7.23% B) 7.00% C) 7.19% D) 7.12% 8) Find the amount of each payment to be made into a sinking fund so that enough will be present to accumulate the following amount. Payments are made at the end of each period. The interest rate given is per period. 9) $8900; money earns 7% compounded annually; 15 annual payments 9) A) $319.13 B) $354.17 C) $225.80 D) $394.67 Solve the problem. 10) Tasha borrowed $11,000 to purchase a new car at an annual interest rate of 6.7%. She is to pay it back in equal monthly payments over a 4 year period. How much total interest will be paid over the period of the loan? Round to the nearest dollar. A) $61 B) $2671 C) $842 D) $1570 Translate the symbolic compound statement into words. 11) Let p represent the statement "Her name is Lisa" and let q represent the statement "She lives in Chicago." p ~q 10) 11) A) Her name is Lisa and she does not live in Chicago. B) It is not true that her name is Lisa or she lives in Chicago. C) Her name is not Lisa or she lives in Chicago. D) Her name is Lisa or she does not live in Chicago. Let p represent a true statement, and let q and r represent false statements. Find the truth value of the given compound statement. 12) (p ~q) r 12) A) True B) False 3 Construct a truth table for the compound statement. 13) p ~(s c) A) p s c p ~(s c) T T T T T T F T T F T T T F F F F T T F F T F T F F T T F F F F C) p s c p ~(s c) T T T T T T F T T F T T T F F T F T T F F T F T F F T T F F F T 13) B) p T T T T F F F F s T T F F T T F F c p ~(s c) T T F F T T F T T F F T T T F F p T T T T F F F F s T T F F T T F F c p ~(s c) T T F T T T F T T F F T T T F F D) Solve the problem. 14) The following statement appears in the instructions for a game: At this time, points are scored but the next round does not begin. Write the negation of the statement. A) At this time, points are not scored and the next round begins. B) At this time, points are scored and next round does not begin. C) At this time, points are scored or the next round does not begin. D) At this time, points are not scored or the next round begins. 14) Find the truth value of the statement. Assume that p and q are false, and r is true. 15) ~(p q) ~q A) True B) False 15) Use a truth table to decide if the statements are equivalent. 16) q p; ~q p A) Not equivalent 16) B) Equivalent For the given direct statement, write the indicated related statement (converse, inverse, or contrapositive). 17) All cats catch birds. (inverse) A) If it's not a cat, then it doesn't catch birds. B) If it doesn't catch birds, then it's not a cat. C) Not all cats catch birds. D) If it catches birds, then it's a cat. 4 17) Construct a truth table for the statement. 18) (p ~q) (p q) A) p q ( p ~q) (~p q) T T T F T T T F T T F F F T F F F T F F T T T T (2) (1) (4) (3) C) p q ( p ~q) (p q) T T F F F T T F T T F F F T F F F T F F F T F T (2) (1) (4) (3) 18) B) p T T F F q ( p ~q) T F F F F T T F F F F T (2) (1) (p q) F T T F F T F F (4) (3) p T T F F q ( p ~q) T F F F T T T F F F F T (2) (1) (p q) F F F T T F F F (4) (3) D) Decide whether the argument is valid or invalid, and give the form (of valid or invalid argument) that applies. 19) If I'm hungry, then I will eat. 19) I'm not hungry. I will not eat. A) Valid; modus ponens C) Invalid; fallacy of the converse B) Invalid; fallacy of the inverse D) Valid; modus tollens Determine whether the argument is valid or invalid. 20) ~q ~p p ~q 20) ~q A) Invalid B) Valid Tell whether the statement is true or false. 21) {all odd integers greater than -3 and less than 5} = {-1, 1, 3} A) True B) False Solve the problem. 22) Martina bought 5 books to bring on vacation. However she decided that her bag was too heavy and that she wouldn't bring all of them. How many possible subsets are there if she brings at least one book but not all 5 books? A) 4 B) 27 C) 30 D) 31 5 21) 22) Shade the Venn diagram to represent the set. 23) C' (A B) 23) A) B) C) D) Find the number of elements in the indicated set by referring to the given table. 24) V (P W), given the following table: U.S. Production (in Thousands of Tons) of Certain Nuts Year Pecans (P) Almonds (A) Walnuts (W) Hazelnuts (H) 1993 (T) 182 584 232 41 1994 (F) 99 583 232 21 1995 (V) 134 304 229 39 1996 (S) 111 412 205 18 A) 163 B) 343 C) 0 D) 363 Find the probability of the given event. 25) A single fair die is rolled. The number on the die is greater than 2. 1 1 2 A) B) C) 6 3 3 5 D) 6 6 24) 25) Find the indicated probability. 26) The distribution of B.A. degrees conferred by a local college is listed below, by major. Major English Mathematics Chemistry Physics Liberal Arts Business Engineering 26) Frequency 2073 2164 318 856 1358 1676 868 9313 What is the probability that a randomly selected degree is in Chemistry or Physics? A) 1174 B) 0.0919 C) 0.126 D) 0.0031 27) A lottery game has balls numbered 1 through 17. If a ball is selected at random, what is the probability of obtaining an even numbered ball or the number 12 ball? 8 17 12 A) B) C) 8 D) 17 12 17 27) Solve the problem, rounding the answer as appropriate. Assume that "pure dominant" describes one who has two dominant genes for a given trait; "pure recessive" describes one who has two recessive genes for a given trait; and "hybrid" describes one who has one of each. 28) Suppose a hybrid mates with a pure dominant. If they produce two offspring, what is the 28) probability that neither is a hybrid? A) 0.125 B) 0.75 C) 0.25 D) 0.50 Solve the problem. 29) If a single fair die is rolled, find the probability of a 4 given that the number rolled is odd. 1 1 A) B) 1 C) 0 D) 6 2 Find the indicated probability. 30) Assume that two marbles are drawn without replacement from a box with 1 blue, 3 white, 2 green, and 2 red marbles. Find the probability that both marbles are red. 3 1 1 1 A) B) C) D) 56 16 4 28 7 29) 30)