D 1. An objective function and a system of linear inequalities representing constraints are given. Graph the system of inequalities representing the constraints. Find the value of the objective function at each corner of the graphed region. Use these values to determine the maximum value of the objective function and the values of x and y for which the maximum occurs. Objective Function z = 7x + 7y Constraints x = 0 0zys5 2x+3y=12 2x+3y=20 maximum: 42; at (6, 0) maximum: 49; at (2, 5) maximum: -28; at (4, 0) O O O O maximum: 70; at (10, 0) W 2. Tell whether the given rational expression is proper or improper. If improper, rewrite it as the sum of a polynomial and a proper rational expression. x- 2 x2+9 O improper; + x +16 x- 16 improper;- x - 2 (x +3)(x - 3) improper; 4 4 x+1/6 x-16 proper3. Find the first term, the common difference, and give a recursive formula for the arithmetic sequence. 6th term is 2; 15th term is 20 a1 = -10, d = 2, an = an-1 - 2 a1 = -8, d = 2, an = an-1 + 2 a1 = -10, d = 2, an = an-1 + 2 O a1 =-8, d = 2, an = an- 1 - 2D 4. An arithmetic sequence is given. Find the common difference and write out the first four terms. {st=1{3n+4} () d=3;51=3,5,=7,53=10,54=13 (D) d=4;51=3,5,=7,53=10,5,=13 (O d=351=7,5,=10,53=13,54=16 (O d=451=7,5,=10,53=13,5,=16 D 5. Solve the problem. From 9 names on a ballot, a committee of 3 will be elected to attend a political national convention. How many different committees are possible? 84 60,480 504 252 O O O O \fD 7. Solve. A theater has 20 rows with 28 seats in the first row, 33 in the second row, 38 in the third row, and so forth. How many seats are in the theater? (O) 3020 seats (O 1510 seats (O) 1560 seats O 3120 seats \fD 9. Determine whether the infinite geometric series converges or diverges. If it converges, find its sum. 12+16+18+20+... (O Converges; co O Converges; 42 O Converges; 31 (O Diverges \fE] 11. Solve the problem. A man has 5 shirts and 2 ties. How many different shirt and tie arrangements can he wear? O 4 O 25 O 20 O 10 12. Find the nth term and the indicated term of the arithmetic sequence {an) whose initial term, a, and common difference, d, are given. a1 = 3; d = -3 an = ?; a14 = ? an = 3 - 3n; a14 = -36 an = 6- 3n; a14 = -36 an = 6 - 3n; a14 = -12 an = 6 + 3n; a14 = -3613. Tell whether the given rational expression is proper or improper. If improper, rewrite it as the sum of a polynomial and a proper rational expression. 7 - X O proper O improper; 1 + 7 7 -x O improper; 1 - 7 improper; -1 + 7 7 -xO O O O 14. Solve. As Sunee improves her algebra skills, she takes 0.9 times as long to complete each homework assignment as she took 1o complete the preceeding assignment. If it took her 65 minutes to complete her first assignment, find how long it took her to complete the fifth assignment. Find the total time she took to complete her first five homework assignments. (Round to the nearest minute.) 38 min; 266 min 38 min; 224 min 43 min; 266 min 43 min; 224 min D 15. Solve the problem. Given that P(A) = 0.10 and P(B) = 0.49, find P(A N B) if A and B are mutually exclusive. (O 0.049 O o O o059 (O o0.5m W 16. Determine whether the given sequence is arithmetic, geometric, or neither. If the sequence is arithmetic, find the common difference; if it is geometric, find the common ratio. O Geometric; r = 3 O Geometric; r = O Neither O Arithmetic; d = 4O O O O 17. Solve the linear programming problem. Maximize and minimize z = 11x + 7y subject to: x=0, y =0, 2x+ 3y =6, x=10, y=5. maximum: 145; minimum: 14 maximum: 145; minimum: 110 maximum: 110; minimum: 21 maximum: 35; minimum: 21 l:l 18. Set up the linear programming problem. A steel company produces two types of machine dies, part A and part B and is bound by the following constraints: - Part A requires 1 hour of casting time and 10 hours of firing time. - Part B requires 4 hours of casting time and 3 hours of firing time. - The maximum number of hours per week available for casting and firing are 100 and 70, respectively. - The cost to the company is $0.75 per part A and $3.00 per part B. Total weekly costs cannot exceed $45.00. Let x = the number of part A produced in a week and = the number of part B produced in a week. Write a system of three inequalities that describes these constraints. x + 10y =100 4x + 3ys 70 075x + 3y= 45 x + 4y=100 1x + 3ys 70 3x + 075y= 45 O x + 4y =100 10x + 3y= 70 075x + 3y= 45 O x + 10y2100 4x + 3y= 70 075x + 3y= 45 D 19. Graph the solution set of the system of inequalities or indicate that the system has no solution. x2 +y2