Math 1324-Final review-Fall 2017-Department
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Apr 3, 2024
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Math 1324 Final Exam Review (A) 6181 1. Graph the equation. 5x ~4y =20 2. Find the x- and y-intercepts of the graph. List all the x-intercepts. Select the correct choice below and, if necessary, fillin the answer box to complete your choice. i A, (Use a comma to separate answers as N - needed.) -6 4 4 i I B. There are no x-intercepts. List all the y-intercepts. Select the correct choice below and, 4= if necessary, fill in the answer box to complete your choice. A, (Use a comma to separate answers as needed.) i B. There are no y-intercepts.
3. 1324 final exam review (A) Find the x-intercepts and y-intercepts of the graph of the equation. yzx2w~64 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. i1 A, The x-intercept(s) is/are {Type an integer or a simplified fraction. Use a comma to separate answers as needed.) i1 B. There are no x-intercepts. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. i A. The y-intercept(s) is/are (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) i 1 B. There are no y-intercepts. Find the slope of the line if it is defined. Through (-3, - 5) and (- 8,4) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. i1 A. The slope is 7 7 . (Type an integer or a simplified fraction.) i+ B. The slope is undefined. Find the slope and the y-intercept of the line. 2x=5y+15 What is the slope? What is the y-intercept? (Type an integer or a fraction.) 2057
10. 11. 1324 final exam review (A) Decide whether the pair of lines is parallel, perpendicular, or neither. 2x +by=8 2x+5y=7 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. i+ A. The slope of 2x+ 5y =8 is . (Type an integer or a simplified fraction.) i+ B. The slope of 2x+ 5y = 8 is undefined. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. { + AL The slope of 2x+ 5y =7 is . (Type an integer or a simplified fraction.) i+ B. The slope of 2x + 5y = 7 is undefined. The lines are (1) (1) ¢ perpendicular. i+ neither parallel nor perpendicular. i1 parallel. Find an eguation of the line that passes through the given points. (=3,1) and (2,16) The equation is . {(Simplify your answer.) Write an equation of the line containing (9, — 4) and parallel to the graph of 8x -7y = 2. The equation of the line is =100. Find an equation for the line which passes through (- 2,5) and is perpendicular to the line containing (0,2) and {4,6). The equation of the line is . (Simplify your answer. Type your answer in slope-intercept form.) The lost value of equipment over a period of time is called depreciation. The simplest method for calculating depreciation is straight-line depreciation. The annual straight-line depreciation D of an item that costs x dollars with a useful life of n years is D = (1/n)x. Find the depreciation for items with the given characteristics. Costis $15,951; life is 16 yr The annual straight-line depreciation is approximately $ per year. (Round to the nearest cent.) In 1992, 524,000 people worked in the air transportation industry. In 2008, the number was 488,000. (a) Find a linear equation giving the number of employees in the air transportation industry in terms of x, the number of years since 1992, (b) Assuming the equation remains valid in the future, in what year will there be 460,000 employees of the air transportation industry? (a) The linear equation determined by the two points in part (a) is y = X+ (Type integers or decimals rounded to one decimal place.) {b) The number of employees of the air transportation industry will reach 460,000 in the year 3/37
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12. 13. 14. 1324 final exam review (A) Determine the vertex of the parabola and state whether it opens upward or downward. - _na 2, . g(x) = = 3(x+5)" +2 What is the vertex of the parabola? (Type an ordered pair.) In which direction does the vertex open? i+ upward I+ downward Match the function with its graph. f(x)=2(x = 5)% + 4 Choose the correct graph of f(x) = 2(x ~ 5)2 + 4 below. Each graph is shown in the viewing window [-10,10,1] x| - 10,10,1]. A, B C G |||x'u|\| ‘«/(...) fo AR R N Y VO O S S T o L O 0 O S S A : ORI VO A N Y G M S S W S S S ST £ F .JLmv»n‘~mlsorrn TS T T SO WOC S - rsxot\llL'\l!mlr! Determine the vertex of the parabola without graphing. a2 f(x)=2x" - 8x+ 16 What is the vertex of the parabola? (Type an ordered pair.) 4137
1324 final exam review (A) 15, Find the vertex and the equation of the line of symmetry. Choose the correct graph below, Graph the function. ] Sraph the function AL B, = N 2 0= (x~5) o] What is the vertex? l A ey B R e e e Fcan o' —_— ‘ -20 j 20 -20 (Type an ordered pair.) /\ - -20- -20- What is the equation of the line of symmetry? X = e, (D, 20 T T -3 20 ~20 20 -2 16. A charter flight charges a fare of $300 per person plus $6 per person for each unsold seat on the plane. If the plane holds 100 passengers and if x represents the number of unsold seats, find the following. A. An expression for the total revenue received for the flight. (Hint: Multiply the number of people flying, 100 - x, by the price per ticket.) B. The number of unsold seats that will produce the maximum revenue. C. The maximum revenue. A. The total revenue R(x) received for the flight is expressed by CUAC R(x) =652 +300x + 30,000 L Be R0 = 6% - 300x + 30,000 LG R = - 6x% + 300% + 30,000 LD Ry = - 6x% + 300% - 30,000 B. The number of unsold seats that will produce the maximum revenue is C. The maximum revenue is $ 17. Find the vertical and horizontal asymptotes. Then graph the function. 2% The vertical asymptote is x= The horizontal asymptote is y = Choose the correct graph. 1A, S B. L i C. oD, 40— [ [ i X i = S NG 5/37
1324 final exam review (A) Find the vertical and horizontal asymptotes. Then graph the function. ~ 4x =1 T 2%+ 3 f(x) The vertical asymptote is x = The horizontal asympiote is y = Choose the correct graph. i v A, B, i1 C. D, Classify the function as linear, quadratic, or exponential. f(x) = x° - Bx + 3 The function is (1) (1) ¢ quadratic i exponential i linear If f(x)=a" and f(3) = 27, find f(2). Assume a > 0. f(2) = If money loses value, then as time passes, it takes more dollars to buy the same item. Use the table to answer the questions. Let t be years and y be the value of $1 in t years. tf1 2 3 4 5 6 y[o.94 0.88 0.83 0.78 0.73 0.69 (a) Suppose a house costs $104,000 today. Estimate the cost of the same house in 3 years. (b) Estimate the cost of a $50 textbook in 2 years. (a) Suppose a house costs $104,000 today. Estimate the cost of the same house in 3 years. The house will cost about dollars. (Round to the nearest dollar as needed.) (b) Estimate the cost of a $50 textbook in 2 years. The textbook will cost about dollars. (Round to the nearest cent as needed.) 6/37
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22. (Round to the nearest cent.) 1324 final exam review (A) The scrap value of a machine at the end of its useful life is given by S(n) = C(1~ N", where C is the original cost, n is the useful life of the machine in years, and r is the constant annual percentage of value lost. Find the scrap value of the following machine. Original cost, $41,000; life, 9 years; annual rate of value lost, 14% S=§% 23. Use the graph of y = Ca* to determine C and a. LY C= 5 6_. a= 4.1 J : L 1 s S B L L L R | -0 -8 -6 -4 ’2»2: 2 4 6 8 10 4] G -8 ~10- [-10, 10] {-10, 10] Xscl=1 Yscl=1 24. Write the equation in equivalent logarithmic form. What is the equivalent logarithmic form? 25. Evaluate the expression without the use of a calculator. log 10,000 log 10,000 = (Type an integer or a simplified fraction.) 26. Write the expression as the logarithm of a single number or expression. log 12~ log 4 The expression simplifies to (Simplify your answer.) 27. 28. Wirite the expression as the logarithm of a single number or expression. Assume that all variables represent positive numbers. 6log x+3logy-4logz 6log x+3logy—4logz= Wirite the expression as a sum and/or a difference of logarithms, with all variables to the first degree. In 5x4y9 In 5x4y9 = (Simplify your answer.) 7137
29. 30. 31. 32. 33, 34. 1324 final exam review (A) Solve the equation. In(5x + 14) ~ Inx = In6 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. ‘:‘::* A,. X = (Simplify your answer. Use a comma to separate answers as needed.) {3 B. There is no solution. Solve. log,(2x—-4)=1 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. i_ " A. The solution is x = . (Type an integer or a simplified fraction.) i 1 B. There is no solution. Solve for x. 8x 43 =956 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 7 A. The solution is x = o (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) 3 B. The solution is not a real number. Solve the following exponential equation without using The solution is x = logarithms. (Simplify your answer.) 47 =16 Solve for t. e "92M=073 The solution is t= (Type an integer or decimal rounded to four decimal places as needed. Use a comma to separate answers as needed) Solve the following equation for c. 8/37
35. The total expenditures (in millions) of current dollars for pollution abatement and control during the period from 2000 36. 37, 38. 39. 40. 41. (Round to the nearest cent.) 1324 final exam review (A) through 2019 can be approximated by the function PO = 168.24 ¢ 9% where x = 0 corresponds to the year 2000. (a) In what year would the total expenditures reach $215 million dollars? (b) If this model remains accurate, when would the total expenditures reach $406 million? (a) The expenditures would reach $215 million in the year early- (Simplify your answer. Type a whole number.) (b) The expenditures would reach $406 million in the year early- (Simplify your answer. Type a whole nurber.) Find the interest. Principal Rate Time in Months Interest $1650 9.5% 3 The interest is $ Find the future value of this loan. $12,069 at 4.7% for 18 months The future value of the loan is $ (Round to the nearest cent as needed.) Find the present value of the given future amount. $173,306 for 191 days at 5.8% simple interest. Assume 360 days in a year. What is the present value? $ (Round to the nearest dollar as needed.) For the following freasury bill bought in 2007, find (a) the price of the T-bill, and (b) the actual interest rate paid by the Treasury. Three-month $23,500 T-bill with discount rate of 5.69% (a) The price of the T-bill is $ (Round to the nearest dollar as needed.) {b) The actual interest rate paid by the Treasury is %. (Type an integer or decimal rounded to two decimal places as needed.) Find the compound amount for the following deposit. The compound amount after 7 years will be 3 . N . $14,000 at 5% compounded semi-annually for 7 years. (Round to the nearest cent) Use the compound interest formula A=P(1 + r)t and the given information to solve for r. A=$3,000,000, P=3$40,000, t=40 r= % (Round to the nearest hundredth.)
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1324 final exam review (A) 42. Find the amount of the ordinary annuity based on the information given. R =$11,500, 5% interest compounded semiannually for 5 years The amount of the ordinary annuity is $ (Round to the nearest dollar as needed.) 43. Find the amount of each payment to be made into a sinking fund which earns 5% compounded quarterly and produces $33,000 at the end of 3.5 years. Payments are made at the end of each period. The payment size is $ . (Round to the nearest cent.) 44. Find the future value of a 6-year annuity due with payments of $10,500 and an annually compounded interest rate of 5%. The future value is $ . (Round fo the nearest cent.) 45. Find the present value of an ordinary annuity which has payments of $2400 per year for 17 years at 6% compounded annually. The present value is $ (Round to the nearest cent.) 46. Find the amount necessary to fund the given withdrawals. Quarterly withdrawals of $700 for 5 years; interest rate is 4.4% compounded quarterly. The amount necessary to fund the given withdrawals is $ (Round to the nearest cent as needed.) 47. Find the lump sum deposited today that will yield the same total amount as payments of $10,000 at the end of each year for 13 years, at an interest rate of 7% compounded annually. The lump sumis $ (Round to the nearest cent.) 48. Find the price a purchaser should be willing to pay for the given bond. Assume that the coupon interest is paid twice a year. $15,000 bond with coupon rate 6% that matures in 4 years; current interest rate is 3% The purchaser should be willing to pay $ (Slmphfy your answer. Round to the nearest cent as needed ) 49. Find the payment necessary to amortize a 8% loan of $1100 compounded quarterly, with 13 quarterly payments. The payment size is $ (Round to the nearest cent.) 50. Solve by the substitution method. What is the solution of the system? 8x+2y = —-20 = 20 (Type an ordered pair.) -6x+ vy 10/37
51, 53. 54, A 5000-seat theater has tickets for sale at $27 and $40. How many tickets should be sold at each price for a sellout 1324 final exam review (A) performance to generate a total revenue of $157,1007 The number of tickets for sale at $27 should be The number of tickets for sale at $40 should be Obtain an equivalent system by performing the stated elementary operation on the system. Replace the second equation by the sum of itself and 2 times the first equation. -8x ~ 14y + 4z Ox - 11y + 9z 6x - 9y + 12z -8x ~ 14y + 4z = 9 - 1y + 9z = 6x - 9y + 12z = = -16 = 18 = 24 X - y + X = y + X - y o+ (Type integers or simplified fractions.) Write an augmented matrix for the following system of equations. 6x - By + 2z = -2 9 - 4y + 9z = 2 9y - 4z = -6 The entries in the matrix are: | | Replace R, by R, + (- 7)R,. 12 -1] -1 74 37 9 -53 6 1 R2+('—7)R1= 11/37
b5, 56. 57. 1324 final exam review (A) =2b5x=Qy =~ z= ~ 34 = 1bx~1by=2z= ~4 20x+ 9y + z=24 Solve the following system of equations using the Gauss-Jordan method. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. i+ A, This systemn has exactly one solution. The solution is (Type an exact answer in simplified form.) i B. This system has infinitely many solutions of the form ( V . m,z), where z is any real number. (Type expressions using z as the variable.) i 1 €. This system has no solution. Solve the system by any method. X=by+3z=1 3x—dy+2z= ~1 Select the correct choice below and fill in any answer boxes within your choice. i A. There is one solution. The solution set is ( 7 ' , (Simplify your answers.) i B. There are infinitely many solutions. The solution set is ( , ,z), where z is any real number. (Simplify your answers. Type expressions using z as the variable. Use integers or fractions for any numbers in the expressions.) {1 €. There is no solution. The solution set is @. Solve the system by any method. X+y+z+w=0 8x—-y+8z-w=0 Ix+tdy-z+4w= -4 X=2y+3z-w=0 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. i1+ A, This system has exactly one solution. The solution is ( » , ) (Type an exact answer in Asi;;npl'if‘ieawi"drrrrn.) i+ B. This system has infinitely many solutions of the form ( - 7 . w) , where w is any real number. (Type expressions using w as the variable.) i1 €. This system has no solution. 12/37
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58. 59. 60. 61. 1324 final exam review (A) A band concert is attended by x adults, y teenagers, and z preteen children. These numbers satisfied the following equations. How many adults, teenagers, and children were present? x+1.02y +0.24z= 440.6 x+0.4y+0.6z= 432 3.87x+3.67y+0.6z= 1603.3 There were adults, teenagers, and children present at the band concert. The U-Drive Rent-A-Truck company plans to spend $13 million on 320 new vehicles. Each commercial van will cost $35,000, each small truck $30,000, and each large truck $80,000. Past experience shows that they need twice as many vans as small trucks. How many of each type of vehicle can they buy? They can buy vans, small trucks, and large trucks. Jim took clothes {o the cleaners three times last month. First, he brought 2 shirts and 2 pairs of slacks and paid $14.96. Then he brought 5 shirts, 4 pairs of slacks, and 1 sports coat and paid $39.90. Finally, he brought 4 shirts and 2 sports coats and paid $23.94. How much was he charged for each shirt, each pair of slacks, and each sports coat? Jim was charged $ for each shirt, $ for each pair of slacks, and $ for each sports coat. A basketball team sells tickets that cost $10, $20, or, for VIP seats, $30. The team has sold 3163 tickets overall. It has sold 167 more $20 tickets than $10 tickets. The total sales are $60,310. How many tickets of each kind have been sold? How many $10 tickets were sold? How many $20 tickets were sold? 62. Perform the operation if possible. -1 -4 -6 21 0 + 1 3 5 -3 4 =2 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. LPACT L4 24 -6 21 0 + - 1 3 5 ~34 -2 i1 B. The operation is not defined. 13/37
63. 64. 65. 1324 final exam review (A) Find the following matrix product, if it exists. 0 -2 -5 -1 4 4 -3 5 , 0 -2 -5 o LA, 0 1 1= (Simplify your answer.) -1 4 4 e -2 =3 i B. The product does not exist. Find the inverse, if it exists, for the given matrix. Find the inverse. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. The inverse is ] . {Type a matrix, using an integer or simplified fraction for each " matrix element. Do not factor out a scalar multiple.) i 1 B. There is no inverse of the given matrix. Find the inverse, if it exists, for the given matrix. [ 2 03 ] 0 -10 3 -2 4 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. The inverse matrix is . {Type a matrix, using an integer or simplified fraction " for each matrix element. Do not factor out a scalar multiple.) "y B. There is no inverse of the given matrix. 14137
66. 67. 68. 1324 final exam review (A) Two departments of a firm, A and B, need differing amounts of steel, wood, Steel | Wood | Plastic and plastic. The table on the right gives the amount of each product the Department A 50 30 10 departments need. Department B 30 10 30 These three products are supplied by two suppliers, Company C and Company C |Company D Company D, with the unit prices given in the table on the right. Sieel 610 560 Wood 310 180 Plastic 310 390 a. Use matrix multiplication to determine how much these orders will Co. C Co. D cost each department at each of the two suppliers. Enter the amounts Dept. A into the cost matrix shown on the right. Dept. B b. From which supplier should each department make its purchase? Which company should department A use”? i+ Company D i+ Company C Which company should department B use? 1 Company D i Company C Graph the inequality on a plane. y 10~ 2x + 8y < 16 & Use the graphing tool on the right to graph the inequality. %] 4._ 2] . X [ I T L | SR L L B | 10 -8 -6 -4 2_2: 2 4 6 8 10 4 6 .8 -0 Graph the feasible region for the system of inequalities. Ay 10 X—2yz6 8- 2x+y<6 o Use the graphing tool on the right to graph the feasible 4] region for the system of inequalities. 24 . | A N L A AL T S LT B | -10 -8 -6 -4 72_2; 2 4 6 810 4] 6 _8T -10- 16/37
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69. 70. 71. 1324 final exam review (A) Graph the feasible region for the given system of inequalities, X+2y 58 2x+y £ 8 xz 0 yz0 Use the graphing tool on the right to graph the system of inequalities. The graph shows a region of feasible solutions. Use this region to find maximum and minimum values of the objective function. Z=T7x+6y Select the correct choice below and, if necessary, fill in the answer box to complete your choice. L VAL The maximum value is i 1 B, The maximum value does not exist. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. i1 A, The minimum value is .1 B, The minimum value does not exist. Solve the following linear programming problem. Maximize: z=9x+ 8y subject to: 6x+4y<24 Ox+y<24 xz20,yz20 The maximum value is The maximum occurs at the point . (Type an ordered pair. If the maximum occurs at more than one point, type either answer. Type an integer or a fraction.) y o’ T T % 10 The coordinates of the corner points are (2,3), (4,8), (8,7), and (9,4). 16/37
73. 1324 final exam review (A) Solve the following linear programming problem. Maximize: z=11x+4y subject to: 8x+4y <32 TIx+y <32 xz0,yz0 The maximum value is The maximum occurs at the point . (Type an ordered pair. If the maximum occurs at more than one point, type either answer. Type an integer or a fraction.) A chain saw requires 8 hours of assembly and a wood chipper 7 hours. A maximum of 112 hours of assembly time is available. The profit is $150 on a chain saw and $220 on a chipper. How many of each should be assembled for maximum profit? To attain the maximum profit, assemble chain saws and wood chippers. 74. Deluxe coffee is to be mixed with regular coffee to make at To attain the minimum cost, use pounds of least 44 pounds of a blended coffee. The mixture must contain at least 13 pounds of deluxe coffee. Deluxe coffee costs $6 per pound and regular coffee $5 per pound. How many pounds of each kind of coffee should be used to minimize costs? deluxe coffee and pounds of regular coffee. 75. 76. Jamaal is planning to invest up to $19000 in City Bank or State Bank. He wants to invest at least $1000 in City Bank, but not more than $12000; since State Bank does not insure more than $9000, he wants to invest no more than this amount in State Bank. The interest at City Bank is 3%, and the interest at State Bank is 6%. How much should he invest in each bank to earn the most interest? What is the maximum amount of interest that Jamaal can earn? He should invest $ in City Bank and $ in State Bank, The maximum amount of interest that Jamaal can earn is $ Introduce slack variables as necessary and then write the Maximize z= X +6xy +2Xg initial simplex tableau for the given linear programmin ) pexta rihe given preg g subject to X4 +2Xy +3X3 <12 problem. 7X1 + Xz + 5)(3 <10 9X1 + 2)(3 <6 X4 20, X9 20, X3 2 0. Complete the initial simplex tableau. X1 X2 X3 S1 32 53 Z 1 2 3 1 0 0 o 12 7 1 5 0 1 0 0 10 9 0 2 0 0 1 0 6 0 0 0 1 0 17137
1324 final exam review (A) 77. Find ihe pivot in the simplex tableau. X{ Xp X3 Sy Sy 83 Z 33 3 1 1 0 0 20 3 3 7 0 0 1 0 13 3 4 3 0 0 0 O 17 =2 0-3 1 0 0 119 The pivot is located in row ) , column The pivot is 78. Use the indicated entry as the pivot and perform the pivoting. X1 X2 X3 51 8 83 z 1 1 1 1 0 0 0|60 31 4 0 1 0 0}240 1T 2 3 0 0 1 0150 | -1-1-40 0 0 1|0 X4 X2 X3 84 $2 83 79. For the given simplex tableau, (a) list the basic and the X{ X9 X3 84 Sy Z nonbasic variables, (b) find the basic feasible solution 6 -2 1 0 3 o 29 determined by setting the nonbasic variables equal to 0, and 4 -3 0 1 0 o 17 (c) decide whether this is a maximum solution. 7 -1 0 0 -3 1| 15 (a) What are the basic variables? mo separate answers as needed.) What are the nonbasic variables? (Use a comma to separate answers as needed.) (b) Find the basic feasible solution by setting the nonbasic variables equal to 0. X,I: ’XZ: )X3: ‘51: 752: yZ_ (c) Is this solution a maximum? i1 No 7 Yes 18/37
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1324 final exam review (A) 80. Solve the linear programming problem using the simplex method. Manximize z = 2x, + 9x, subject to 5%y + Xy 560 9x4 + 2%, 580 Xq Xy 570 Xq, Xg 2 0. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. {1 A, The maximum is z = when x4 = , Xo = s1= 8y = E and sq = S i ' B. There is no maximum solution for this linear programming problem. 81. A biologist has 400 kg of nutrient A, 800 kg of nutrient B, PIlQ R S and 200 kg of nutrient C. These nutrients will be used to A 010 (375|875 make 4 types of food, whose contents (in percent per B 020} 50 [125 kilogram of food) and whose 'growth values' are shown on C 100/ 801|125 © the right. Set up the initial simplex tableau that would be Growth 110l100! 80 | 70 used to determine how many kilograms of each food Value should be produced in order to maximize total growth. Let x4be the number of kilograms of food type P. Let x, be the number of kilograms of Q. Let x5 be the number of kilograms of R, and let x4 be the number of kilograms of S. What is the objective function? Z= X1 + X2 + X3 + X4 Set up the initial simplex tableau for the problem. X/, X2 X3 X4 S»] SZ 53 r 0 0 1 0 0 400 | 0 0.2 0.5 0125 0 1 0 1 0.8 0.125 0o 0 0 1 - 80 -70 0 0 O 0 (Type an integer or decimal for each matrix element.) 82. A company sells sets of kitchen knives. A Basic Set consists of 4 utility knives and 1 chef's knife. A Regular Set consists of 2 utility knives, 1 chef's knife, and 1 slicer. A Deluxe Set consists of 3 utility knives, 1 chef's knife, and 1 slicer. The profit is $30 on a Basic Set, $40 on a Regular Set, and $80 on a Deluxe Set. The factory has on hand 1600 utility knives, 800 chef's knives, and 400 slicers. If all sets will be sold, how many of each type should be made up in order to maximize profit? What is the maximum profit? How many Basic Sets should be made up? How many Regular Sets should be made up? How many Deluxe Sets should be made up? What is the maximum profit? $ 19/37
83. 84. 1324 final exam review (A) Find the number of subsets for the following set. {D,E,F} How many subsets does this set have? (Type a whole number.) Use A={2, 6,7, 8 9 and B={3, 7, 8, 9} to find the set A N B. ANB= (Use a comma to separate answers as needed.) 85. 86. 87. 88. 89. { p (Use a comma to separate answers as needed.) Use the roster method to write the set A”. A= Use a comma to separate answers as needed. p Let X={p, a,r, 11, 12,13}, Y ={q, s, t, 11, 13, 15}, and Z={q, s, 12, 13, 15}. List the members of the given set, using set braces. XU (YN2Z) 4 b (Type a list of letters and integers.) U is the set of universities in the United States. A is the set of universities in the United States that have the name of a city in their name. B is the set of universities in the United States that have the word North in their name. Describe the set A' in words. Choose the correct answer below. L A, A'is the set of universities in the United States that have the name of a city and do not have the word North in their name. i1 B. A'isthe set of universities in the United States that have the word North and do not have the name of a city in their name. i1 €. A'isthe set of universities in the United States that do not have the word North in their name. i1 D. A'is the set of universities in the United States that do not have the name of a city in their name. Find the set of outcomes that occur when we flip 3 coins and obtain more tails than heads. Enter the outcomes using H and T to represent heads and tails respectively. For example, an outcome of two heads tosses followed by one tails toss would be HHT. A single fair die is tossed. Find the probability of rolling a number greater than 5. What is the probability of rolling a number greater than 57 (Simplify your answer. Type a fraction.) 20137
50, 1324 final exam review (A) Several friends chartered a boat for a day's fishing. They caught a total of 59 fish. The table below provides inforrmation about the type and number of fish caught. Determine the empirical probability that the next fish caught is a flounder. Fish Number caught Grouper 12 Shark 19 Flounder 6 Kingfish 22 P(flounder) = (Simplify your answer. Type a fraction.) 91. A produce buyer for a juice company is buying peaches. He makes a choice of either Oregon, Wisconsin, Michigan, or imported peaches. For this contract he must also choose large, extra large, or unsized. If each option has an equally likely chance of being selected, find the probability of the following event. The peaches are imported. What is the probability of this event? (Type the ratio as a simplified fraction.) 92. A single, fair 6-sided die is tossed. Find the odds in favor of rolling a 3, 4, 5, or 6. What are the odds in favor of rolling a 3, 4, 5, or 6?2 to (Simplify your answer.) 93. The odds in favor of Nolan getting promoted are 5:4. Find The probability that Nolan gets promoted is the probability that Nolan gets promoted. ) (Type an integer or a simplified fraction.) 94. This problem involves empirical probability. The table shows the breakdown of 87 thousand single parents on active duty in the U.S. military in a certain year. All numbers are in thousands and rounded to the nearest thousand. Use the data in the table to find the probability that a randomly selected single parent in the U.S. military is in the Army. Marine Air Army Navy | Corps | Force | Total {Male 22 27 5 11 65 Female 9 8 1 4 22 Total 31 35 6 15 87 The probability that a randomly selected single parent in the U.S. military is in the Army is (Type an integer or decimal rounded to the nearest hundredth as needed.) 95. Two cards are drawn without replacement from an ordinary deck, find the probability that the second is a diamond, given that the first is a diamond. What is the conditional probability? (Type an integer or a simplified fraction.) 21137
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1324 final exam review (A) 96. A bicycle factory runs two assembly lines, A and B. 98% of line A's products pass inspection and 94% of line B's products pass inspection. 40% of the factory's bikes come off assembly line B and the rest come off line A. Find the probability that one of the factory's bikes did not pass inspection and came off assembly line B. The probability is (Type a decimal. Do not round.) 97. The table shows the result of a restaurant survey. Meals | Service good | Service poor | Total Lunch 43 32 75 Dinner 42 29 71 Total 85 61 146 Find the probability the service was poor, given that the meal was dinner. The probability the service was poor, given that the meal was dinner, is (Type an integer or a simplified fraction.) 98. The Motor Vehicle Department has found that the probability of a person passing the test for a driver's license on the first try is 0.73. The probability that an individual who fails on the first test will pass on the second try is 0.82. Find the probability that an individual fails both the first and second tests. P(fails both the first and second tests) = (Simplify your answer. Type an integer or a decimal. Round to the nearest hundredth.) 99. Let x determine a random variable, and use your knowledge of probability to prepare a probability distribution. A family has four children and the number of boys is recorded. (Assume an equal chance of a boy or girl for each birth.) Complete the probability distribution. X 0 1 2 3 4 1 1 P{x —-— — x) 4 16 (Type an integer or a simplified fraction.) 100. Find the expected value of the random variable. x |2 3 4 5 P()|0.2 04 0.1 03 What is the expected value? (Type an integer or a decimal.) 101. Suppose you are invited to play a game in which you bet $1 on any number from 000 to 699. If your number comes up, you get $175. Find the expected winnings. Expected winnings = $ (Type an integer or decimal rounded to the nearest cent as needed.) 102. Evaluate the expression. oP2 The solution is 22137
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1324 final exam review (A) 103, Evaluate ,Cq. Cn = 12+3 (Simplify your answer. Type an integer or a fraction.) 104. The owner of a stereo store wants to advertise that he has How many different sound systems can the owner many different sound systems in stock. The store carries advertise? 7 different CD players, 9 different receivers, and 6 different speakers. Assuming a sound system consists of one of each, how many different sound systems can he advertise? 105. A company wants to have 6-digit phone extensions with the first digit not being zero. How many different extensions are possible? The number of different extensions that are possible is 106. Use the formula for , P, to solve the following question. A club with six members is to choose three officers: president, vice-president, and secretary-treasurer. If each office is o be held by one person and no person can hold more than one office, in how many ways can those offices be filled? ways 23/37
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1324 final exam review (A) y 10~ SA G- 4 - 9. . X I T e e e T s -10 -8 -6 -4 -2 ?" 274 8 10 -4, 8 10 LA ~3,1 (Use a comma to separate answers as needed.) A 3 (Use a comma to separate answers as needed.) . A. The x-intercept(s) is/are 8,~8 (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) A. The y-intercept(s) is/are - 64 (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) . A. The slope is - . (Type an integer or a simplified fraction.) oo . A. The slope of 2x+ 5y =8 is A. The slope of 2x +5y =7 is (1) parallel. 2 s . (Type an integer or a simplified fraction.) . (Type an integer or a simplified fraction.) Ly =3x+10 . 8x—Ty Ly=E X +3 25137
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10. 1324 final exam review (A) 996.94 1. - 2250 524,000 2020 i2. (=52) downward 13. 14. 15. 16. C. R(X) = = 6x° +300x + 30,000 25 33,750 26/37
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18. 1324 final exam review (A) 19. (1) quadratic 20. 21. 22, 10,550.42 23. 24, Iog 813= 25. 26. 27. 28. In 5+4in x+9in v 29. A x= 14 (Simplify your answer. Use a comma to separate answers as needed.) 30 . A. The solution is x = 3 .(Type an integer or a simplified fraction.) 27137
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31 1324 final exam review (A) . A. The solution is x = 7 (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) 32. 33. 1.4986 34, 35. 36. 39.19 37. 12,919.86 38. 168,132 39. 23,166 5.77 40. 19,781.63 41. 11.40 42, 128,839 43. 2171.57 44, 74,991.09 45, 25145.42 46. 12,505.60 28137
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47, 83,676.51 1324 final exam review (A) 48. 16684.34 49, 96.93 50. 51. 52. 53. 29137
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1324 final exam review (A) 54. 1 55. A. This system has exactly one solution. The solution is ( 2 , -2 , 2 ) . (Type an exact answer in simplified form.) 56. B. 9 2 7 4 _ | ETRETER 112" 71 2 , Where z is any real number. (Simplify your answers. Type expressions using z as the variable. Use integers or fractions for any numbers in the expressions.) There are infinitely many solutions. The solution set is 57. A This system has exactly one solution. The solution is ( -1 , 2 : 1 , -2 ) . (Type an exact answer in simplified form.) 58. 260 130 200 59. 180 90 50 60. 1.99 549 7.99 30/37
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1324 final exam review (A) 61. 1097 1264 802 -1 -4 -6 ] ] 21 o0 1 -3 -6 62. A + = 1 3 5 -3 4 -2 -2 7 3 -3 5 0 -2 -5 16 13 o 63. A 0 1 1= (Simplify your answer.) -1 4 4 -5 =13 -2 =3 64. A. 3 1 . 10 4 . , , . ) The inverse is . (Type a matrix, using an integer or simplified fraction for each matrix element. Do not 1 1 10 4 factor out a scalar multiple.) 65. A, -4 -6 3 The inverse matrix is 0 -1 g | . (Type a matrix, using an integer or simplified fraction for each matrix element. | 3 4 -2 Do not factor out a scalar multiple.) 66. 42,900 37,300 30,700 30,300 Company D Company D 31/37
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1324 final exam review (A) 68. Ay 69. y 70. A. The maximum value is A. The minimum value is 98 32 32/37
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72. 4 1324 final exam review (A) 73. 74. 75. 76. 77. 33/37
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1324 final exam review (A) —T ois o 78. 34/37
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1324 final exam review (A) 79. 80. A. The maximum is z = 360 when x = 0 , Xp = 40 , 897 20 i 81. 82. 83. 84. 85. 35/37
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1324 final exam review (A) . p,a,rs,11,12,13,15 87. D. A'is the set of universities in the United States that do not have the name of a city in their name. 88. TTT,TTH,THTHTT 89. ol - 90. 91. sl 92. 93. oo 94, 0.36 - 96. 0.024 97. 98. 0.05 99. w|lw - 36/37
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100. 1324 final exam review (A} 101. -0.75 102. 72 103. 220 104. 378 105. 900000 106. 120 37137
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