Math 1324 Final Exam Review (A)

Transcription

1 Math 13 Final Eam Review (A) Graph the equation. 5 = Find the - and -intercepts of the graph. List all the -intercepts. Select the correct choice below and, if necessar, fill in the answer bo to complete our choice. 6 A. (Use a comma to separate answers as needed.) B. There are no -intercepts. List all the -intercepts. Select the correct choice below and, if necessar, fill in the answer bo to complete our choice. A. (Use a comma to separate answers as needed.) B. There are no -intercepts /37

2 13 final eam review (A) 3. Find the -intercepts and -intercepts of the graph of the equation. = 6 Select the correct choice below and, if necessar, fill in the answer bo to complete our choice. A. The -intercept(s) is/are. (Tpe an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There are no -intercepts. Select the correct choice below and, if necessar, fill in the answer bo to complete our choice. A. The -intercept(s) is/are. (Tpe an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There are no -intercepts.. Find the slope of the line if it is defined. Through ( 3, 5) and ( 8, ) Select the correct choice below and, if necessar, fill in the answer bo to complete our choice. A. The slope is. (Tpe an integer or a simplified fraction.) B. The slope is undefined. 5. Find the slope and the -intercept of the line. = What is the slope? What is the -intercept? (Tpe an integer or a fraction.) /37

3 6. 13 final eam review (A) Decide whether the pair of lines is parallel, perpendicular, or neither. + 5 = = 7 Select the correct choice below and, if necessar, fill in the answer bo to complete our choice. A. The slope of + 5 = 8 is. (Tpe an integer or a simplified fraction.) B. The slope of + 5 = 8 is undefined. Select the correct choice below and, if necessar, fill in the answer bo to complete our choice. A. The slope of + 5 = 7 is. (Tpe an integer or a simplified fraction.) B. The slope of + 5 = 7 is undefined. The lines are (1) (1) perpendicular. neither parallel nor perpendicular. parallel. 7. Find an equation of the line that passes through the given points. ( 3,1) and (,16) The equation is. (Simplif our answer.) 8. Write an equation of the line containing ( 9, ) and parallel to the graph of 8 7 =. The equation of the line is = Find an equation for the line which passes through (, 5) and is perpendicular to the line containing (, ) and (, 6). The equation of the line is. (Simplif our answer. Tpe our answer in slope-intercept form.) 1. 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 dollars with a useful life of n ears is D = (1/n). Find the depreciation for items with the given characteristics. Cost is $ 15,951; life is 16 r The annual straight-line depreciation is approimatel $ per ear. (Round to the nearest cent.) 11. In 199, 5, people worked in the air transportation industr. In 8, the number was 88,. (a) Find a linear equation giving the number of emploees in the air transportation industr in terms of, the number of ears since 199. (b) Assuming the equation remains valid in the future, in what ear will there be 6, emploees of the air transportation industr? (a) The linear equation determined b the two points in part (a) is = +. (Tpe integers or decimals rounded to one decimal place.) (b) The number of emploees of the air transportation industr will reach 6, in the ear. 3/37

4 1. 13 final eam review (A) Determine the verte of the parabola and state whether it opens upward or downward. g() = 3 ( + 5) + What is the verte of the parabola? (Tpe an ordered pair.) In which direction does the verte open? upward downward 13. Match the function with its graph. f() = ( 5) + Choose the correct graph of [ 1,1,1] [ 1,1,1]. f() = ( 5) + below. Each graph is shown in the viewing window A. B. C. D. E. F. 1. Determine the verte of the parabola without graphing. f() = What is the verte of the parabola? (Tpe an ordered pair.) /37

5 15. Find the verte and the equation of the line of smmetr. Graph the function. f() = ( 5) What is the verte? 13 final eam review (A) Choose the correct graph below. A. B. (Tpe an ordered pair.) What is the equation of the line of smmetr? = - C. - - D A charter flight charges a fare of $3 per person plus $ 6 per person for each unsold seat on the plane. If the plane holds 1 passengers and if represents the number of unsold seats, find the following. A. An epression for the total revenue received for the flight. (Hint: Multipl the number of people fling, 1, b the price per ticket.) B. The number of unsold seats that will produce the maimum revenue. C. The maimum revenue. A. The total revenue R() received for the flight is epressed b A. R() = , B. R() = , C. R() = , D. R() = , B. The number of unsold seats that will produce the maimum revenue is. C. The maimum revenue is $. 17. Find the vertical and horizontal asmptotes. Then graph the function. f() = The vertical asmptote is =. The horizontal asmptote is =. Choose the correct graph. A. B. C. D /37

6 final eam review (A) Find the vertical and horizontal asmptotes. Then graph the function. f() = The vertical asmptote is =. The horizontal asmptote is =. Choose the correct graph. A. B. C. D Classif the function as linear, quadratic, or eponential. f() = The function is (1). (1) quadratic eponential linear. If f() = a and f( 3 ) = 7, find f( ). Assume a >. f( ) = 1. If mone loses value, then as time passes, it takes more dollars to bu the same item. Use the table to answer the questions. Let t be ears and be the value of $1 in t ears. t (a) Suppose a house costs $ 1, toda. Estimate the cost of the same house in 3 ears. (b) Estimate the cost of a $ 5 tetbook in ears. (a) Suppose a house costs $ 1, toda. Estimate the cost of the same house in 3 ears. The house will cost about dollars. (Round to the nearest dollar as needed.) (b) Estimate the cost of a $ 5 tetbook in ears. The tetbook will cost about dollars. (Round to the nearest cent as needed.) 6/37

7 . 13 final eam review (A) The scrap value of a machine at the end of its useful life is given b S(n) = C(1 r) n, where C is the original cost, n is the useful life of the machine in ears, and r is the constant annual percentage of value lost. Find the scrap value of the following machine. Original cost, $ 1,; life, 9 ears; annual rate of value lost, 1% S = $ (Round to the nearest cent.) 3. Use the graph of = Ca to determine C and a. 1 C = a = [-1, 1] [-1, 1] Xscl=1 Yscl=1. 5. Write the equation in equivalent logarithmic form. 1 3 = 81 Evaluate the epression without the use of a calculator. log 1, log 1, = (Tpe an integer or a simplified fraction.) What is the equivalent logarithmic form? 6. Write the epression as the logarithm of a single number or epression. log 1 log The epression simplifies to. (Simplif our answer.) 7. Write the epression as the logarithm of a single number or epression. Assume that all variables represent positive numbers. 6 log + 3 log log z 6 log + 3 log log z = 8. Write the epression as a sum and/or a difference of logarithms, with all variables to the first degree. 9 ln 5 9 ln 5 = (Simplif our answer.) 7/37

8 13 final eam review (A) 9. Solve the equation. ln( 5 + 1) ln = ln6 Select the correct choice below and, if necessar, fill in the answer bo to complete our choice. A. = (Simplif our answer. Use a comma to separate answers as needed.) B. There is no solution. 3. Solve. log ( ) = 1 Select the correct choice below and, if necessar, fill in the answer bo to complete our choice. A. The solution is =. (Tpe an integer or a simplified fraction.) B. There is no solution. 31. Solve for. 8 3 = 56 Select the correct choice below and, if necessar, fill in the answer bo to complete our choice. A. The solution is =. (Tpe an integer or a simplified fraction. Use a comma to separate answers as needed.) B. The solution is not a real number. 3. Solve the following eponential equation without using logarithms. 7 = 16 The solution is =. (Simplif our answer.) 33. Solve for t. e.1t =.73 The solution is t =. (Tpe an integer or decimal rounded to four decimal places as needed. Use a comma to separate answers as needed) 3. Solve the following equation for c. 3c 1 = d c = 8/37

9 final eam review (A) The total ependitures (in millions) of current dollars for pollution abatement and control during the period from through 19 can be approimated b the function. P() = 168. e, where = corresponds to the ear. (a) In what ear would the total ependitures reach $ 15 million dollars? (b) If this model remains accurate, when would the total ependitures reach $ 6 million? (a) The ependitures would reach $ 15 million in the ear earl-. (Simplif our answer. Tpe a whole number.) (b) The ependitures would reach $ 6 million in the ear earl-. (Simplif our answer. Tpe a whole number.) 36. Find the interest. Principal Rate Time in Months Interest $ % 3 The interest is $. (Round to the nearest cent.) 37. Find the future value of this loan. $1,69 at.7% for 18 months The future value of the loan is $. (Round to the nearest cent as needed.) 38. Find the present value of the given future amount. $ 173,36 for 191 das at 5.8% simple interest. Assume 36 das in a ear. What is the present value? $ (Round to the nearest dollar as needed.) 39. For the following treasur bill bought in 7, find (a) the price of the T-bill, and (b) the actual interest rate paid b the Treasur. Three-month $ 3,5 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 b the Treasur is %. (Tpe an integer or decimal rounded to two decimal places as needed.). Find the compound amount for the following deposit. $ 1, at 5% compounded semi-annuall for 7 ears. The compound amount after 7 ears will be $. (Round to the nearest cent.) 1. Use the compound interest formula A = P(1 + r) t and the given information to solve for r. A = $ 3,,, P = $,, t = r = % (Round to the nearest hundredth.) 9/37

10 . 13 final eam review (A) Find the amount of the ordinar annuit based on the information given. R = $ 11,5, 5% interest compounded semiannuall for 5 ears The amount of the ordinar annuit is $. (Round to the nearest dollar as needed.) 3. Find the amount of each pament to be made into a sinking fund which earns 5% compounded quarterl and produces $ 33, at the end of 3.5 ears. Paments are made at the end of each period. The pament size is $. (Round to the nearest cent.). Find the future value of a 6-ear annuit due with paments of $ 1,5 and an annuall compounded interest rate of 5%. The future value is $. (Round to the nearest cent.) 5. Find the present value of an ordinar annuit which has paments of $ per ear for 17 ears at 6% compounded annuall. The present value is $. (Round to the nearest cent.) 6. Find the amount necessar to fund the given withdrawals. Quarterl withdrawals of $ 7 for 5 ears; interest rate is.% compounded quarterl. The amount necessar to fund the given withdrawals is $. (Round to the nearest cent as needed.) 7. Find the lump sum deposited toda that will ield the same total amount as paments of $1, at the end of each ear for 13 ears, at an interest rate of 7% compounded annuall. The lump sum is $. (Round to the nearest cent.) 8. Find the price a purchaser should be willing to pa for the given bond. Assume that the coupon interest is paid twice a ear. $ 15, bond with coupon rate 6% that matures in ears; current interest rate is 3% The purchaser should be willing to pa $. (Simplif our answer. Round to the nearest cent as needed.) 9. Find the pament necessar to amortize a 8% loan of $ 11 compounded quarterl, with 13 quarterl paments. The pament size is $. (Round to the nearest cent.) 5. Solve b the substitution method. 8 + = 6 + = What is the solution of the sstem? (Tpe an ordered pair.) 1/37

11 final eam review (A) A 5-seat theater has tickets for sale at $ 7 and $. How man tickets should be sold at each price for a sellout performance to generate a total revenue of $ 157,1? The number of tickets for sale at $ 7 should be. The number of tickets for sale at $ should be. 5. Obtain an equivalent sstem b performing the stated elementar operation on the sstem. Replace the second equation b the sum of itself and times the first equation z = z = z = z = z = z = + z = + z = + z = (Tpe integers or simplified fractions.) 53. Write an augmented matri for the following sstem of equations z = 9 + 9z = 9 z = 6 The entries in the matri are: 5. Replace R b R + ( 7)R R + ( )R 7 1 = 11/37

12 55. Solve the following sstem of equations using the Gauss-Jordan method. 13 final eam review (A) 5 9 z = z = z = Select the correct choice below and, if necessar, fill in the answer boes to complete our choice. A. This sstem has eactl one solution. The solution is,, (Tpe an eact answer in simplified form.) B. This sstem has infinitel man solutions of the form,,z, where z is an real number. (Tpe epressions using z as the variable.) C. This sstem has no solution Solve the sstem b an method z = z = 1 Select the correct choice below and fill in an answer boes within our choice. A. There is one solution. The solution set is,,. (Simplif our answers.) B. There are infinitel man solutions. The solution set is,,z, where z is an real number. (Simplif our answers. Tpe epressions using z as the variable. Use integers or fractions for an numbers in the epressions.) C. There is no solution. The solution set is. 57. Solve the sstem b an method. + + z + w = 8 + 8z w = 3 + z + w = + 3z w = Select the correct choice below and, if necessar, fill in the answer boes to complete our choice. A. This sstem has eactl one solution. The solution is,,, (Tpe an eact answer in simplified form.) B. This sstem has infinitel man solutions of the form,,,w (Tpe epressions using w as the variable.) C. This sstem has no solution.., where w is an real number. 1/37

13 final eam review (A) A band concert is attended b adults, teenagers, and z preteen children. These numbers satisfied the following equations. How man adults, teenagers, and children were present? z = z = z = There were adults, teenagers, and children present at the band concert. 59. The U-Drive Rent-A-Truck compan plans to spend $ 13 million on 3 new vehicles. Each commercial van will cost $ 35,, each small truck $ 3,, and each large truck $ 8,. Past eperience shows that the need twice as man vans as small trucks. How man of each tpe of vehicle can the bu? The can bu vans, small trucks, and large trucks. 6. Jim took clothes to the cleaners three times last month. First, he brought shirts and pairs of slacks and paid $ Then he brought 5 shirts, pairs of slacks, and 1 sports coat and paid $ Finall, he brought shirts and sports coats and paid $ 3.9. 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. 61. A basketball team sells tickets that cost $1, $, or, for VIP seats, $3. The team has sold 3163 tickets overall. It has sold 167 more $ tickets than $1 tickets. The total sales are $ 6,31. How man tickets of each kind have been sold? How man $1 tickets were sold? How man $ tickets were sold? How man $3 tickets were sold? 6. Perform the operation if possible Select the correct choice below and, if necessar, fill in the answer bo to complete our choice. A B. The operation is not defined. + 1 = 3 13/37

14 63. Find the following matri product, if it eists. 13 final eam review (A) Select the correct choice below and, if necessar, fill in the answer bo to complete our choice. A = (Simplif our answer.) B. The product does not eist. 6. Find the inverse, if it eists, for the given matri Find the inverse. Select the correct choice below and, if necessar, fill in the answer bo to complete our choice. A. The inverse is matri element. Do not factor out a scalar multiple.). (Tpe a matri, using an integer or simplified fraction for each B. There is no inverse of the given matri. 65. Find the inverse, if it eists, for the given matri Select the correct choice below and, if necessar, fill in the answer bo to complete our choice. A. The inverse matri is for each matri element. Do not factor out a scalar multiple.). (Tpe a matri, using an integer or simplified fraction B. There is no inverse of the given matri. 1/37

15 final eam review (A) Two departments of a firm, A and B, need differing amounts of steel, wood, and plastic. The table on the right gives the amount of each product the departments need. These three products are supplied b two suppliers, Compan C and Compan D, with the unit prices given in the table on the right. Steel Wood Plastic Department A Department B Compan C Compan D Steel Wood Plastic a. Use matri multiplication to determine how much these orders will cost each department at each of the two suppliers. Enter the amounts into the cost matri shown on the right. Dept. A Dept. B Co. C Co. D b. From which supplier should each department make its purchase? Which compan should department A use? Compan D Compan C Which compan should department B use? Compan D Compan C 67. Graph the inequalit on a plane Use the graphing tool on the right to graph the inequalit Graph the feasible region for the sstem of inequalities Use the graphing tool on the right to graph the feasible region for the sstem of inequalities /37

16 69. Graph the feasible region for the given sstem of inequalities Use the graphing tool on the right to graph the sstem of inequalities. 13 final eam review (A) The graph shows a region of feasible solutions. Use this region to find maimum and minimum values of the objective function. 1 z = Select the correct choice below and, if necessar, fill in the answer bo to complete our choice. A. The maimum value is. B. The maimum value does not eist. 1 The coordinates of the corner points are (, 3), (, 8), ( 8, 7), and ( 9, ). Select the correct choice below and, if necessar, fill in the answer bo to complete our choice. A. The minimum value is. B. The minimum value does not eist. 71. Solve the following linear programming problem. Maimize: z = subject to: , The maimum value is. The maimum occurs at the point. (Tpe an ordered pair. If the maimum occurs at more than one point, tpe either answer. Tpe an integer or a fraction. ) 16/37

17 7. Solve the following linear programming problem. Maimize: z = 11 + subject to: , 13 final eam review (A) The maimum value is. The maimum occurs at the point. (Tpe an ordered pair. If the maimum occurs at more than one point, tpe either answer. Tpe an integer or a fraction. ) 73. A chain saw requires 8 hours of assembl and a wood chipper 7 hours. A maimum of 11 hours of assembl time is available. The profit is $15 on a chain saw and $ on a chipper. How man of each should be assembled for maimum profit? To attain the maimum profit, assemble chain saws and wood chippers. 7. Delue coffee is to be mied with regular coffee to make at least pounds of a blended coffee. The miture must contain at least 13 pounds of delue coffee. Delue coffee costs $ 6 per pound and regular coffee $ 5 per pound. How man pounds of each kind of coffee should be used to minimize costs? To attain the minimum cost, use delue coffee and pounds of pounds of regular coffee. 75. Jamaal is planning to invest up to $ 19 in Cit Bank or State Bank. He wants to invest at least $ 1 in Cit Bank, but not more than $ 1; since State Bank does not insure more than $ 9, he wants to invest no more than this amount in State Bank. The interest at Cit 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 maimum amount of interest that Jamaal can earn? He should invest $ in Cit Bank and $ in State Bank. The maimum amount of interest that Jamaal can earn is $. 76. Introduce slack variables as necessar and then write the initial simple tableau for the given linear programming problem. Maimize z = subject to ,, 3. Complete the initial simple tableau. 1 3 s 1 s s 3 z /37

18 final eam review (A) Find the pivot in the simple tableau. 1 3 s 1 s s 3 z The pivot is located in row, column. The pivot is. 78. Use the indicated entr as the pivot and perform the pivoting. 1 3 s 1 s s 3 z s 1 s s 3 z 79. For the given simple tableau, (a) list the basic and the nonbasic variables, (b) find the basic feasible solution determined b setting the nonbasic variables equal to, and (c) decide whether this is a maimum solution. (a) What are the basic variables? 1 3 s 1 s z (Use a comma to separate answers as needed.) What are the nonbasic variables? (Use a comma to separate answers as needed.) (b) Find the basic feasible solution b setting the nonbasic variables equal to. 1 =, =, 3 =, s 1 =, s =, z = (c) Is this solution a maimum? No Yes 18/37

19 8. 13 final eam review (A) Solve the linear programming problem using the simple method. Maimize z = subject to ,. Select the correct choice below and, if necessar, fill in the answer bo to complete our choice. A. The maimum is z = when 1 =, =, s 1 =, s =, and s 3 =. B. There is no maimum solution for this linear programming problem. 81. A biologist has kg of nutrient A, 8 kg of nutrient B, and kg of nutrient C. These nutrients will be used to make tpes of food, whose contents (in percent per kilogram of food) and whose 'growth values' are shown on the right. Set up the initial simple tableau that would be used to determine how man kilograms of each food should be produced in order to maimize total growth. P Q R S A B C Growth 11 1 Value 8 7 Let 1 be the number of kilograms of food tpe P. Let be the number of kilograms of Q. Let 3 be the number of kilograms of R, and let be the number of kilograms of S. What is the objective function? z = Set up the initial simple tableau for the problem. 1 3 s 1 s s (Tpe an integer or decimal for each matri element.) A compan sells sets of kitchen knives. A Basic Set consists of utilit knives and 1 chef's knife. A Regular Set consists of utilit knives, 1 chef's knife, and 1 slicer. A Delue Set consists of 3 utilit knives, 1 chef's knife, and 1 slicer. The profit is $ 3 on a Basic Set, $ on a Regular Set, and $ 8 on a Delue Set. The factor has on hand 16 utilit knives, 8 chef's knives, and slicers. If all sets will be sold, how man of each tpe should be made up in order to maimize profit? What is the maimum profit? How man Basic Sets should be made up? How man Regular Sets should be made up? How man Delue Sets should be made up? What is the maimum profit? $ 19/37

20 83. Find the number of subsets for the following set. { D,E,F} How man subsets does this set have? (Tpe a whole number.) 13 final eam review (A) 8. Use A = {, 6, 7, 8, 9} and B = { 3, 7, 8, 9} to find the set A B. A B = (Use a comma to separate answers as needed.) 85. Let U = {, 3,, 5, 6, 7, 8 }, A = {, 5, 6, 8 }. A Use the roster method to write the set. A = (Use a comma to separate answers as needed.) 86. Let X = {p, q, r, 11, 1, 13}, Y = {q, s, t, 11, 13, 15}, and Z = {q, s, 1, 13, 15}. List the members of the given set, using set braces. X ( Y Z) (Tpe a list of letters and integers.) 87. 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 cit 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. A. A' is the set of universities in the United States that have the name of a cit and do not have the word North in their name. B. A' is the set of universities in the United States that have the word North and do not have the name of a cit in their name. C. A' is the set of universities in the United States that do not have the word North in their name. D. A' is the set of universities in the United States that do not have the name of a cit in their name. 88. 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 respectivel. For eample, an outcome of two heads tosses followed b one tails toss would be HHT. (Use a comma to separate answers as needed.) 89. A single fair die is tossed. Find the probabilit of rolling a number greater than 5. What is the probabilit of rolling a number greater than 5? (Simplif our answer. Tpe a fraction.) /37

21 9. 13 final eam review (A) Several friends chartered a boat for a da's fishing. The caught a total of 59 fish. The table below provides information about the tpe and number of fish caught. Determine the empirical probabilit that the net fish caught is a flounder. Fish Number caught Grouper 1 Shark 19 Flounder 6 Kingfish P( flounder ) = (Simplif our answer. Tpe a fraction.) 91. A produce buer for a juice compan is buing peaches. He makes a choice of either Oregon, Wisconsin, Michigan, or imported peaches. For this contract he must also choose large, etra large, or unsized. If each option has an equall likel chance of being selected, find the probabilit of the following event. The peaches are imported. What is the probabilit of this event? (Tpe the ratio as a simplified fraction.) 9. A single, fair 6-sided die is tossed. Find the odds in favor of rolling a 3,, 5, or 6. What are the odds in favor of rolling a 3,, 5, or 6? to (Simplif our answer.) The odds in favor of Nolan getting promoted are 5:. Find The probabilit that Nolan gets promoted is the probabilit that Nolan gets promoted.. (Tpe an integer or a simplified fraction.) This problem involves empirical probabilit. The table shows the breakdown of 87 thousand single parents on active dut in the U.S. militar in a certain ear. All numbers are in thousands and rounded to the nearest thousand. Use the data in the table to find the probabilit that a randoml selected single parent in the U.S. militar is in the Arm. Arm Nav Marine Corps Air Force Total Male Female Total The probabilit that a randoml selected single parent in the U.S. militar is in the Arm is. (Tpe an integer or decimal rounded to the nearest hundredth as needed.) 95. Two cards are drawn without replacement from an ordinar deck, find the probabilit that the second is a diamond, given that the first is a diamond. What is the conditional probabilit? (Tpe an integer or a simplified fraction.) 1/37

22 final eam review (A) A biccle factor runs two assembl lines, A and B. 98% of line A's products pass inspection and 9% of line B's products pass inspection. % of the factor's bikes come off assembl line B and the rest come off line A. Find the probabilit that one of the factor's bikes did not pass inspection and came off assembl line B. The probabilit is. (Tpe a decimal. Do not round.) 97. The table shows the result of a restaurant surve. Meals Service good Service poor Total Lunch Dinner 9 71 Total Find the probabilit the service was poor, given that the meal was dinner. The probabilit the service was poor, given that the meal was dinner, is. (Tpe an integer or a simplified fraction.) 98. The Motor Vehicle Department has found that the probabilit of a person passing the test for a driver's license on the first tr is.73. The probabilit that an individual who fails on the first test will pass on the second tr is.8. Find the probabilit that an individual fails both the first and second tests. P(fails both the first and second tests) = (Simplif our answer. Tpe an integer or a decimal. Round to the nearest hundredth.) 99. Let determine a random variable, and use our knowledge of probabilit to prepare a probabilit distribution. A famil has four children and the number of bos is recorded. (Assume an equal chance of a bo or girl for each birth.) Complete the probabilit distribution. 1 3 P() (Tpe an integer or a simplified fraction.) Find the epected value of the random variable. 3 5 P() What is the epected value? (Tpe an integer or a decimal.) 11. Suppose ou are invited to pla a game in which ou bet $1 on an number from to 699. If our number comes up, ou get $ 175. Find the epected winnings. Epected winnings = $ (Tpe an integer or decimal rounded to the nearest cent as needed.) 1. Evaluate the epression. P 9 The solution is. /37

23 13. Evaluate 1C3. 13 final eam review (A) 1C3 = (Simplif our answer. Tpe an integer or a fraction.) 1. The owner of a stereo store wants to advertise that he has man different sound sstems in stock. The store carries 7 different CD plaers, 9 different receivers, and 6 different speakers. Assuming a sound sstem consists of one of each, how man different sound sstems can he advertise? How man different sound sstems can the owner advertise? 15. A compan wants to have 6-digit phone etensions with the first digit not being zero. How man different etensions are possible? The number of different etensions that are possible is. 16. Use the formula for npr to solve the following question. A club with si members is to choose three officers: president, vice-president, and secretar-treasurer. If each office is to be held b one person and no person can hold more than one office, in how man was can those offices be filled? was 17. How man different committees can be formed from 8 teachers and students if the committee consists of 3 teachers and students? In how man was can the committee of 7 members be selected? 18. The sales force of a business consists of 1 men and 1 women. A production unit of a. What is the probabilit that it will consist of 5 men and 5 women? b. What is the probabilit that it will consist of all men? c. What is the probabilit that it will consist of at least one woman. 1 people is set up at random. a. The probabilit that it will consist of 5 men and 5 women is. (Simplif our answer. Tpe an integer or a fraction.) b. The probabilit that it will consist of all men is. (Simplif our answer. Tpe an integer or a fraction.) c. The probabilit that it will consist of at least one woman is. (Simplif our answer. Tpe an integer or a fraction.) % of the population is 65 or older. Find the probabilit that the following number of persons selected at random from 5 people are 65 or older. The probabilit that all are 65 or older is. (Tpe an integer or decimal rounded to the nearest thousandth as needed.) The probabilit at least 3 are 65 or older is. (Tpe an integer or decimal rounded to the nearest thousandth as needed.) 3/37

24 13 final eam review (A) % of the population is 65 or older. Find the probabilit that the following number of persons selected at random from 5 people are 65 or older. The probabilit that at most are 65 or older is. (Round to three decimal places as needed.) /37

25 13 final eam review (A) A. 3,1 (Use a comma to separate answers as needed.) A. 3 (Use a comma to separate answers as needed.) 3. A. The -intercept(s) is/are 8, 8. (Tpe an integer or a simplified fraction. Use a comma to separate answers as needed.) A. The -intercept(s) is/are 6. (Tpe an integer or a simplified fraction. Use a comma to separate answers as needed.). A. The slope is 9. (Tpe an integer or a simplified fraction.) A. The slope of + 5 = 8 is. (Tpe an integer or a simplified fraction.) 5 A. The slope of + 5 = 7 is. (Tpe an integer or a simplified fraction.) 5 (1) parallel. 7. = = + 3 5/37

26 13 final eam review (A) , 1. ( 5,) downward 13. E. 1. (,8) 15. (5,) 5 - B C. R() = , 5 33, B. -1 6/37

27 13 final eam review (A) B (1) quadratic , , log 3 = log 3 7. log 6 3 z 8. ln 5 + ln + 9 ln 9. A. = 1 (Simplif our answer. Use a comma to separate answers as needed.) 3. A. The solution is = 3.(Tpe an integer or a simplified fraction.) 7/37

28 13 final eam review (A) A. The solution is =. 8 (Tpe an integer or a simplified fraction. Use a comma to separate answers as needed.) log d , , , , , , ,55.6 8/37

29 13 final eam review (A) 7. 83, ( 3,) /37

30 13 final eam review (A) A. This sstem has eactl one solution. The solution is,,. (Tpe an eact answer in simplified form.) 56. B. There are infinitel man solutions. The solution set is 9 + z , z 11, where z is an real number. (Simplif our answers. Tpe epressions using z as the variable. Use integers or fractions for an numbers in the epressions.) 11,z 57. A. This sstem has eactl one solution. The solution is 1,, 1,. (Tpe an eact answer in simplified form.) /37

31 13 final eam review (A) A = A. 1 = (Simplif our answer.) A. The inverse is (Tpe a matri, using an integer or simplified fraction for each matri element. Do not factor out a scalar multiple.) 65. A. The inverse matri is (Tpe a matri, using an integer or simplified fraction for each matri element. Do not factor out a scalar multiple.) 66.,9 37,3 3,7 3,3 Compan D Compan D 31/37

32 13 final eam review (A) A. The maimum value is 98. A. The minimum value is , 5 5 3/37

33 13 final eam review (A) , /37

34 13 final eam review (A) /37

35 13 final eam review (A) 79.,s,z 3 1,s, No 8. A. The maimum is z = 36 when 1 =, =, s 1 =, s =, and s 3 = , ,8,9 85.,3,7 35/37

36 13 final eam review (A) 86. p,q,r,s,11,1,13, D. A' is the set of universities in the United States that do not have the name of a cit in their name. 88. TTT,TTH,THT,HTT /37

37 final eam review (A) /37