MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A) 4 13 C) 2 3 2) A) 0 B) 1 3 C) 5 13

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1 Math 30 Final Eam Review Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the slope of the line passing through the given pair of points. ) (5, ) and (, 3) ) ) (-9, -) and (-3, -) ) Not defined 3) (-, -9) and (, -9) ) Find the slope of the line. ) A line parallel to - = ) 5) A line perpendicular to -5 + = -0 5) Find an equation in slope-intercept form (where possible) for the line. ) Through (, -7), parallel to + 7 = -7 = = = = ) 7) Through (-, 3), perpendicular to - 5 = 7 7) = = = 5-7 =

2 Find the slope of the line. ) 0 ) ) 9) Write a cost function for the problem. Assume that the relationship is linear. 0) A cab compan charges a base rate of $.00 plus 0 cents per minute. Let C() be the cost in dollars for using the cab for minutes. C() = C() = C() = C() = ) ) A cable TV compan charges $9 for the basic service plus $7 for each movie channel. Let C() be the total cost in dollars of subscribing to cable TV, using movie channels. C() = 7-9 C() = 9-7 C() = C() = ) ) An electrician charges a fee of $55 plus $0 per hour. Let C() be the cost in dollars of using the electrician for hours. C() = C() = 55-0 C() = C() = 0-55 )

3 Find the correlation coefficient. 3) The test scores of randoml picked students and the number of hours the prepared are as follows: Hours Score ) ) The following are the temperatures on randoml chosen das and the amount a certain kind of plant grew (in millimeters): Temp Growth ) 5) The following are the temperatures on randoml chosen das and the amount a certain kind of plant grew (in millimeters): Temp Growth ) Find the simple interest. Assume a 30-da ear. Round results to the nearest cent. ) $,000 at 3% for das $,09.33 $0.00 $09.33 $0.00 ) 7) $,000 at.5% for 0 das $,.00 $70.00 $.00 $.00 7) ) $0,5 at.% for 5 months $95.90 $3.9 $79.9 $0.59 ) Find the amount of compound interest earned. 9) $7000 at 5% compounded quarterl for ears $33.9 $539.3 $35. $0. 9) 0) $5000 at % compounded semiannuall for ears $9.9 $. $.5 $5.30 0) ) $000 at 5.5% compounded monthl for 5 ears $5.0 $55. $55.3 $5. ) Solve the problem. ) Tasha borrowed $,000 to purchase a new car at an annual interest rate of.%. She is to pa it back in equal monthl paments over a ear period. What is her monthl pament? $5.0 $03.0 $35.7 $00.33 ) 3) You want to take out a loan to bu a new car for which ou need to finance $,30. Your bank will give ou a loan at 7% compounded monthl. You look at our budget and decide that ou can afford a pament of $57 a month. How man ears, to the nearest tenth of a ear, must the loan need to be to meet these conditions? 9.5 ears 3.3 ears 9.9 ears 5.7 ears 3) 3

4 ) Cara has a loan from her credit union at a rate of 9.% for which her paments are $5 per month. The interest is computed on a dail basis on the unpaid balance of the loan. If the loan balance after her last pament was $ and Cara makes her net pament 3 das later, how much of the pament is paid toward interest? $7. $7. $.5 $. ) 5) Amara borrowed $000 to purchase a new car at an annual interest rate of.9%. She is to pa it back in equal monthl paments over a 3 ear period. How much total interest will be paid over the period of the loan? Round to the nearest dollar. $3 $ $79 $75 5) Solve the sstem of equations using an method ou would like. ) + = = - (-, -) (, -) (-, ) No solution ) 7) + + z = - + z = z = (3, 5, -) (3,-, 5) (-, 5, 3) No solution 7) ) z = z = z = -59 (, 9, ) (,, 9) (-,, ) No solution ) 9) - - z = z = - + z = 5 (-,, ) (, 3, ) (,, 3) No solution 9) 30) - + 3z = 5 + z = + + z = 0 (,-, 0) (0,-, ) (, 0, -) No solution 30) Write the sstem of equations associated with the augmented matri. Use the variables X and Y in that order. 3) = = -3+5= = 3-5= = 3-5= = 3) Provide an appropriate response. 3) Write the augmented matri for the sstem. + = 30 = 7 3)

5 Find the inverse, if it eists, for the matri. 33) No inverse 33) 3) ) 35) ) Solve the problem. 3) A compan makes three chocolate candies: cherr, almond, and raisin. Matri A gives the amount of ingredients in one batch. Matri B gives the costs of ingredients from suppliers J and K. Multipl the matrices. 3) A = sugar 5 choc 7 milk cherr almond raisin B = J K 3 5 J K J K sugar choc milk cherr almond raisin cherr almond raisin J K J K sugar choc milk cherr almond raisin 5

6 37) A compan makes three chocolate candies: cherr, almond, and raisin. Matri A gives the amount of ingredients in one batch. Matri B gives the costs of ingredients from suppliers J and K. What is the cost of 00 batches of each cand using ingredients from supplier J? 37) A = sugar 5 choc 7 milk cherr almond raisin J K B = 3 5 sugar choc milk $,000 $5,000 $5,00 $000 3) A compan makes three chocolate candies: cherr, almond, and raisin. Matri A gives the amount of ingredients in one batch. Matri B gives the costs of ingredients from suppliers J and K. What is the cost of 00 batches of each cand using ingredients from supplier K? 3) A = sugar 5 choc 7 milk cherr almond raisin J K B = 3 5 sugar choc milk $000 $,000 $5,00 $900

7 Graph the feasible region for the sstem of inequalities. When ou are choosing our answer the feasible region is represented b the shaded area. 39) )

8 0) + 3 Graph the feasible region for the sstem of inequalities. When ou are - 3 choosing our answer the feasible region is represented b the shaded area. 0)

9 ) )

10 Use the indicated region of feasible solutions to find the maimum and minimum values of the given objective function. When looking at the graph the feasible region is represented b the shaded area. ) z = + 0 ) (0, 5) (0, 5) (0, 3) (, 0) (0, 0) Maimum of 30; minimum of 0 Maimum of 0; minimum of 30 Maimum of 50; minimum of 30 Maimum of 30; minimum of 30 3) z = - 3) (0, ) (., 5) (5, 0) Maimum of -7.5; minimum of -0 Maimum of 55; minimum of 0 Maimum of -0; minimum of 0 Maimum of 55; minimum of -0 ) z = +. ) (0, 5) (.5, 5) (0, ) (, 0) (0, 0) Maimum of 5 minimum of 3 Maimum of minimum of 0 Maimum of -3 minimum of -5 Maimum of 0; minimum of 3 0

11 Let A = {, 3, 5, 7}; B = {5,, 7, }; C = {5, }; D = {, 5, }; and U = {,, 3,, 5,, 7, }. Determine whether the given statement is true or false. 5) C D 5) True False ) A {7, 5, 3, } True False ) 7) B D True False 7) Use the Gauss-Jordan method to solve the sstem of equations. ) + + z = z = z = z + 3 5, 5 z - 5, z -7 5 z + 3 5, 5 z + 5, z 7 5 z + 3 5, 5 z + 5, z 7 5 z + 3 5, 5 z - 5, z ) 9) z = z = z = z + 33, 7 z +, z - z + 33, 7 z -, z z + 33, 7 z -, z - z + 33, -7 z -, z 9) 50) z = z = z = - 3 z + 3, -5 3 z + 7 3, z 3 z + 3, -5 3 z - 7 3, z 3 z - 3, 5 3 z - 7 3, z - 3 z + 3, -5 3 z - 7 3, z 50) Find the value. 5) Let A = ; A ) 5) Let A = -5 and B = 0 ; 3A + B ) 53) Let A = and B = 0 - ; 3A + B )

12 Use graphical methods to solve the linear programming problem. 5) Maimize z = + subject to: ) Maimum of 00 when = and = 3 Maimum of 0 when = 3 and = Maimum of 9 when = 9 and = Maimum of 9 when = and = 5 55) Minimize z = subject to: ) Minimum of.0 when = and = 3 Minimum of. when = and = Minimum of. when = 9 and = Minimum of.0 when = 3 and =

13 5) Maimize z = + 5 subject to: ) Maimum of 0 when = 0 and = Maimum of 3 3 when = 3 and = Maimum of 9 when = and = 9 Maimum of 9 when = and = 3 Use a Venn diagram to answer the question. 57) At East Zone Universit (EZU) there are 7 students taking College Algebra or Calculus. 35 are taking College Algebra, 509 are taking Calculus, and 0 are taking both College Algebra and Calculus. How man are taking Algebra but not Calculus? ) 5) At East Zone Universit (EZU) there are 9 students taking College Algebra or Calculus. 50 are taking College Algebra, 07 are taking Calculus, and 3 are taking both College Algebra and Calculus. How man are taking Calculus but not Algebra? ) 59) A surve of 0 families showed that 9 had a dog; 70 had a cat; 3 had a dog and a cat; 9 had neither a cat nor a dog, and in addition did not have a parakeet; 7 had a cat, a dog, and a parakeet. How man had a parakeet onl? ) 3

14 Use the given table to find the indicated probabilit. 0) College students were given three choices of pizza toppings and asked to choose one favorite. The following table shows the results. 0) Toppings Freshman Sophomore Junior Senior Totals Cheese 9 Meat Veggie A student is selected at random. Find the probabilit that the student's favorite topping is meat given that the student is a junior ) College students were given three choices of pizza toppings and asked to choose one favorite. The following table shows the results. ) Toppings Freshman Sophomore Junior Senior Totals Cheese Meat Veggie A student is selected at random. Find the probabilit that the student's favorite topping is veggie given that the student is a junior or senior ) People in a surve were given three choices of soft drinks and asked to choose one favorite. The following table shows the results. ) cola root beer lemon-lime totals under ears of age between and over 0 ears of age One of the participants is selected at random. Find the probabilit that the person is over 0 and prefers cola none of the above

15 3) People in a surve were given three choices of soft drinks and asked to choose one favorite. The following table shows the results. 3) cola root beer lemon-lime totals under ears of age between and over 0 ears of age One of the participants is selected at random. Find the probabilit that the person is over 0 given that the prefer root beer Solve the problem. ) Let the suppl and demand functions for a certain model of electric pencil sharpener be given b q = S(p) = 3 p andq = D(p) = - 3 p ) Where p is the price in dollars and q is the quantit of pencil sharpeners (in hundreds), find the equilibrium quantit and the equilibrium price. Equilibrium quantit: 0 Equilibrium price: $9.0 Equilibrium quantit: 950 Equilibrium price: $7 Equilibrium quantit: 90 Equilibrium price: $.0 Equilibrium quantit: 00 Equilibrium price: $ SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 5) (This question tpe will be multiple choice on the final eam) 5) Duffin House is planning its annual Song Festival when it will serve three kinds of delicacies: granola treets, nutt granola treats, and nuttiest granola treats. The following table shows the ingredients required (in ounces) for a single serving of each delicac. as well as the total amount of each ingredient avaliable: Granola Nutt Granola Nuttiest Granola Total Available Toasted Oats 3,00 Raisins,000 Almonds 0,00 The Song Festival planners at Duffin House would like to use up ALL the ingredients. How man servings of each kind of delicac can the make? 5

16 ) (This question tpe will be multiple choice on the final eam) ) Jeremiah Calhoun's 3-gallon tropical fish tank contains three tpes of carnivorous creatures (bab sharks, piranhas, and squids) and he feeds them three tpes of food: goldfish, angelfish, and butterfl fish. Each bab shark can eat goldfish, angelfish, and butterfl fish; each piranha can eat goldfish and 3 butterfl fish per da; while each squid can eat goldfish and angelfish per da. Bill-Sean will feed goldfish, angelfish, and 35 butterflfish to satisf all the creatures. How man bab sharks, piranhas, and squids are in the tank?

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