MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 2) A) Not defined B) - 2 5

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1 Stud Guide for TEST I 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. ) (7, ) and (7,-) 0 Not defined ) ) (-, ) and (-9, ) ) Not defined Find the slope of the line. ) = 0 Not defined ) ) A line perpendicular to - = 9 ) - - ) A line parallel to = + - ) Find an equation in slope-intercept form (where possible) for the line. ) Through (, 0), m = - = - = - + = = - ) 7) Through (, ), m = - 7) = - + = - = + = - + ) Through (, -) and (7, ) = - = - 7 = - + = - ) 9) Through (-, ) and (0, -) = 9 - = - - = = - 9) ) Through (, 7), perpendicular to - - = - = + = + = = - - )

2 ) Through (-, -7), parallel to = -7 = = = = ) Find the slope of the line. ) ) ) ) undefined Solve the problem. ) In a certain cit, the cost of a tai ride is computed as follows: There is a fied charge of $.90 as soon as ou get in the tai, to which a charge of $.0 per mile is added. Find a linear equation that can be used to determine the cost, C, of an -mile tai ride. C =.0 C = C =.0 C = ) ) After two ears on the job, an engineer's salar was $0,000. After seven ears on the job, her salar was $7,00. Let represent her salar after ears on the job. Assuming that the change in her salar over time can be approimated b a straight line, give an equation for this line in the form = m + b. =,00 +,000 = ,000 = 00 +,000 =,00 + 0,000 )

3 ) The change in a certain engineer's salar over time can be approimated b the linear equation = ,00 where represents salar in dollars and represents number of ears on the job. According to this equation, after how man ears on the job was the engineer's salar $,000? ears ears ears ears ) 7) The relationship between the list price,, in thousands of dollars, and the dealer invoice price,, also in thousands of dollars, for pickup trucks can be approimated b the linear equation = Use this equation to predict the dealer invoice price for a pickup truck with a list price of. thousand dollars.. thousand dollars.7 thousand dollars.09 thousand dollars.9 thousand dollars 7) Evaluate the function as indicated. ) Find f(-) when f() = ) 9) Find f(-r) when f() = -. - r + r + r r - 9) Write a cost function for the problem. Assume that the relationship is linear. 0) A moving firm charges a flat fee of $ plus $0 per hour. Let C() be the cost in dollars of using the moving firm for hours. C() = - 0 C() = + 0 C() = 0 - C() = 0 + 0) ) A cab compan charges a base rate of $.00 plus cents per minute. Let C() be the cost in dollars of using the cab for minutes. C() = C() = C() = C() = ) Solve the problem. ) Let the suppl and demand functions for a certain model of electric pencil sharpener be given b ) p = S(q) = q andp = D(q) = - q, where p is the price in dollars and q is the quantit of pencil sharpeners (in hundreds). Graph these functions on the same aes (graph the suppl function as a dashed line and the demand function as a solid line). Also, find the equilibrium quantit and the equilibrium price. 0 p 0 q

4 0 p 0 p 0 q Equilibrium quantit: 90 Equilibrium price: $7 0 p 0 q Equilibrium quantit: 90 Equilibrium price: $.0 0 q Equilibrium quantit: 0 Equilibrium price: $9.0 0 p 0 q Equilibrium quantit: 00 Equilibrium price: $ ) Let the demand and suppl functions be represented b D(p) and S(p), where p is the price in dollars. Find the equilibrium price and equilibrium quantit for the given functions. D(p) = 00-0p S(p) = 0p $0; 70 $0; 00 $; 0 $; 70 ) ) A book publisher found that the cost to produce 00 calculus tetbooks is $,00, while the cost to produce 000 calculus tetbooks is $,000. Assume that the cost C() is a linear function of, the number of tetbooks produced. What is the marginal cost of a calculus tetbook? $0.0 $,00.00 $. $.0 ) ) A shoe compan will make a new tpe of shoe. The fied cost for the production will be $,000. The variable cost will be $0 per pair of shoes. The shoes will sell for $0 for each pair. What is the profit if 00 pairs are sold? $,000 $,000 $,000 $,000 )

5 ) Regrind, Inc. regrinds used tpewriter platens. The cost per platen is $.0. The cost to regrind platens is $00. Find the linear cost function to regrind platens. If reground platens sell for $.0 each, how man must be reground and sold to break even? C() =.0 + C() = break-even = break-even = 0 C() =.0 + break-even = 7 C() = break-even = 7) For the following table of data, a. Draw a scatterplot. b. Calculate the correlation coefficient. c. Calculate the least squares line and graph it on the scatterplot. d. Predict the -value when is 7. ) 7) a. a. b c. Y = b. 0.9 c. Y = d. -. d. -.

6 a. a. b c. Y = b. 0.9 c. Y = d. -. d.. ) For the following table of data, a. Draw a scatterplot. b. Calculate the correlation coefficient. c. Calculate the least squares line and graph it on the scatterplot. d. Predict the -value when is 7. )

7 a. a. 0 0 b c. Y =.7 0 d..9 a. 0 b c. Y = d.. b c. Y = d.. a. 0 b c. Y = +. 0 d. 0. 7

8 Find the correlation coefficient. 9) Consider the data points with the following coordinates: ) 0) The test scores of randoml picked students and the number of hours the prepared are as follows: Hours 9 Score ) Find the equation of the least squares line. ) The paired data below consist of the test scores of randoml selected students and the number of hours the studied for the test. ) Hours () 9 Score () =.7 -. = =.7 +. = Use the echelon method to solve the sstem of two equations in two unknowns. ) - = - - = (, 0) (0, -) (, -7) No solution ) ) - = = 7 + 9, (, 0), - No solution ) Use the echelon method to solve the sstem. ) - = 0 ) 7 + =,,,, ) 7 + = - = (, -) (-, ) (-, -) (, ) )

9 Solve the problem. ) Best Rentals charges a dail fee plus a mileage fee for renting its cars. Barne was charged $ for das and 00 miles, while Mar was charged $ for das and 00 miles. What does Best Rental charge per da and per mile? $ per da, per mile $ per da, per mile $7 per da, per mile $ per da, per mile 7) Alan invests a total of $,000 in three different was. He invests one part in a mutual fund which in the first ear has a return of %. He invests the second part in a government bond at 7% per ear. The third part he puts in the bank at % per ear. He invests twice as much in the mutual fund as in the bank. The first ear Alan's investments bring a total return of $00. How much did he invest in each wa? $000 in mutual fund, $7000 in bond, and $000 in bank $00 in mutual fund, $7900 in bond, and $700 in bank $00 in mutual fund, $0 in bond, and $00 in bank $000 in mutual fund, $000 in bond, and $000 in bank ) 7) Write the augmented matri for the sstem. Do not solve. ) z = z = z = ) 9) - + z = + z = z = ) Use the indicated row operation to change the matri. 0) Replace R b R + (-)R ) ) Replace R b R + R ) Use the Gauss-Jordan method to solve the sstem of equations. ) + + z = z = z = -7 (-,, -) (-,, -) (-, -, ) No solution ) 9

10 ) z = z = z = (-,, ) (,, ) (,, ) No solution ) Solve the problem. ) Barges from ports X and Y went to cities A and B. X sent 0 barges and Y sent. Cit A received barges and B received 7. Shipping costs $0 from X to A, $00 from X to B, $00 from Y to A, and $0 from Y to B. $70 was spent. How man barges went where? from X to A, 9 from X to B, 0 from Y to A, and from Y to B 9 from X to A, from X to B, from Y to A, and from Y to B 7 from X to A, 7 from X to B, from Y to A, and from Y to B from X to A, from X to B, from Y to A, and from Y to B ) ) Factories A and B sent rice to stores and. A sent loads and B sent. Store received loads and store received. It cost $00 to ship from A to, $0 from A to, $00 from B to, and $0 from B to. $90 was spent. How man loads went where? 0 from A to, from A to, from B to, and 7 from B to from A to, 0 from A to, 7 from B to, and from B to from A to, from A to, 9 from B to, and from B to from A to, from A to, from B to, and from B to ) Perform the indicated operation, where possible. ) Not possible ) 7) Not possible 7) Write a matri to displa the information. ) Barges from ports X and Y went to cities A and B. Shipping costs $0 from X to A, $00 from X to B, $00 from Y to A, and $0 from Y to B. Make a matri showing the shipping costs. Assign the ports to the rows and the cities to the columns ) A compan makes tpes of cable. Cable A requires black wires, white wires, and red wires. Cable B requires black, white, and red. Cable C requires black, white, and red. Make a matri showing the wire requirements. Assign the cable tpes to the rows and the wire tpes to the columns. ) 9)

11 Find the matri product, if possible. 0) Does not eist 0) Solve the problem. ) 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 X and Y. Multipl the matrices. ) A = sugar choc milk cherr almond raisin B = X Y X Y 7 X Y 0 0 sugar choc milk cherr almond raisin cherr almond raisin X Y 0 0 X Y 7 sugar choc milk cherr almond raisin ) 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 R and S. What is the cost of 0 batches of each cand using ingredients from supplier S? ) A = sugar 7 choc milk cherr almond raisin R S B = 7 sugar choc milk $,00 $,000 $00 $,00

12 Find the inverse, if it eists, for the matri. ) ) ) ) Find the production matri for the input-output and demand matrices using the open model ) A = , D = ) Find the matri product, if possible. ) Does not eist ) Solve the problem. 7) Suppose the following matri represents the input-output matri of a primitive econom that depends on two basic goods, ams and pigs. How much of each commodit should be produced to get bushels of ams and pigs? (It is not necessar to round to a whole-number quantit of pigs.) 7) ams pigs ams / / pigs / 0. bushels of ams and. pigs. bushels of ams and. pigs.7 bushels of ams and. pigs. bushels of ams and 0. pigs

13 ) Suppose the following matri represents the input-output matri of a simplified econom that involves just three commodit categories: manufacturing, agriculture, and transportation. How man units of each commodit should be produced to satisf a demand of 700 units for each commodit? ) Mfg Agri Trans Mfg 0 / / Agri / 0 / Trans / / 0 90 units of manufacturing, units of agriculture, and 77 units of transportation 77 units of manufacturing, 90 units of agriculture, and units of transportation 7 units of manufacturing, 97 units of agriculture, and units of transportation 77 units of manufacturing, units of agriculture, and 7 units of transportation

14 Graph the linear inequalit. 9) + - 9)

15 0) - 0) Graph the feasible region for the sstem of inequalities.

16 ) + - )

17 ) + - ) Find the equation of the least squares line. ) The paired data below consist of the temperatures on randoml chosen das and the amount a certain kind of plant grew (in millimeters). ) Temp () Growth () = = = =

18 Answer Ke Testname: TESTI ) D ) C ) D ) D ) B ) B 7) A ) B 9) C ) A ) D ) C ) C ) D ) C ) B 7) D ) B 9) C 0) D ) C ) D ) D ) D ) D ) A 7) A ) C 9) B 0) A ) D ) B ) D ) B ) A ) B 7) A ) C 9) B 0) C ) A ) A ) B ) A ) B ) D 7) C ) B 9) D 0) D

19 Answer Ke Testname: TESTI ) C ) D ) D ) C ) D ) C 7) D ) C 9) A 0) A ) B ) D ) B 9