5) In a local election, 48,900 people voted. This was an increase of 6% over the last election. How many people voted in the last election?


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1 Final Eam Review ( ) Math ) Evaluate the epression 6  (a  b) 2, when a = 13 and b = 3 2) Simplif using the distributive law and combining like terms. 3(2t  )  (t  ) + t 3) Solve: (27) = ) Translate the situation into mathematical language. You need not actuall solve the problem. A piece of wire 13 m long is to be cut into two pieces, one of them 2 3 as long as the other. How should the wire be cut? ) In a local election, 8,900 people voted. This was an increase of 6% over the last election. How man people voted in the last election? 6) One angle of a triangle is times as great as a second angle. The third angle measures less than twice the second angle. Find the measures of the angles. 7) Solve V = 1 Bh, for B 3 8) Solve F = 9 C + 32, for C 9) Simplif. 1 + (9)   (19) + (8) 10) Simplif using onl positive eponents. ( )( 3 ) 11) Simplif using onl positive eponents. 2a 2 b 3 6a 6 b 12) From the graph below, find f(3)
2 13) Given the graph of the function, where is f() = ) Find the domain ) Find f(3) when f() = ) Find the domain of the function, f() = + 17) Graph f() = ) Using the graph below, find the rate of change in the value of the car with respect to time. 30 Value of Car in Thousands of Dollars Number of Years of Use 2
3 19) The value, in dollars, of a cop machine is given b the function f() = , where is the number of ears that have passed since the machine was purchased. Interpret the slope of the graph of f as a rate of change. 20) Find the slope of the line 2  = 21 21) Graph = 3 22) Graph = 2 23) Find the  and intercepts for the equation. Then graph the equation = 2 2) Find the equation of the line through 0, 3 7 and perpendicular to = 3 2) Find an equation of the line having the specified slope and containing the indicated point. Write our answer as function, f() m = ; (8, 0) 26) In 198, John invested $8,000 in the stock market. B 1990 his investment had grown to $9,00. If the market continued to grow at the same rate, how much was in his account in 1992? Give our answer to the nearest dollar. 27) Let f() = and g() = Find (fg)(3) 28) f() = 29, g() = 7 . Find (f  g)(). 29) f() = 89, g() = Find (f + g)(). 30) Given f() = 7 + 3, g() = + 7, Find (f g)(). 31) Find P(2) when P() = ) Simplif: ( )  ( )  ( ) 33) Total profit is defined as total revenue minus total cost. R() and C() are the revenue and cost from the sale of televisions. If R() = and C() = , find the profit from the sale of 80 televisions. Hint: P() = R()  C() 3) Multipl: (  )(  3) 3) Simplif: (8m + )2 3
4 36) Let f() = 72 and g() = Find (f g)() 37) Factor: ) Factor: ) Solve for : 92  = 0 0) Solve for : = 0 1) Solve for : 822 = 0 2) Let g() = 2 +. For what value(s) of is g() = 21. 3) The length of a rectangular frame is 8 cm more than the width. The area inside the frame is 10 square cm. Find the width of the frame. ) A rock falls from a tower that is 00 feet high. As it is falling, its height is given b the formula h = 0016t2. How man seconds will it take for the rock to hit the ground (h =0)? Round to the nearest tenth of a second. ) Simplif. Assume that variables can represent an value.: ) For f() = 3 21, find f(13). 7) Find the domain of the radical function, f() =  6 8) Rewrite with positive eponents: 7 9) Simplif: 3/ 1/ 0) Simplif: ) Simplif: 2) Multipl and Simplif: 1 8 3) Rational the denominator: 3
5 ) Solve: 2 = 3 ) Let f() = ( + 10)2. Find so that f() = 26. 6) Let f() = Find so that f() = 9. 7) Find the intercepts: f() = ) Let f() = For what values of is f() = 0. Round to the nearest thousandth. 9) Write the equation for the function having a graph that meets all of the specified conditions. Has the same general shape as the graph of g() = 2 and has a maimum value at (2, 6). 60) Find the verte: f() = ) Find the line of smmetr: f() = ) Find the  and intercepts. If no intercepts eist, state so. f() = ) A projectile is thrown upward so that its distance, in feet, above the ground after t seconds is H(t) = 1t2 + 20t. What is its maimum height? 6) Bob owns a watch repair shop. He has found that the cost of operating his shop is given b C() = , where C is the cost in dollars, and is the number of watches repaired. How man watches must he repair to have the lowest cost? 6) Given f() = and g() = 31, find (f g)(). 66) Given f() = 23 and g() =  10, find (f g)(). 67) Find (f g)() if f() = 81 and g() = ) Determine whether the function is onetoone. If so, find a formula for the inverse. g() = ) Determine whether the function is onetoone. If so, find a formula for the inverse. h() = 38
6 70) Graph = 2 71) Graph = 1 72) Simplif: log ) Simplif: 10log 7) Epress as a sum, difference, and product of logarithms, without using eponents. log b m p9 nb8 7) Epress as a single logarithm. 7 log m  6 log n 76) Approimate to the nearest tenthousandths: log ) Graph: f() = ln() 78) Graph: f() = e 79) Solve: (  3) = 28 80) Solve: 17 = e 2 81) Solve: log 2 = ) Solve: log (  9) = 3 83) Suppose that $000 is invested at an interest rate of.7% per ear, compounded continuousl. What is the balance after 7 ears? 8) How long will it take for the population of a certain countr to double if its annual growth rate is. %? (Round to the nearest ear.) 8) Write a sstem of equations that ields the solution. DO NOT SOLVE. Two angles are supplementar. One angle is 9 more than three times the other angle. Find the measures of the angles. (Let and represent the angles.) 6
7 86) Solve. 3 + = = 8 87) Solve = = 8 88) Solve.  =  = 89) Solve. + 2 = = ) Ron and Kath are ticket sellers for their class pla. Ron sells student tickets for $2.00 each, and Kath sells adult tickets for $.0 each. If their total revenue for 36 tickets is $117.0, then how man tickets did Ron sell? 91) Walt made an etra $9000 last ear from a parttime job. He invested part of the mone at 10% and the rest at 9%. He made a total of $870 in interest. How much was invested at 9%? 92) A childʹs bank contains $1.92 in pennies and nickels. If the number of pennies is 6 less than 2 times the number of nickels, then how man pennies are in the bank? 93) Solve the sstem. + + z = z = z = 1 9) Solve the sstem z = z = z = 27 9) The sum of a studentʹs three scores is 219. The first is 12 more than the second, and the sum of the first two is 2 more than twice the third. Find the studentʹs first score. 7
8 96) Find the totalprofit function for the totalcost and totalrevenue functions. C() = ,000 R() = 8 97) Find the equilibrium point for the pair of demand and suppl functions. D(p) = p S(p) = p 98) The MetroCit paint compan is planning to produce a new line of paint. The paint will be produced b the gallon. For the first ear, the fied costs for setting up production are $200. The variable costs for producing each gallon are $10. The revenue for each gallon is $0. Find the number of gallons of paint that are sold at the breakeven point. 99) Solve and graph the inequalit. Write the solution set using interval notation ) Solve and write our answer in interval notation. + 7(33) 9101) Given the function f() = 7 , find all values of where f() > ) Find the domain of the function f() = 8103) A salesperson has two job offers. Compan A offers a weekl salar of $00 plus commission of 10% of sales. Compan B offers a weekl salar of $800 plus commission of % of sales. What is the amount of sales above which Compan Aʹs offer is the better of the two? 10) Solve the inequalit and graph the solution set. 96 < 3 or ) Solve the inequalit and graph the solution set. 7 3t ) Solve the inequalit and graph the solution set and 98 < 10 8
9 107) Graph ) Graph the sstem of linear inequalities < 0 109) Graph the sstem of inequalities. Find the coordinates of the vertices. 39, , 0 110) Find the maimum and minimum values of the objective function. F =  7, subject to ) Joe has to take a test which consists of shortanswer questions worth 6 points each and essa questions worth 20 points each. He must do at least 3 shortanswer questions, but wonʹt have time to do more than 16. He has to answer at least 9 essa questions but canʹt spend time to do more than 16. If no more than 26 questions can be done, what is his maimum score? 112) Write a negation for the statement. Everone is asleep. 113) Let p represents the statement ʺItʹs Monda.ʺ and q represents the statement ʺItʹs raining toda.ʺ Translate the following compound statement into words: ~p ~q 11) Let p represents the statement : ʺ < 2ʺ and q represents the statement: ʺ > 1ʺ Translate the following compound statement into words: p ~q 11) Let p represent the statement, ʺJim plas footballʺ, and let q represent the statement ʺMichael plas basketballʺ. Convert the compound statement into smbols. Jim does not pla football or Michael plas basketball. 9
10 116) Construct a truth table for the statement. ~p ~q A) p q (~p ~q) B) p q (~p ~q) T T F T F F F T F F F F T T F T F T F T T F F T C) p q (~p ~q) T T T T F F F T F F F T D) p q (~p ~q) T T F T F F F T F F F T 117) Construct a truth table for the statement. (s q) (~s ~q) 118) Use De Morganʹs laws to write the negation of the statement. It is Saturda and it is not raining. 119) Let p = ʺI eat too much.ʺ and q = ʺIʹll eercise.ʺ Write the compound statement in smbols. If I eercise, then I wonʹt eat too much. 120) Construct a truth table for the statement.: ~p ~q 121) Construct a truth table for the statement.: ~p (~p q) 122) Write the inverse of the statement: q ~p 123) Write the converse of the statement: If I were oung, I would be happ. 12) Write the contrapostive of the statement: If ou like me, then I like ou. 10
11 Answer Ke Testname: FINAL EXAM REVIEW (MATH 11000, ) 1) 9 2) 22t + 3 3) 1 ) Let be the length of the longer piece of wire; = 13 or = 13 ) 6,132 people 6) 10, 28, 12 7) B = 3V h 8) C = (F  32) 9 9) ) 11 11) a b 2 12) 2 13) = 1 and = 1 1) { 3 3 } 1) 3 16) { is a real number and } 17) ) $6 thousand per ear 19) The cop machine decreases in value b $10 each ear. 20) 2 11
12 Answer Ke Testname: FINAL EXAM REVIEW (MATH 11000, ) 21) ) ) (0, 2); (, 0) ) = ) f() = ) $0,100 27) ) ) ) ) 6 32) ) $
13 Answer Ke Testname: FINAL EXAM REVIEW (MATH 11000, ) 3) ) 6m2 + 80m ) ) 7(21)( + ) 38) (3  )2 39) 2 3, )  1, 6 1) 1, 0 2) {3, 7} 3) 7 cm ) sec ) + 6) 3 7) [6, ) 8) 1/7 9) 1/2 0) 3 2 1) 20 2) ) ) ± 7 ) , ) 2, 12 7) ( + 21, 0), (  21, 0) 8) 1.09, ) f() = (  2) ) (, 3) 61) = 26 ± 21 62), 0, (0, 3) 63) 290 ft 6) 31 watches 6) (f g)() = ) (f g)() = ) ) g 1 () = ) h1() =
14 Answer Ke Testname: FINAL EXAM REVIEW (MATH 11000, ) 70) 71) 72) 2 73) 7) log b m + 9log b p  log b n  8 7) log m7 n 6 76) ) 1
15 Answer Ke Testname: FINAL EXAM REVIEW (MATH 11000, ) 78) 79) ) ) 82) 73 83) $ ) 1 ears 8) + = 180, = ) (, 2) 87) (0, 2) 88) No solution 89) Infinitl man solutions 90) 18 tickets 91) $ ) 22 93) (, 2, 3) 9) (, 3, 6) 9) 83 96) P() = 026,000 97) ($7, 62) 98) 8 gallons 9 99) 8, ) (, 1] 101) (6, ) ) { 8} 103) $ )
16 Answer Ke Testname: FINAL EXAM REVIEW (MATH 11000, ) 10) 106) ) ) (0, ) 3 2 (0, 1) 1 (2, 0) ) (9, 0), (3, ), (, 0) 110) Maimum: 26; minimum: ) ) Not everone is asleep. 16
17 Answer Ke Testname: FINAL EXAM REVIEW (MATH 11000, ) 113) Itʹs not Monda and itʹs not raining toda. 11) is less than 2 or is not greater than 1. 11) ~p q 116) D 117) s q (s q) (~s ~q) T T T T F F F T F F F T 118) It is not Saturda or it is raining. 119) q ~p 120) p q (~p ~q) T T F T F F F T F F F T 121) p q ~p (~p q) T T T T F T F T T F F F 122) ~q p 123) If I were happ, I would be oung. 12) If I donʹt like ou, then ou donʹt like me. 17
2, g(x) = 4x ) x  12
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