Solution Manual for Finite Mathematics and Its Applications, 12th Edition

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SOLUTIONSMANUALSALVATORESCIANDRANiagara County Community CollegeFINITEMATHEMATICS&ITSAPPLICATIONSTWELFTHEDITIONLarry J. GoldsteinGoldstein Educational TechnologiesDavid I. SchneiderUniversity of MarylandMartha J. SiegelTowson UniversitySteven M. HairPennsylvania State University

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ContentsChapter 1: Linear Equations and Straight Lines1–1Chapter 2: Matrices2–1Chapter 3: Linear Programming, A Geometric Approach3–1Chapter 4: The Simplex Method4–1Chapter 5: Sets and Counting5–1Chapter 6: Probability6–1Chapter 7: Probability and Statistics7–1Chapter 8: Markov Processes8–1Chapter 9: The Theory of Games9–1Chapter 10:The Mathematics of Finance10–1Chapter 11:Logic11–1Chapter 12:Difference Equations and Mathematical Models12–1

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1-1Chapter 1Exercises 1.11.Right 2, up 3xy(2, 3)2.Left 1, up 4xy(–1, 4)3.Down 2xy(0, –2)4.Right 2xy(2, 0)5.Left 2, up 1xy(–2, 1)6.Left 1, down52xy–1, –()527.Left 20, up 40xy(–20, 40)8.Right 25, up 30xy(25, 30)9.PointQis 2 units to the left and 2 units up or(2, 2).-10.PointPis 3 units to the right and 2 units down or(3,2).-11.12(1)(3)2113-+= -+= -so yes the point ison the line.12.12(2)(6)13-+= -is false, so no the point is noton the line

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Chapter 1:Linear Equations and Straight LinesISM:Finite Math1-213.1213xy-+= -Substitute the x and ycoordinates of the point into the equation:( )111,3231111223æöæö÷÷çç -+= - - += -÷÷çç÷÷ççèøèøisa false statement. So no the point is not on theline.14.112(1)133æ öæ ö÷÷çç-+-= -÷÷çç÷÷ççè øè øis true so yes the point ison the line.15.m= 5,b= 816.m = –2 and b = –617.y= 0x+ 3;m= 0,b= 318.220;,033yxmb=+==19.147217142123xyyxyx+== -+= -+20.333xyyxyx-=-= -+=-21.3553xx==22.12–10232110323154xyyxyx+==+=+23.048482xxx= -+==x-intercept: (2, 0)y= –4(0) + 8y= 8y-intercept: (0, 8)24.0 = 5no solutionx-intercept: noneWhenx= 0,y= 5y-intercept: (0, 5)25.Wheny= 0,x= 7x-intercept: (7, 0)0 = 7no solutiony-intercept: none26.0 = –8xx= 0x-intercept: (0, 0)y= –8(0)y= 0y-intercept: (0, 0)27.10– 13x=x= 3x-intercept: (3, 0)1 (0) – 13y=y= –1y-intercept: (0, –1)xy(3, 0)(0, –1)28.Whenx= 0,y= 0.Whenx= 1,y= 2.xy(1, 2)(0, 0)

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ISM:Finite MathChapter 1:Linear Equations and Straight Lines1-329.502=no solutionx-intercept: noneWhenx= 0,52y=y-intercept:50, 2æö÷ç÷ç÷çèøxy520,()30.The line coincides with they-axis.xyx= 031.34(0)248xx+==x-intercept: (8, 0)3(0)4246yy+==y-intercept: (0, 6)xy(8, 0)(0, 6)32.033xx+==x-intercept: (3, 0)033yy+==y-intercept: (0, 3)xy(0, 3)(3, 0)33.52x= -34.11 (0)1232xx-= -= -x intercept (–2, 0)11(0)1233yy-= -=yintercept (0, 3)

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Chapter 1:Linear Equations and Straight LinesISM:Finite Math1-435.236326223xyyxyx+== -+= -+a.46126412223xyyxyx+== -+= -+Yesb.Yesc.332332223xyyxyx=-= -+= -+2–23yx=+Yesd.6206226xyyxx--==-= -+Noe.222 ––233yxx==+Yesf.11xyyx+== -+No36.1– 5121–5–1211–105xyyxyx==+=a.12–151215105xyyxyx=-= -+=-Nob.52521255xyyxyx=+=-=-Noc.2510010521125xyyxyx-+=-= -+=-Nod..1(2).1.211105yxyxyx=-=-=-Yese.10210211105yxyxyx-= -=-=-Yesf.1.5255.5111105xyyxyx+=+=-=-Yes

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ISM:Finite MathChapter 1:Linear Equations and Straight Lines1-537.a.33xyyx+== - +m= –1,b= 33Lb.222222xyyxyx-= --= --=+m= 2,b= 21Lc.3333113xyyxyx=+=-=-1 ,3m=b= –12L38.a.No; 5 + 4≠3b.No; 2≠1 – 1c.Yes; 2(2) = 1 + 3 and 2(4) = 5 + 339.3072yx=+a.When x = 0, y = 72. This is the temperatureof the water at time = 0 before the kettle isturned on.b.30(3)72162yyF=+=oc.Water boils when y = 212 so we have2123072.x=+Solving for x gives234xminutes or 4 minutes 40 seconds.40.a.A person born in 1960 has a life expectancyof 70 years.b.175706156xxæö÷ç=+÷ç÷çèøæö÷ç=÷ç÷çèøx= 301960 + 30 = 1990c.1999196039-=1 (39)7066.57076.5yyyæö÷ç=+÷ç÷çèø=+=A person born in 1999 has a life expectancyof 76.5 years.41.a.x-intercept:1–33, 03æö÷ç÷ç÷çèøy-intercept: (0, 2.5)xy(0, 2.5)–33, 0()13b.In 1960, 2.5 trillion cigarettes were sold.c.4 = .075x+ 2.5x= 201960 + 20 = 1980d.2024 – 1960 = 64y= .075(64) + 2.5y= 7.37.3 trillion42.a.x-intercept: (–12.17, 0)y-intercept: (0, 14)b.In 2000 the income from ecotourism was$14,000.c.20 = 1.15x+ 14x≈5.222000 + 5.22 = 2005.22The year 2005 should have had $20,000 inecotourism income.

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Chapter 1:Linear Equations and Straight LinesISM:Finite Math1-6d.2022 – 2000 = 22y= 1.15(22) + 14y= 39.3$39,30043.a.x-intercept: (–32.9, 0)y-intercept: (0, 756)b.In 1999 the car insurance rate for a small carwas $756.c.2007 – 1999 = 8y= 23(8) + 756y= 940$940d.13082375655223241999242023xxx=+==+=The yearly rate will be $1308 in 2023.44. a.x-intercept:100 , 03æö÷ç-÷ç÷çèøy-intercept: (0, 1000)b.30(2)10006010001060yyy=+=+=$1060 will be in the account after 2 years.c.1180301000180306xxx=+==The balance will be $1180 after 6 years.45.a.In 2000, 4.1% of entering college freshmenintended to major in biology.b.2014200014-=0.2(14)4.16.9yy=+=6.9% of college freshmen in 2014 intendedto major in biology.c.5.50.24.11.40.27200072007xxx=+==+=In 2007, the percent of college freshmenwho intended to major in biology was 5.5.46.a.In 2004, 6.32% of college freshmen smoked.b.2014200410-=0.46(10)6.321.72yy= -+=1.72% of college freshmen smoked in 2014.c.2.60.466.323.720.468200482012xxx= -+-= -»+=In 2012, the percent of college freshmenwho smoked was 2.6.47. a.201120047-=461(7)1680020, 027yy=+=$20,027 was the approximate average tuitionin 2011.b.2500046116800820046117.82004172021xxx=+=»+=In 2021, the approximate average cost oftuition will be more than $25,000.

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ISM:Finite MathChapter 1:Linear Equations and Straight Lines1-748. a.200720034-=667(4)1240315071yy=+=Approximately 15,071 bachelor degrees inmathematics and statistics were awarded in2007.b.25000667124031259766718.892003182021xxx=+=»+=In 2021, there will be more than 25,000bachelor degrees in mathematics andstatistics awarded.49.8(0)8ymxbmbb=+=+=0(16)812mm=+= -182yx= -+50.0.9(0)0.9ymxbmbb=+=+=0(0.6)0.91.5mm=+= -1.50.9yx= -+51.y=mx+b5 =m(0) +bb= 50 =m(4) + 55– 4m=5–54yx=+52.Since the equation is parallel to theyaxis, it willbe in the formx= a. Therefore the equation willbe x = 5.53.On thex-axis,y= 0.54.No, because two straight lines (the graphed lineand thex-axis) cannot intersect more than once.55.The equation of a line parallel to theyaxis willbe in the formx= a.56.y = b is an equation of a line parallel to the x-axis.57.23xy-= -58.34xy-+= -59.2532315xyxy+= -+= -60.5462465xyxy-=-=61.Since (a,0) and (0,b) are points on the line theslope of the line is (b-0)/(0-a) = -b/a. Since the yintercept is (0,b), the equation of the line is(/)yba xb= -+or.aybxab= -+In generalform, the equation is bx + ay = ab.62.If (5, 0) and (0, 6) are on the line, then a = 5 andb = 6. Substituting these values into the equationbx + ay = ab gives 6x + 5y = 30.63.One possible equation is9.yx=-64.One possible equation is10.yx=+65.One possible equation is7.yx=+66.One possible equation is6.yx=-67.One possible equation is2.yx=+68.One possible equation is.yx=69.One possible equation is9.yx=+70.One possible equation is5.yx=-

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Chapter 1:Linear Equations and Straight LinesISM:Finite Math1-871.Thex– intercept has aycoordinate of 0,therefore thexcoordinate of the first equation is:20232233xxx=-==Using thisxcoordinate in the second equationwill find the value ofc.04(3)01212ccc= -+= -+=72.They– intercept has axcoordinate of 0,therefore theycoordinate of the first equation is:6(0)39393yyy-=-== -Using thisycoordinate in the second equationwill find the value ofb.34(0)3bb-=+-=73.a.y = –3x + 6b.The intercepts are at the points (2, 0) and(0, 6)c.Whenx= 2,y= 074.a.y = .25x – 2b.(0, –2) and ( 8,0) are interceptsc.When x = 2, y = –1.5.75.a.329329233yxyxyx-==+=+b.The intercepts are at the points (–4.5, 0) and(0, 3).c.Whenx= 2,y= 4.33 or 13 / 3.76.a.2y + 5x = 8. So y = –2.5x + 4.b.The intercepts are (0, 4) and (1.6, 0).c.When x = 2 then y = –1.

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ISM:Finite MathChapter 1:Linear Equations and Straight Lines1-977.2y + x = 100. When y = 0, x = 100, and when x= 0, y = 50. An appropriate window might be[-10, 110] and [-10,60]. Other answers arepossible.78.x – 3y = 60. When x = 0, then y = - 20 and wheny = 0 x = 60. An appropriate window might be[-40, 100] and [-40 , 20] but other answers areequally correct.Exercises 1.21.23m=2.y= 0x– 4m= 03.y– 3 = 5(x+ 4)y= 5x+ 23m= 54.75107–25xyyx+==+7– 5m=5.65442454–245xyxyyx+=+==+4– 5m=6.178887887xyxyyx-=-==-87m=7.9 – 457 – 34m==8.3 –13 – (–2)m-=4– 5=9.4 – 045 – 05m==

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Chapter 1:Linear Equations and Straight LinesISM:Finite Math1-1010.17 –170–2 – 4m==11.The slope of a vertical line is undefined.12.The slope of a vertical line is undefined.13.14.15.16.17.–2–21m==y– 3 = –2(x– 2)y= –2x+ 718.12112m==1–1(– 3)21122yxyx==-19.0 – 2–22 –1m==y– 0 = –2(x– 2)y= –2x+ 420.122 –31 – (–1)4m==3– 2(– 1)43544yxyx==+21.11– –44m==1– 2(– 2)41342yxyx==+22.13m=1– 3(– 5)31433yxyx==+23.m= –1y– 0 = –1(x– 0)y= –x24.121–2–m==y– (–1) = 2(x– 2)y= 2x– 525.11221 – 01m- --=== -y– (1) = –2(x– 0)y= –2x+ 1

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ISM:Finite MathChapter 1:Linear Equations and Straight Lines1-1126.21330 – 11m---===-y– (1) = 3(x– 1)y= 3x– 227.02214 – 042m--===--1– 0(4)2122yxyx=+=+28.01113 – 033m--=== -1– 0(3)3113yxyx= --= -+29.m= 0y– 3 = 0(x– 2)y= 330.m= undefined, therefore the equation is of theformx=a.x= 231.3– 6(– 5)5335yxyx==+y-intercept: (0, 3)32.6334 – (1)5m-==-3– 6(– 4)531265531855yxyxyx=-=-=+y-intercept:185(0,)33.m= undefined, therefore the equation is of theformx=a.x= 034.4 – 400 – 1m==–40(0)4yxy=-=35.Lety= cost in dollars.y= 4x+ 200036.a.p-intercept: (0, 1200); at $1200 no one willbuy the item.b.0 = –3q+ 1200q= 400 unitsq-intercept: (400, 0); even if the item isgiven away, only 400 will be taken.c.–3; to sell an additional item, the price mustbe reduced by $3.d.p= –3(350) + 1200 = $150e.30031200300 itemsqq= -+=f.37.a.Letx= altitude andy= boiling point.212 – 202.80.001840 – 5000m== -2120.00184(0)0.00184212yxyx-= --= -+b.0.001842120.00184(29029)212158.6 Fyxyy» -+» -+»38.a.172 – 124480 – 68m==1244(68)4148cFcF-=-=-

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Chapter 1:Linear Equations and Straight LinesISM:Finite Math1-12b.137,4Fc=+so add 37 to the number ofchirps counted in 15 seconds1 of a minute .4æö÷ç÷ç÷çèø39.a.Letx= quantity andy= cost.9500 – 68009050 – 20m==680090(20)905000yxyx-=-=+b.$5000c.$90d.40.a.y= 40(100) + 2400 = $6400b.3600 = 40x+ 2400x= 30 coatsc.y= 40(0) + 2400 = $2400(0, 2400); even if no coats are made there isa cost for having the ability to make them.d.40; each additional coat costs $40 to make.41.a.100(300) = $30,000b.600010060 coatsxx==c.y= 100(0) = 0(0, 0); if no coats are sold, there is norevenue.d.100; each additional coat yields anadditional $100 in revenue.42.a.Profit = revenue – costy= 100x– (40x+ 2400)y= 60x– 2400b.(0, –2400); if no coats are sold, $2400 willbe lost.c.0 = 60x– 2400x= 40(40, 0); the break-even point is 40 coats.Less than 40 coats sold yields a loss, morethan 40 yields a profit.d.60; each additional coat sold yields anadditional $60 profit.e.y= 60(80) – 2400 = $2400f.6000 = 60x– 2400x= 140 coatsg.43.a.b.On February 1, 31 days have elapsed sinceJanuary 1. The amount of oil y = 30,000 –400(31) = 17,600 gallons.c.On February 15, 45 days have elapsed sinceJanuary 1. Therefore, the amount of oilwould be y = 30,000- 400(45) = 12,000gallons.d.The significance of the y-intercept is thatamount of oil present initially on January 1.This amount is 30,000 gallons.e.The t-intercept is (75,0) and corresponds tothe number of days at which the oil will bedepleted.

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ISM:Finite MathChapter 1:Linear Equations and Straight Lines1-1344.a.b.y= 2.3 – 0.15(15) = $0.05 million$50,000c.(0, 2.3); $2.3 million is the amount of cashreserves on July 1.d.0 = 2.3 – 0.15t115 3t=115, 0 ;3æö÷ç÷ç÷çèøthe cash reserves will be depletedafter115 3days.e.y= 2.3 – 0.15(3) = $1.85 millionf.0.8 = 2.3 – 0.15tt= 10After 10 days, on July 1145.a.0.10220yx=+b.0.10(2000)220420yy=+=c.5400.10220$3200xx=+=46.Each unit sold yields a commission of $5. Inaddition, she receives $60 per week base pay.47.1–,2m=b= 01– 2yx=48.m= 3,b= –1y= 3x– 149.1– 3m=1– (–2)–(– 6)313yxyx== -50.m= 1y– 2 = 1(x– 1)y=x+ 151.12m=1– (–3)(– 2)2142yxyx==-52.m= –7y– 0 = –7(x– 5)y= –7x+ 3553.2– 5m=2– 5–(– 0)5255yxyx== -+54.m= 0y– 4 = 0(x– 7)y= 455.3 – (–3)–1–1 – 5m==y– 3 = –1[x– (–1)]y= –x+ 256.2 – 114 – 22m==11(– 2)212yxyx-==57.–1 – (–1)03 – 2m==y– (–1) = 0(x– 2)y= –1

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