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Solution Manual for Developmental Mathematics, 1st Edition

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Solution Manual for Developmental Mathematics, 1st Edition - Page 1 preview imageINSTRUCTOR’SSOLUTIONSMANUALDANIELS.MILLERNiagara CountyCommunityCollegeDEVELOPMENTALMATHFORCOLLEGESTUDENTSRobert BlitzerMiami Dade College
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Solution Manual for Developmental Mathematics, 1st Edition - Page 2 preview image
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Solution Manual for Developmental Mathematics, 1st Edition - Page 3 preview imageiiiTABLE OF CONTENTSforINSTRUCTORSOLUTIONSDEVELOPMENTALMATH FORCOLLEGESTUDENTSChapter1:Whole Numbers and Introduction to Algebra..................................1Chapter2:Integers and Introduction to Solving Equations.............................61Chapter3:Fractions.......................................................................................107Chapter4:Decimals.......................................................................................219Chapter5:Percents........................................................................................309Chapter6:Geometry......................................................................................357Chapter7:Statistics and Probability..............................................................407Chapter8:Linear Equations and Inequalities in One Variable.....................443Chapter9:Linear Equations in Two Variables.............................................521Chapter 10:Systems of Linear Equations.......................................................587Chapter11:Exponents and Polynomials.........................................................691Chapter12:FactoringPolynomials.................................................................775Chapter13:Rational Expressions....................................................................837Chapter14:Basics of Functions......................................................................971Chapter15:Inequalities and Problem Solving..............................................1011Chapter16:Radicals, Radical Functions, and Rational Exponents..............1077Chapter17:Quadratic Equations and Functions...........................................1165Chapter18:Exponential and Logarithmic Functions....................................1325Chapter19:Conic Sections and Systems of Nonlinear Equations................1407Chapter20:Sequences, Series, and the Binomial Theorem..........................1515Appendices:....................................................................................................1591
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Solution Manual for Developmental Mathematics, 1st Edition - Page 4 preview image
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Solution Manual for Developmental Mathematics, 1st Edition - Page 5 preview imageChapter1Whole Numbers andIntroduction to Algebra11.1 Check Points1.a.millions placeb.ones placec.hundredsplaced.millions place2.Work from left to right. Write the name of the three-digit number in eachperiod, followed by the nameof the period and a comma.Do not write the nameof the last period, “ones.”a.twenty-seven thousand, one hundred forty-threeb.five hundred twenty-one million, six hundredthirty thousand, fifty-seven3.a.Begin by noting how to write the number withineach period.53406fifty-three thousand, four hundred sixWrite the digits for the number in each period,followed bya comma.The standard form for the number is 53,406.
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Solution Manual for Developmental Mathematics, 1st Edition - Page 6 preview imageChapter1Whole Numbers and Introduction to Algebra2b.Begin by noting how to write the number within each period.204932016two hundred four million, nine hundred thirty-two thousand, sixteenWrite the digits for the number in each period, followed bya comma.The standard form for the number is 204,932,016.4.a.The place value chart shows that 704,663 contains 7 hundred-thousands, 0 ten-thousands, 4 thousands, 6 hundreds, 6tens, and 3 ones. Thus 704,663 is written in expanded form as follows:704,663700,0004000600603.=++++b.The place value chart shows that 49,063,400 contains 4 ten-millions, 9 millions, 0 hundred-thousands, 6 ten-thousands, 3 thousands, 4 hundreds, 0 tens, and 0 ones. Thus 49,063,400 is written in expanded form as follows:49, 063, 40040, 000,0009, 000, 00060, 0003000400.=++++5.a.145because 14 is to the right of 5 on the number line.b.016because 0 is to the left of 16 on the number line.6.a.The digit to the right of the thousands digit is 4, which is less than 5. Thisindicatesto leave the thousands digit thesame. Replace all digits to the right with zeros.57, 49857,000b.The digit to the right of the hundred-thousands digit is 5. Thisindicatestoadd one tothehundred-thousands digit.Replace all digits to the right with zeros.4,856,9024,900, 000c.The digit to the right of the thousands digit is6, which isgreaterthan 5. This implies toadd one tothe thousandsdigit. Replace all digits to the right with zeros.960210, 000d.The digit to the right of themillionsdigit is2, which is less than 5. This implies to leave themillionsdigit the same.Replace all digits to the right with zeros.684, 236, 042684,000,0007.a.The digit to the right of the billions digit is 0, which is less than 5. This implies to leave the billions digit the same.Replace all digits to the right with zeros.7, 058, 746,8577, 000, 000, 000b.The digit to the right of the ten-thousands digit is 6, which is greater than 5. This implies to add one to the ten-thousands digit. Replace all digits to the right with zeros.7, 058,746,8577,058, 750,0008.a.The cost of a coronary bypass in the United States is $67,583b.The country with the least amount in the CT scan column is India.The average cost for this procedure in India is $43.c.The charge for an appendectomy in Chile is $5509.Thecountries in which an appendectomy costs more than inChile are Canada, Switzerland, and United States.9.a.We begin with the number of marriages betweenan African-American husband and a white wife in 2010. Look atthe bars labeled with the year 2010. The yellow bar to the right represents the number of marriages between anAfrican-American husband and a white wife. The number above this bar is 390, representing 390 thousand. Thus, in2010, there were 390,000 marriagesbetweenan African-American husband and a white wife.b.Look for the red bar labeled 61 (for 61 thousand, or 61,000). This is the bar to the left for the year labeled 1990.Thus, in 1990, there were 61,000 marriages between a white husband and an African-American wife.
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Solution Manual for Developmental Mathematics, 1st Edition - Page 7 preview imageSection 1.1Basics of Whole Numbers31.1Concept and Vocabulary Check1.whole; 02.standard3.periods4.millions;hundred-thousands;thousands; tens5.millions; forty-two; nine6.expanded;5000; 60; 87.number line8.<9.>10.8; 5; add 1; 9,000,00011.2; 3; do not change; 8,542,0001.1 Exercise SetNote that exercises #1-22usethe following table:1.hundreds2.hundreds3.ones4.ones5.hundred-thousands6.hundred-thousands7.millions8.millions9.ten-millions10.ten-millions11.hundred-millions12.hundred-millions13.two hundred fifty-eight14.three hundred twenty-four15.eight thousand, three hundred seventy-six16.six thousand, two hundred twenty-six17.thirty-six thousand, eight hundred eighty18.fifty-two thousand, seven19.seven million, five hundred sixty-six thousand20.four million, three hundred two thousand21.thirty-five million, two hundred sixty thousand,three hundred seventy-five22.fifty-seven million, forty-fourthousand, twohundred eight23.The standard form is 3468.24.The standard form is 5283.25.The standard form is 86,500.26.The standard form is 58,004.27.The standard form is 16,402,012.28.The standard form is 14,204,015.29.The standard form is 9,000,009.30.The standard form is 5,000,005.31.The standard form is 26,034,203.32.The standard form is 52,028,706.33.The standard form is 620,595.34.The standard form is 430,696.35.The expanded form is600403.++36.The expanded form is500702.++37.The expanded form is5000406.++38.The expanded form is3000507.++39.The expanded form is80,0001000300604.++++
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Solution Manual for Developmental Mathematics, 1st Edition - Page 8 preview imageChapter1Whole Numbers and Introduction to Algebra440.The expanded form is70, 0002000500406.++++41.The expanded form is50, 0005000308.+++42.The expanded form is40, 0004000209.+++43.The expanded form is20,000,0008,000,000600,00040,000.+++44.The expanded form is50,000,0006,000,000300,0007000302.+++++45.93because 9 is to the right of 3 on the numberline.46.72because 7 is to the right of 2 on the numberline.47.014because 0 is to the left of 14 on the numberline.48.016because 0 is to the left of 16 on the numberline.49.36004500because 36000 is to the left of 4500 onthe number line.50.23003200because 2300 is to the left of 3200 onthe number line.51.200,00020, 000because 200,000 is to the right of20,000 on the number line.52.300, 00030, 000because 300,000 is to the right of30,000 on the number line.53.624 rounded to the nearest ten is 620.54.372 rounded to the nearest ten is 370.55.627 rounded to the nearest ten is 630.56.378 rounded to the nearest ten is 380.57.4891 rounded to the nearest hundred is 4900.58.5482 rounded to the nearest hundred is 5500.59.4831 rounded to the nearest hundred is 4800.60.5432 rounded to the nearest hundred is 5400.61.61,529 rounded to the nearest thousand is 62,000.62.72,503 rounded to the nearest thousand is 73,000.63.61,129 rounded to the nearest thousand is 61,000.64.72,103 rounded to the nearest thousand is 72,000.65.24,628 rounded to the nearest ten-thousand is20,000.66.34,628 rounded to the nearest ten-thousand is30,000.67.345,207 rounded to the nearest ten-thousand is350,000.68.645,308 rounded to the nearest ten-thousand is650,000.69.86,609,100rounded to the nearest million is87,000,000.70.75,809,100 rounded to the nearest million is76,000,000.71.86,409,100 rounded to the nearest million is86,000,000.72.75,309,100 rounded to the nearest million is75,000,000.73.86,609,100 rounded to the nearest ten-million is90,000,000.74.75,809,100 rounded to the nearest million is80,000,000.75.ninety-two quadrillion, two hundred thirty-threetrillion, seven hundred twenty billion, three hundredsixty-eight million, five hundred forty-seventhousand, eight hundred.76.ten-quadrillions77.700,000, 000, 00020,000, 000,000+78.90,000,000,000,000, 0002,000,000, 000,000,000+79.92,233,720,368,547,800 rounded to the nearest ten-quadrillion is 90,000,000,000,000,000.The word name is ninety quadrillion.80.92,233,720,368,547,800 rounded to the nearestquadrillion is 92,000,000,000,000,000.The word name is ninety-twoquadrillion81.Steven Spielberg generates the greatest revenue peryear which is $27,400,000. In word form this istwenty-seven million, four hundred thousanddollars.
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Solution Manual for Developmental Mathematics, 1st Edition - Page 9 preview imageSection 1.1Basics of Whole Numbers582.Tom Cruise generates the greatest revenue permovie which is $17,100,000. In word form this isseventeen million, one hundred thousand dollars.83.Samuel L. Jackson generates the least revenue permovie.His yearly revenueis $24,400,000. In wordform this is twenty-four million, four hundredthousand dollars.84.Johnny Depp generates between ten million dollarsand eleven million dollars per movie. His yearlyrevenue is $24,300,000. In word form this is twenty-four million, three hundred thousand dollars.85.Tom Cruise andTom Hanks generate the samerevenue per year.Tom Cruise generates the greatest revenue permovie which is $17,100,000. In word form this isseventeen million, one hundred thousand dollars.86.Tom Cruise andTom Hanks generate the samerevenue per year.Tom Hanks generates the lesser revenue per moviewhich is$12,000,000. In word form this is 12million dollars.87.$53,66488.$53,28589.201190.201091.The maximum is shown by the highest bar in thegraph. This occurs in 2007 at $55,627.92.The minimum is shown by the lowest bar in thegraph. This occurs in 2012 at $51,017.93.2,376,206; two million, three hundred seventy-sixthousand, two hundred six94.1,857,160; one million; eight hundred fifty-seventhousand, one hundred sixty95.Williams96.Brown and Jones97.1,857,160 rounded to the nearest hundred-thousandis 1,900,000.98.2,376,206 rounded to the nearest hundred-thousandis 2,400,000.99.The 3 is in the ten-thousands place.100.The 8 is in the ten-thousands place.101.1,380,145 < 1,534,042102.1,857,160>1,380,145103.two thousand, four hundred fifty-three104.two hundred two thousand, twenty-two105.102,063106.12,042107.–117.Answers will vary.118.does not make sense; Explanations will vary.Sample explanation:Adding one to this numberwould create a bigger number.119.makes sense120.makes sense121.makes sense122.true123.false; Changes to make the statement true will vary.A sample change is:The number 32,864 is writtenin standard form.124.false; Changes to make the statement true will vary.A sample change is:When rounding wholenumbers, the digit to be rounded either stays thesame or increases by 1.125.false; Changes to make the statement true will vary.A sample change is:When comparing numbers ofvarious items, tables are just as effective as bargraphs.126.The whole numbers from 10 to 40 would berounded to 10 or 20 or 30 or 40. So there are fourdifferent rounded numbers.127.a.46 rounded to the nearest ten is 50.b.23 rounded to the nearest ten is 20.c.4623502070++=128.a.10; 10b.8; 8c.No the order does not make a difference.
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Solution Manual for Developmental Mathematics, 1st Edition - Page 10 preview imageChapter1Whole Numbers and Introduction to Algebra6129.a.9b.9c.No the group changes does not change theanswer.1.2Check Points1.72436327875+2.112, 09 78,5 4 410, 6 4 1+3.2 2 225,572329,8744,882360,328+4.ExactEstimate25,57226,000329,874330,0004,8825,000361,000++The exact sumfrom Check Point 3seemsreasonable.5.a.associative property of additionb.identity property of additionc.commutative property of additiond.commutative property of addition6.153578++++could be rearranged as2010155378++++which is2010838.++=7.a.Billy Crystal's numberJohnny Carson's number4549=+=+=Billy Crystal hosted the Oscars 9 times.b.Bob Hope's numberJohnny Carson's number1351318=+=+=Bob Hope hosted the Oscars 18 times.c.591832++=Johnny Carson,Billy Crystal, and Bob Hopehosted the Oscars a total of 32 times.8.11 feet11 feet9 feet9 feet13 feet53 feet++++=9.38 yd19 yd38 yd19 yd114 yd+The yard requires 114 yd of fencing.1.2Concept and Vocabulary Check1.sum;addends2.carrying3.identity4.commutative5.associative6.rectangle; length7.perimeter1.2Exercise Set1.234265+2.263359+3.53340393+
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Solution Manual for Developmental Mathematics, 1st Edition - Page 11 preview imageSection 1.2Adding Whole Numbers74.67230297+5.47621244886+6.56433255968+7.25421262668+8.34272613688+9.8932121+10.9754151+11.430829567264+12.570636459351+13.5274629811,572+14.3748839712,145+15.7413259862052+16.8765219942391+17.62,8338,7639871,694+18.57,9265,8437963,848+19.804,12739,7052,008845,840+20.906,23829,5074,007939,752+21.3,7889,5462,030+ 83,94799,31122.5,8778,4935,060+ 94,726114,156
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Solution Manual for Developmental Mathematics, 1st Edition - Page 12 preview imageChapter1Whole Numbers and Introduction to Algebra823.ExactEstimate495037402220110++24.ExactEstimate626043401920120++25.ExactEstimate25132500864900193719005300++26.ExactEstimate34163400778800192619006100++27.ExactEstimate62,53463,00041074 00086129 00076,000++28.ExactEstimate84,51785,00061036 0007814800099,000++29.a.623479836000800014, 000++=b.No, the estimate does not seem reasonable.30.a.680741507000400011, 000++=b.No, the estimate does not seem reasonable.31.a.18,972378,641687420,000380,0007000407,000++++=b.Yes, the estimate seemsreasonable.32.a.28,612287,611786230,000290,0008000328,000++++=b.Yes, the estimate seemsreasonable.33.commutative property of addition34.commutative property of addition35.associative property of addition36.associative property of addition37.identity property of addition38.identity property of addition39.identity property of addition40.identity property of addition41.commutative property of addition42.commutative property of addition43.20101278312873201030+++=+++=+=44.20101892118291201030+++=+++=+=45.504032711839328113974050797++++=++++=++=46.3060224185922815943060494++++=++++=++=
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Solution Manual for Developmental Mathematics, 1st Edition - Page 13 preview imageSection 1.2Adding Whole Numbers947.20010096541951796451951710020017317++++=++++=++=48.20010093471961293741961210020012312++++=++++=++=49.412123535+=50.514226740+=51.8945134+=52.9328121+=53.549212,32617,818+=54.894313,51722, 460+=55.127,8132799130,612+=56.138,5143786142,300+=57.8793820152203+++=58.9472530173188+++=59.291730614,99918, 222++=60.371650415,99820, 218++=61.8 inches10 inches8 inches10 inches36 inches+Theperimeter is 36 inches.62.14 inches9 inches14 inches9 inches46 inches+Theperimeter is 46 inches.63.9 feet7 feet11 feet27 feet+Theperimeter is27 feet.64.10 feet16 feet9 feet35 feet+Theperimeter is 35 feet.65.6 yards8 yards6 yards8 yards28 yards+Theperimeter is 28 yards.66.7 yards18 yards7 yards18 yards50 yards+Theperimeter is 50 yards.67.250 inches250 inches250 inches250 inches1000 inches+Theperimeter is 1000 inches.68.50 inches50 inches50 inches50 inches200 inches+Theperimeter is 200 inches.
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Solution Manual for Developmental Mathematics, 1st Edition - Page 14 preview imageChapter1Whole Numbers and Introduction to Algebra1069.9 yards9 yards12 yards12 yards21 yards21 yards84 yards+Theperimeter is 84 yards.70.5 inches13 inches9 inches4 inches14 inches17 inches62 inches+Theperimeter is 62 inches.71.51751751705143+=+72.82582582508214+=+73.11711553644174++74.9490621418234918++++75.718561105035++76.878857306622++77.3097191723912681590598124871++++78.929749282105289243001400342999++++79.Number of dogs named BellaNumber of dogs named Lucy2089357120895660=+=+=5660 dogs are named Bella.
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Solution Manual for Developmental Mathematics, 1st Edition - Page 15 preview imageSection 1.2Adding Whole Numbers1180.Number of dogs named BaileyNumber of dogs named Lucy41735714173988=+=+=3988 dogs are named Bailey.81.Number of dogs named BaileyNumber of dogs named Molly70732817073988=+=+=3988 dogs are named Bailey.82.Number of dogs named BellaNumber of dogs named Molly2379328123795660=+=+=5660 dogs are named Bella.83.5660Named Bella (from a previous exercise)3958Named Max (from bar graph)3571Named Max (from bar graph)13,189+84.3988Named Bailey (from a previous exercise)3958Named Max (from bar graph)3571Named Max (from bar graph)11,517+85.a.ExactEstimate59 feet60 feet23 feet20 feet25 feet30 feet46 feet50 feet43 feet40 feet200 feet++Theestimate is 200 feet.b.59 feet23 feet25 feet46 feet43 feet196 feet+Theperimeter is 196 feet.
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Solution Manual for Developmental Mathematics, 1st Edition - Page 16 preview imageChapter1Whole Numbers and Introduction to Algebra1286.a.ExactEstimate3 feet0 feet15 feet20 feet21 feet20 feet15 feet20 feet9 feet10 feet24 feet20 feet90 feet++Theestimate is90 feet.b.3 feet15 feet21 feet15 feet9 feet24 feet87 feet+Theperimeter is87feet.87.–96.Answers will vary.97.does not make sense; Explanations will vary.Sample explanation:No column's sum exceeded 9.98.makes sense99.makes sense100.makes sense101.false; Changes to make the statement true will vary.A sample change is:The expressions are equalbecause of the commutativeproperty of addition.102.true103.true104.true105.The two smaller vertical sides total 7 inches, so theunlabeled vertical side must also be 7 inches.Thetwo smallerhorizontalsides total9inches, so theunlabeledhorizontalside must also be9inches.3 inches4 inches7 inches3 inches6 inches9 inches32 inches+Theperimeter is 32 inches.106.Thelabeledvertical sideis 8inches, so the2 smallervertical sidesmusttotal 8inches.Since one of thesevertical sides is labeled 3 inches, the unlabeledvertical side must be 5 inchesThehorizontalvertical sideis 10inches, so the2smallerhorizontalsidesmusttotal 10inches.Sinceone of these horizontalsides is labeled 5 inches, theunlabeled horizontalside must also be 5 inches.8 inches5 inches3 inches10 inches5 inches5 inches36 inches+Theperimeter is 36inches.107.Answers will vary.108.826−=because628.+=109.Yes, the sum is 92.781492+110.532−=1.3Check Points1.a.13103−=Check:31013+=b.826−=Check:628+=c.12120−=Check:01212+=d.40040−=Check:40040+=
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Solution Manual for Developmental Mathematics, 1st Edition - Page 17 preview imageSection 1.3Subtracting Whole Numbers132.6893Check:617272172161726893−+3.5 125 6 2Check:5174 5455 17562−+4.154175 6 7 4Check:47818 9 38934 7 8 15674−+5.1067 01090Check:4442 5 62564 4 4700−+6.ExactEstimate5674600089310005000−−The exact difference of 4781, determined in CheckPoint 4, seems reasonable.7.a.130, 490(Lawyers)45,230(All Occupations)85, 260−The difference is$85,260.b.130, 490(Lawyers)60,36070,130(Accountants)−The average salary for accountants is $70,130.8.Withdrawls on orBalancebefore May 10May 1Balance after May 10820(45085537)820577243=−+++=−=The balance after May 10 is $243.1.3Concept and Vocabulary Check1.minuend; subtrahend; difference2.2; 10; 123.04.borrowing1.3Exercise Set1.87Check:6225256287−+2.73Check:3142423173−+3.598Check:273325325273598−+4.752Check:321431431321752−+5.376Check:3245252324376−+6.387Check:3226565322387−+7.6288Check:611017817861106288−+8.9366Check:912024624691209366−+
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Solution Manual for Developmental Mathematics, 1st Edition - Page 18 preview imageChapter1Whole Numbers and Introduction to Algebra149.6785Check:44002385238544006785−+10.8453Check:52003253325352008453−+11.78,993Check:74,5024, 4914, 49174,50278,993−+12.67,876Check:64,6053, 2713, 27164,60567,876−+13.25,176Check:025,17625,176025,176−+14.32,574Check:032,57432,574032,574−+15.82Check:4735354782−+16.63Check:3528283563−+17.80Check:5327275380−+18.90Check:4743434790−+19.857Check:184673673184857−+20.634Check:182452452182634−+21.933Check:476457457476933−+22.746Check:347399399347746−+23.800Check:277523523277800−+24.500Check:224276276224500−+25.253Check:2064747206253−+26.468Check:4095959409468−+27.7382Check:692246046069227382−+28.8249Check:792932032079298249−+29.1533Check:1484494914841533−+30.1746Check:1657898916571746−+
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Solution Manual for Developmental Mathematics, 1st Edition - Page 19 preview imageSection 1.3Subtracting Whole Numbers1531.1967Check:3919281928391967−+32.2952Check:52947294752952−+33.42,566Check:28,85813,70813,70828,85842,566−+34.65, 722Check:38,91526,80726,80738,91565,722−+35.60, 000Check:32,01727,98327,98332,01760, 000−+36.80, 000Check:40,01839,98239,98240,01880, 000−+37.86, 497Check:60,64725,85025,85060,64786, 497−+38.71,111Check:52,11318,99818,99852,11371,111−+39.ExactEstimate338340223220120−−40.ExactEstimate586590123120470−−41.ExactEstimate1875190013871400500−−42.ExactEstimate2813280022712300500−−43.ExactEstimate18,96319,00016,21816,0003000−−44.ExactEstimate24,81725,00013,19913,00012,000−−45.a.ExactEstimate363536004625003100−−b.No; Anexact difference of2173 does not seemreasonable.46.a.ExactEstimate185219004274001500−−b.No; Anexact difference of1025 does not seemreasonable.47.53647−=48.73766−=49.711160−=50.573522−=51.886226−=52.975542−=53.49742−=
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Solution Manual for Developmental Mathematics, 1st Edition - Page 20 preview imageChapter1Whole Numbers and Introduction to Algebra1654.55451−=55.43340−=56.68860−=57.803644−=58.903951−=59.54830518−=60.87660816−=61.758654104−=62.497293204−=63.90831348949−=64.39358853050−=65.905,008280,034624,974−66.2,013,000507,0931,505,907−67.202035158060−=−68.5540358580−=−69.37438645884716330−−70.685512153761706−−71.70(Minuend)40(Subtrahend)30(Difference)−72.100(Minuend)90(Subtrahend)10(Difference)−73.15501221428−The difference is 1428 years.74.15504051145−The difference is 1145 years.75.405195210−Theextreme lifespanof a whale is 210 years.76.40532877−Theextreme lifespanof acockatoois 77 years.77.1222894−Theextreme lifespanof a dog is 94 years less thanthe extreme lifespan of ahuman.78.1223884−Theextreme lifespanof a cat is 84 years less thanthe extreme lifespan of ahuman.79.DepositsWithdrawlsBalance(1050435)(5251854100190)14851004481=+−++++=−=Thebalanceafter June 25is $481.80.DepositsWithdrawlsBalance(1120350)(6151452253004)14701289181=+−++++=−=The balance after December 31 is $181.
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Solution Manual for Developmental Mathematics, 1st Edition - Page 21 preview imageSection 1.3Subtracting Whole Numbers1781.Rectangle:Square:17 feet14 feet13 feet14 feet17 feet14 feet13 feet14 feet60 feet56 feet++Difference:60 feet(Rectangle)56 feet(Square)4 feet−The rectangular garden requires 4 more feet offencing than the square garden.82.Rectangle:Square:23 feet16 feet11 feet16 feet23 feet16 feet11 feet16 feet68 feet64 feet++Difference:68 feet(Rectangle)64 feet(Square)4 feet−The rectangular garden requires 4 more feet offencing than the square garden.83.–88.Answers will vary.89.does not make sense; Explanations will vary.Sample explanation:To checkasubtractionproblem by add the difference to thesubtrahend.90.does not make sense; Explanations will vary.Sample explanation:Borrowing is unnecessarybecause each digit inthesubtrahend exceeds thecorresponding digit in the minuend.91.makes sense92.makes sense93.true94.true95.false; Changes to make the statement true will vary.A sample change is:When 30 is subtracted from 50,30 is thesubtrahend.96.true97.479184295−98.849355494−99.No; the associative propertycannotbe applied tosubtraction.10(61)1055−−=−=(106)1413−−=−=100.Answers will vary.101.eighty-nine thousand, one hundred sixty-two102.35, 2874,95640, 243+103.ExactEstimate35, 28735,0004,9565,00040,000++104.a.5355515=++=b.2422228=+++=c.67666666642=++++++=105.a.(23)56530==b.2(35)21530==c.No; the grouping did not change the answer.106.a.28393000b.621600c.28396213000600
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Solution Manual for Developmental Mathematics, 1st Edition - Page 22 preview imageChapter1Whole Numbers and Introduction to Algebra181.4Check Points1.a.73 173=b.7300=c.0(14)0=d.1 1313=2.a.associative property of multiplicationb.commutative property of multiplicationc.commutative property of multiplication3.a.10(45)10 410 5+=+b.10(45)10(9)90+==10 410 5405090+=+=Yes, both methods give the same answer.4.24324865.1 28 2 3757616.25824103251606192+7.43725313112185087400110,561+8.7232053615144600148, 215+9.a.953 1000953, 000=b.4026 100402, 600=10.10212 7 5 32 5 7 310 21210===11.a.287196Attach 3 zeros to 196.28(7000)196,000=b.2816=Attach23,+or 5 zeros to 16.200 80001,600,000=12.479681750008004, 000, 000=13.amount spent on housing and utilities(5 126)3563035665=+=+=The amount spent on housing and utilities is $665.14.Adult ticketsChild ticketsTotal Sales83 1257 59962851281=+=+=The total amount collected in ticket sales is $1281.15.a.2118168210378+The area of the floor is 378 square feet.b.37872646The cost of thecarpetingis $2646.1.4Concept and Vocabulary Check1.666++2.factors; product3.04.identity5.commutative
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Solution Manual for Developmental Mathematics, 1st Edition - Page 23 preview imageSection 1.4Multiplying Whole Numbers196.associative7.distributive;distributes8.five9.length;width;square1.4Exercise Set1.27 127=2.39 139=3.0 270=4.0 390=5.(1)(1205)1205=6.(1)(1372)1372=7.7 0 30=8.7 0 50=9.commutative property of multiplication10.commutative property of multiplication11.associative property of multiplication12.associative property of multiplication13.distributive property14.distributive property15.commutative property of addition16.commutative property of addition17.commutative property of multiplication18.commutative property of multiplication19.a.4(35)4 34 5+=+b.4(35)4(8)32+==4 34 5122032+=+=Yes, both methods give the same answer.20.a.3(45)3 43 5+=+b.3(45)3(9)27+==3 43 5121527+=+=Yes, both methods give the same answer.21.2336922.4128223.62424824.73214625.4023120626.5033150927.52841628.48314429.56950430.38934231.61463684
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Solution Manual for Developmental Mathematics, 1st Edition - Page 24 preview imageChapter1Whole Numbers and Introduction to Algebra2032.6137429133.2778221634.4886292835.3074515,37036.4038520,19037.1918152190342+38.2315115230345+39.535315926502809+40.646425638404096+41.1632348932603749+42.1363227240804352+43.7068321185648058,598+44.8074648423228037,122+45.23577921213164990186, 203+46.57329740124515880556, 004+47.13511227013501350015,120+48.351114140435103510040, 014+49.3427828274166854027416002,837,556+
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Solution Manual for Developmental Mathematics, 1st Edition - Page 25 preview imageSection 1.4Multiplying Whole Numbers2150.4372288349763497608744001, 259,136+51.3246092916194400197,316+52.7218075047576800581,847+53.98523029550197000226,550+54.65832013160197400210,560+55.332240013280664000796,800+56.234420046800936000982,800+57.(749)(58)(0)0=58.(972)(85)(0)0=59.157 101570=60.238 102380=61.8100800=62.7100700=63.22(1000)22,000=64.37(1000)37,000=65.420710, 00042, 070, 000=66.530610, 00053,060, 000=67.1004 6 254 25 6100 6600===68.1004 7 254 25 7100 7700===69.10272 9 5 32 5 9 310 27270===70.10275 9 3 25 2 9 310 27270===71.7400028, 000=72.3800024, 000=73.537371Attach 4 zeros to 371.53(70,000)3,710,000=74.478376Attach 4 zeros to 376.47(80,000)3,760,000=75.7963=Attach12,+or 3 zeros to 63.7090063, 000=
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Solution Manual for Developmental Mathematics, 1st Edition - Page 26 preview imageChapter1Whole Numbers and Introduction to Algebra2276.9436=Attach12,+or 3 zeros to 36.9040036, 000=77.2 1632=Attach33,+or 6 zeros to 32.200016, 00032, 000, 000=78.3 1236=Attach33,+or 6 zeros to 36.300012, 00036,000, 000=79.832980302400=Yes, an exact product of 2407 seemsreasonable.80.483350301500=Yes, an exact product of1584seemsreasonable.81.312583006018, 000=Yes, an exact product of18,906seemsreasonable.82.519385004020, 000=Yes,an exact product of 19,722seemsreasonable.83.27311430010030, 000=No, an exact product of311,222does notseemreasonable.84.38621740020080, 000=No, an exact product of837,622does notseemreasonable.85.(4826)(523)(5000)(500)2,500,000=Yes,an exact product of2,523,998seemsreasonable.86.(3906)(517)(4000)(500)2,000,000=Yes,an exact product of2,019,402seemsreasonable.87.90 4360=88.60 7420=89.18 9162=90.26 5130=91.4 8003200=92.3 9002700=93.2 307614=94.2 408816=95.2 18733746=96.2 29465892=97.3 32409720=98.3 432012,960=99.6954=The area is 54 square feet.100.202480400480+The area is 480 square feet.101.3015150300450+The area is 450 square yards.102.14342The area is 42 square yards.103.5286031584316800318,384+three hundred eighteen thousand, three hundredeighty-four104.5286032562341600344,162+three hundred forty-fourthousand, one hundredsixty-two
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Solution Manual for Developmental Mathematics, 1st Edition - Page 27 preview imageSection 1.4Multiplying Whole Numbers23105.22721264 83003 7910−−106.32233187 620053 740−−107.18010459 63 5839 852 4−−108.848512(43)2 413++109.3 48623214582321226−=−=There were 1226 billionaires in 2012.110.7 1403498034946−=−=There were946 billionaires in 2007.111.4851297048505820+It will travel 5820 miles.112.381276380456+You cantravel456miles.113.121896120216+It will take 216 minutes.114.283128840868+You use 868 gallons.115.food/lodgingairfareTotal cost16 37816 2606048416010, 208=+=+=The total cost is $10,208.116.biographiesnovelsTotal17 1413 23238299537=+=+=They took in $537.117.9 A.M. to 5 P.M. is 8 hours.7 2514519+=+=The total cost is $19.118.Cost if using monthly payments14 50100700100800=+=+=Savings:80075050−Paying the total amountat the time of the purchasewill save $50.119.a.181472180252+The area of the floor is 252 square feet.b.25282016The cost of the carpeting is $2016.120.a.191595190285+The area of the floor is 285 square feet.b.28582280The cost of the carpeting is $2280.
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Solution Manual for Developmental Mathematics, 1st Edition - Page 28 preview imageChapter1Whole Numbers and Introduction to Algebra24121.a.509420045004700+The area of the court is 4700 square feet.b.4001280040004800+12 gallons will cover 4800 square feet.c.Yes;12 gallons are enough to refinish the court.122.a.508420040004200+The area of the court is 4200 square feet.b.400936009 gallons will cover 3600 square feet.c.No; 9 gallonsare not enough to refinish thecourt.123.–132.Answers will vary.133.makes sense134.makes sense135.does not make sense; Explanations will vary.Sample explanation:You must attach23,+or 5zeros.136.does not make sense; Explanations will vary.Sample explanation:The area of a regulation tenniscourt is 2808squarefeet.137.false; Changes to make the statement true will vary.A sample change is:Deleting 0 as a factor mightchange the product from being 0 to being non-zero.138.false; Changes to make the statement true will vary.A sample change is:The distributive property statesthat multiplicationdistributesover addition.139.true140.true141.61363678142.3214128320448+143.a.5(73)5(4)20−==5 75 3351520−=−=b.10(82)10(6)60−==10 810 2802060−=−=c.yes144.Answers will vary.145.305,640146.86376978560+147.90028978105+148.2137=because7321.=149.Yes, the product is 1206.67185366701206+150.(50247)1523,5941523,609+=+=
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Solution Manual for Developmental Mathematics, 1st Edition - Page 29 preview imageMid-Chapter Check Point25Mid-Chapter Check Point–Chapter 11.eight billion, sixty-three million, five hundred sixty-one thousand, four2.54,302,6283.a.nearest hundred:64,51764,500b.nearestthousand:64,51765,0004.1805.18196.580937629571+7.652378274−8.876435049.873652226103132+10.324162648194403240052, 488+11.4936=Attach23,+or 5 zeros to 36.400 90003,600,000=12.57 93 00=13.1796113+14.8000577943−15.523814−16.(8 3)624618−=−=17.2 15730723−=−=18.ExactEstimate87690033730010581002300++19.ExactEstimate984610,000231720008000−−20.ExactEstimate(2893)(648)(3000)(600)1,800,000=21.associative property of multiplication22.distributive property23.commutative property of addition24.Perimeter:4 yards13 yards4 yards13 yards34 yards+Area:13 yards4 yards52 square yards
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Solution Manual for Developmental Mathematics, 1st Edition - Page 30 preview imageChapter1Whole Numbers and Introduction to Algebra2625.a.The James Bond franchise had the greatestnumber of movies.Thetotal world gross for thisfranchisewas$5,116,147,171.b.three billion, two hundred eighty-seven million,two hundred eighty-five thousand, five dollarsc.Star Wars had 7 movies.$4,279,632,749$4,000,000,000d.Shrek and Lord of the Rings each had totalworld gross less than $3,500,000,000.26.a.61(1980)28(Ancient Greece and Rome)33−People born in 1980areexpected tolive 33years morethan people born in ancient Greeceand Rome.b.Average life expectancy was 48 years in 1950.c.The followinglife expectanciesround to 30.Stone Age:2530Ancient Greece and Rome:2830Middle Ages:30301900:3130d.life expectancy1950: 48life expectancyMiddle Ages: 30???482 30124860124848 true=−=−=27.DepositsWithdrawlsBalance(730250)(29156347)980532448=+−++=−=The balance is $448.28.58,95251,7237 229−The change in the city’s population was 7229.29.(8)(1480)(5)(1245)11,840622599628518,065+=+=+=Thetotal costis $18,065.30.141228140168+The area of the floor is 378 square feet.168101680=The cost of the carpeting is $1680.1.5Check Points1.a.5678=because8 756.=b.2739=because3 927.=c.93 27because9 327.=2.a.13113=because13 113.=b.13131=because1 1313.=c.117 17because1 1717.=d.171 17because17 117.=e.230623061=because2306 12306.=f.12306 2306because1 23062306.=3.a.09 0because0 90.=b.02530=because0 2530.=c.008=because0 80.=
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Solution Manual for Developmental Mathematics, 1st Edition - Page 31 preview imageSection 1.5Dividing Whole Numbers27d.8undefined0=e.0undefined0=4.1713 51332121003200232Check:17135135.22207486 44884228244882004020Check:748644886.70866 42520420505242222020200200840364200042,52067086 R 4=Check:7086642516442520+7.8329 2407232820202700870Check:832974716602407+8.2022241532 132921284932102 0206007211213, 29232415 R 12=Check:415328301245010032801213292++9.121386 16649138627222018927721716, 649138612 R 17=Check:13861227721386000166321716649++10.a.24060240602464===b.53,000530005305301001001===c.30005000 15,000,0005000 150000005 15000==
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