Solution Manual for Pathways to College Mathematics, 2nd Edition

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SOLUTIONSMANUALDANIELS.MILLERNiagara County Community CollegePATHWAYSTOCOLLEGEMATHEMATICSSECONDEDITIONRobert BlitzerMiami Dade College

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iTable of ContentsChapter PPrealgebra Pathways ..............................................................................................1Chapter 1Numerical Pathways ............................................................................................77Chapter 2Algebraic Pathways:Equations and Inequalities .................................................................................143Chapter 3Algebraic Pathways:Graphs, Functions, Linear Functions, and Linear Systems ...............................215Chapter 4Algebraic Pathways:Polynomials, Quadratic Equations, and Quadratic Functions ...........................295Chapter 5Geometric Pathways:Measurement......................................................................................................373Chapter 6Geometric Pathways ..........................................................................................393Chapter 7Pathways to Probability:Counting Methods and Probability Theory ........................................................435Chapter 8Statistical Pathways ...........................................................................................491

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Chapter PPrealgebra Pathways1Check Points P.11.a.millions placeb.ones placec.hundreds placed.millions place2.Work from left to right. Write the name of the three-digit number in each period, followed by the name of the period anda comma. Do not write the name of the last period, “ones.”a.twenty-seven thousand, one hundred forty-threeb.five hundred twenty-one million, six hundred thirty thousand, fifty-seven3.a.Begin by noting how to write the number within each period.53406fifty-three thousand, four hundred sixWrite the digits for the number in each period, followed by a comma.The standard form for the number is 53,406.b.Begin by noting how to write the number within each period.204932016two hundred four million, nine hundred thirty-two thousand, sixteenWrite the digits for the number in each period, followed by a comma.The standard form for the number is 204,932,016.

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Chapter PPrealgebra Pathways24.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.145because 14 is to the right of 5 on the number line.b.016because 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. This indicates to leave the thousands digit thesame. Replace all digits to the right with zeros.57, 49857, 000b.The digit to the right of the hundred-thousands digit is 5. This indicates to add one to the hundred-thousands digit.Replace all digits to the right with zeros.4,856,9024,900, 000c.The digit to the right of the thousands digit is 6, which is greater than 5. This implies to add one to the thousandsdigit. Replace all digits to the right with zeros.960210, 000d.The digit to the right of the millions digit is 2, which is less than 5. This implies to leave the millions digit the same.Replace all digits to the right with zeros.684, 236, 042684, 000, 0007.a.The digit to the right of the billions digit is 5. This implies to add one to the billions digit. Replace all digits to theright with zeros.7,599, 445,1838, 000,000, 000b.The digit to the right of the ten-thousands digit is 5. This implies to add one to the ten-thousands digit. Replace alldigits to the right with zeros.7,599, 445,1837,599, 450, 000c.The digit to the right of the thousands digit is 1, which is less than 5. This implies to leave the thousands digit thesame. Replace all digits to the right with zeros.7,599, 445,1837,599, 445, 0008.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. The countries in which an appendectomy costs more than inChile are Canada, Switzerland, and United States.9.a.We begin with the number of marriages between an 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 marriages between an 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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Section P.1Whole Numbers3Concept and Vocabulary Check P.11.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; 8,542,000Exercise Set P.1Note that exercises #1 - 22 use the 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-four thousand, 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.

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Chapter PPrealgebra Pathways439.The expanded form is80, 0001000300604.40.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.45.93because 9 is to the right of 3 on the number line.46.72because 7 is to the right of 2 on the number line.47.014because 0 is to the left of 14 on the number line.48.016because 0 is to the left of 16 on the number line.49.36004500because 36000 is to the left of 4500 on the number line.50.23003200because 2300 is to the left of 3200 on the number line.51.200, 00020, 000because 200,000 is to the right of 20,000 on the number line.52.300, 00030,000because 300,000 is to the right of 30,000 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 is 20,000.66.34,628 rounded to the nearest ten-thousand is 30,000.67.345,207 rounded to the nearest ten-thousand is 350,000.

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Section P.1Whole Numbers568.645,308 rounded to the nearest ten-thousand is 650,000.69.86,609,100 rounded to the nearest million is 87,000,000.70.75,809,100 rounded to the nearest million is 76,000,000.71.86,409,100 rounded to the nearest million is 86,000,000.72.75,309,100 rounded to the nearest million is 75,000,000.73.86,609,100 rounded to the nearest ten-million is 90,000,000.74.75,809,100 rounded to the nearest million is 80,000,000.75.ninety-two quadrillion, two hundred thirty-three trillion, seven hundred twenty billion, three hundred sixty-eight million,five hundred forty-seven thousand, 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 nearest quadrillion is 92,000,000,000,000,000.The word name is ninety-two quadrillion.81.The greatest yearly earnings are for males with a Doctorate which is $131,569. In word form this is one hundred thirty-one thousand, five hundred sixty-nine dollars.82.The least yearly earnings are for females with a 9thto 12thgrade, non-graduate which is $16,812. In word form this issixteen thousand, eight hundred twelve dollars.83.Women with bachelor’s degree earns $50,856. In word form this is fifty thousand, eight hundred fifty-six dollars.84.Men with associate degree earns $51,865. In word form this is fifty-one thousand, eight hundred sixty-five dollars.85.Men with bachelor’s degree will earns $79,927 which would round to $80,000. In word form this is seventy-ninethousand, nine hundred twenty-seven dollars.86.Women with master’s degree will earns $64,834 which would round to $60,000. In word form this is sixty-fourthousand, eight hundred thirty-four dollars.87.In 1960 there were only 9,700,000 immigrants.88.In 2016 there were 43,700,000 immigrants.89.In 1900 there were only 10,300,000 immigrants.In 1940 there were only 11,600,000 immigrants.In 1960 there were only 9,700,000 immigrants.90.In 1980 there were 14,100,000 immigrants.In 2000 there were 31,100,000 immigrants.In 2016 there were 43,700,000 immigrants.91.In 1980 there were 14,100,000 immigrants.

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Chapter PPrealgebra Pathways692.In 2000 there were 31,100,000 immigrants.93.2,376,206; two million, three hundred seventy-six thousand, two hundred six94.1,857,160; one million; eight hundred fifty-seven thousand, one hundred sixty95.Williams96.Brown and Jones97.1,857,160 rounded to the nearest hundred-thousand is 1,900,000.98.2,376,206 rounded to the nearest hundred-thousand is 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 number would create a biggernumber.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 written in standard form.124.false; Changes to make the statement true will vary. A sample change is: When rounding whole numbers, the digit to berounded either stays the same or increases by 1.125.false; Changes to make the statement true will vary. A sample change is: When comparing numbers of various items,tables are just as effective as bar graphs.126.The whole numbers from 10 to 40 would be rounded to 10 or 20 or 30 or 40. So there are four different roundednumbers.

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Section P.2Fractions and Mixed Numbers7Check Points P.21.a.310Numerator is 3. Denominator is 10.b.103Numerator is 10. Denominator is 3.c.180Numerator is.Denominator is180 .2.a.There are 7 parts shaded out of a total 10 equal parts. Thus, the fraction710(seven-tenths) represents the shadedportion of the figure.b.There are 2 parts shaded out of a total 5 equal parts. Thus, the fraction25(two-fifths) represents the shaded portionof the figure.c.There are 13 parts shaded out of a total 16 equal parts. Thus, the fraction1316(thirteen-sixteenths) represents theshaded portion of the figure.3.Fraction of fatal gun accidents with children between 15 and 34 isnumber of fatal gun accidents withchildren between 15 and 34.total number of fatal gun accidents1451076062526064.a.310Because the numerator is less than the denominator,310 is a proper fraction.b.1010Because the numerator and denominator are equal, 1010 is an improper fraction.c.103Because the numerator is greater than the denominator,103is an improper fraction.5.a.Improper Fraction: Each whole object is divided into 3 equal parts, or thirds. A total of 5 of the thirds are shaded.The improper fraction53represents the shaded portion of the group of figures.Mixed Number: The shaded portions include 1 whole object and23 of a second object. The mixed number21 3represents the shaded portion of the group of figures.

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Chapter PPrealgebra Pathways8b.Improper Fraction: Each whole object is divided into 4 equal parts, or fourths. A total of 9 of the fourths are shaded.The improper fraction94represents the shaded portion of the group of figures.Mixed Number: The shaded portions include 2 whole object and14of a second object. The mixed number12 4represents the shaded portion of the group of figures.6.a.58 25165212 8888b.716 127192719912 161616167.a.5313 532Write the mixed number usingremainderquotient.original denominatorThus, 521.33b.867127 867161224Write the mixed number usingremainderquotient.original denominatorThus, 86212.77c.513192719 51338133320130Write the mixed number usingremainderquotient.original denominatorThus, 51327.19Concept and Vocabulary Check P.21.numerator; denominator2.33; 8; 83.proper; improper4.mixed5.5; 3; 2; 5

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Section P.2Fractions and Mixed Numbers96.2; 1Exercise Set P.21.513Numerator is 5. Denominator is 13.2.719Numerator is 7. Denominator is 19.3.135Numerator is 13. Denominator is 5.4.197Numerator is 19. Denominator is 7.5.60Numerator is. Denominator is 60.6.180Numerator is. Denominator is 180.7.There are 3 parts shaded out of a total 5 equal parts. Thus, the fraction35represents the shaded portion of the figure.8.There are 2 parts shaded out of a total 5 equal parts. Thus, the fraction 25 represents the shaded portion of the figure.9.There is 1 part shaded out of a total 6 equal parts. Thus, the fraction16 represents the shaded portion of the figure.10.There are 2 parts shaded out of a total 6 equal parts. Thus, the fraction26represents the shaded portion of the figure.11.There are 7 parts shaded out of a total 16 equal parts. Thus, the fraction716 represents the shaded portion of the figure.12.There are 11 parts shaded out of a total 16 equal parts. Thus, the fraction1116 represents the shaded portion of the figure.13.a.Probability of landing on a red regionred region3 .total regions10b.Probability of landing on a blue regionblue region2 .total regions10c.Red is more likely.

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Chapter PPrealgebra Pathways1014.a.Probability of landing on a brown regionbrown region3 .total regions10b.Probability of landing on a yellow regionyellow region2 .total regions10c.Brown is more likely.15.911Because the numerator is less than the denominator,911is a proper fraction.16.813Because the numerator is less than the denominator,813 is a proper fraction.17.c.119Because the numerator is greater than the denominator, 119is an improper fraction.18.c.138Because the numerator is greater than the denominator,138is an improper fraction.19.21 9is a mixed number.20.51 8is a mixed number.21.66Because the numerator and denominator are equal,66is an improper fraction.22.88Because the numerator and denominator are equal, 88 is an improper fraction.23.Improper Fraction: 4 .3Mixed Number:11.324.Improper Fraction: 5 .3Mixed Number:21.325.Improper Fraction:11.4Mixed Number:32.4

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Section P.2Fractions and Mixed Numbers1126.Improper Fraction:5 .2Mixed Number:12.227.Improper Fraction: 17 .5Mixed Number:23.528.Improper Fraction: 18 .5Mixed Number:33.529.Improper Fraction: 25 .7Mixed Number:43.730.Improper Fraction: 26 .7Mixed Number:53.731.38 23192 88832.79 27252 99933.35 73387 55534.25 62326 55535.716 87135816161636.516 951499 16161637.1825 121831812 25252538.2125 152139615 252525

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Chapter PPrealgebra Pathways1239.23345540.47758841.76489942.59569943.7111135202044.7881331252545.1247294346.1665453747.48.49.50.51.a.Shark attacks24143211146b.Florida had the greatest number of attacks, 24. Thus, the fraction of attacks that occurred in Florida is24 .46c.Alabama, North Carolina, and Texas had one shark attack each. Thus, the fraction of attacks that occurred in thesethree states is3 .4652.a.Shark attacks24143211146

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Section P.3Simplifying Fractions; Operations with Fractions13b.Hawaii had the second greatest number of attacks, 14. Thus, the fraction of attacks that occurred in Hawaii is14 .46c.South Carolina and California had a combined 5 shark attacks. Thus, the fraction of attacks that occurred in thesetwo states is5 .4653. – 58.Answers will vary.59.does not make sense; Explanations will vary. Sample explanation: Since32is an improper fraction the price would behigher than the original price.60.makes sense61.does not make sense; Explanations will vary. Sample explanation: There are 8 total people, so the denominator would be8.62.true63.true64.false; Changes to make the statement true will vary. A sample change is: A mixed number has a whole number and aproper fraction.54is not a proper fraction.65.false; Changes to make the statement true will vary. A sample change is: 1723.55Check Points P.31.a.3003 1003 10 103 2 5 2 52 2 3 5 5b.366 62 3 2 32 2 3 32.a.1025153523

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