Solution Manual for Mathematics: Its Power and Utility, 10th Edition

Preview (31 of 832 Pages)

100%

Purchase to unlock

Loading page image...

Student's Survival and Solutions Manual forMATHEMATICSIts Power and UtilityTENTH EDITIONKarl J. Smith

Loading page image...

CONTENTSPage iiiCONTENTSPART I:FOUNDATIONS: THE POWER OF MATHEMATICS1Arithmetic, Calculators, and Problem Solving .........................12Sets of Numbers .........................................................................353Introduction to Algebra ..............................................................634Percents and Problem Solving ...................................................915Introduction to Geometry .........................................................1136Measurement and Problem Solving .........................................131PART II:APPLICATIONS: THE UTILITY OF MATHEMATICS7Applications of Percent ............................................................. 1578Sets and Logic ........................................................................... 1959Probability ................................................................................. 22910 Statistics.....................................................................................25111 Graphs .......................................................................................279

Loading page image...

PREFACEPage vPREFACEThis manual was designed to help you bridge the gap between the textbook and aworking knowledge of mathematics.It has been said that “Mathematics is not aSpectator Sport" and this means you cannot learn mathematics by simply attendingclass, but instead you must build a body of information that will enable you to doproblem solving in the real world.I decided to entitle this supplement,Student'sSurvival and Solutions Manualbecause I want it to be more than a StudentSolutions Manual. Thirty years of teaching experience have given me the ability toanticipate the types of errors and difficulties you may have while taking this course.Here I will show you some of the steps that are left out of the text, and most all ofthese steps in the included problems.There are several things you must do if you wish to be successful withmathematics:Attend every class.Read the book.Regardless of how clear and lucid your professor's lecture on aparticular topic may be, do not attempt to do the problemswithout first reading the text and studying the examples.It willserve to reinforce and clarify the concepts and procedures.Problems, problems...Problems,Problems,You must work problems every day; work the assigned problems;workproblems.LookovertheentireESSENTIALIDEAproblem set (even those problems which are not assigned).Ask questions when you are stuck (and you will get stuckthatis part of the process).Keepaskingquestionsuntilreceivinganswersthatareunderstandable to you.Today's calculators are good at obtaining answers, and if all thatis desired is an answer, then you have relegated yourself to thelevel of a machine.Do not work problems to obtain answers.Itis thethat are important.Even though a solutionsconceptsmanual is basically a “how to" document, always askawhyparticular approach was used, and understand the concept theproblem is illustrating.

Loading page image...

PREFACESTUDENT'S SURVIVAL AND SOLUTION MANUAL FORMathematics Its Power and Utility, Ninth EditionPage viFor the most part, this manual includes complete solutions to the odd-numberedproblems.Notice that the complete solutions for the self-tests are given at the endof the review sections in the textbook.

Loading page image...

STUDENT'S SURVIVAL AND SOLUTION MANUAL FORSECTION 1.1Mathematics Its Power and Utility, Ninth EditionPage1CHAPTER 1Arithmetic, Calculators, and Problem SolvingSURVIVAL HINT:If your instructor does not begin with Chapter 1, you might wish to take some timelooking over this chapter anyway.Please read page 1 of the textbook because it tells you what thispart of the book is all about.As you look through this first chapter you will notice that we coverfractions, decimals, and numeration systems.We also introduce you to using a calculator. If you havea manual for your calculator, do not attempt to read it; part of what this book will do is to teach you howto use a calculator to do the type of problems you are considering at the time.You may remembersome things about fractions, decimals, and numeration systems, or you may have forgotten more thanyou remember. That is ok;--- it is our job.... the book and your instructor have been assigned therelaxtask of making sure you understand the topic.Find out from your instructor what is expected of you.You will probably need a copy of thistextbook, pencils and paper, a straight-edge, and a calculator.(By the way, the cover for yourcalculator makes a good straight-edge.)Put your name and phone number inside the cover of yourcalculator, so if you lose it, it is, at least, possible that it be returned.As you begin on your mathematics journey, Bon Voyage!1.1 Math Anxiety, page 4SURVIVAL HINT:There are, of course, no right or wrong answers to Problems 1-25.In the book fromwhich these myths were obtainedthere is a whole chapter justifying that these are()Mind Over Mathmyths, and the authors cite specific studies to support their conclusions.As you do these problems,remember that ais a popular belief or tradition that has grown up around something which is anmythunfounded or false notion. Don't be afraid to express your own ideas when answering these questions.Problem Setpage 91.1,1.Write a couple of paragraphs about your math history. You are writing this for yourself,not for your teacher.2.Read the “Math Anxiety Bill of Rights” on page 6 and then make up your own list.3.When you see this stop signal, stop and study the material because it will be used later.4.When you see this caution sign, make a special note of the material next to the cautionsign, because it will be used throughout the rest of the book.5.The yield sign means that you will need to remember the result, but it is not necessary foryou to understand the derivation.6.The bump sign means that some unexpected or difficult material follows, and you willneed to slow down to understand the discussion.7-36.We will generally not give answers to those questions markedIN YOUR OWN WORDS.This problems do not have “right” or “wrong” answers, but rather are included to help youadvance your success in this course. Do you best to answer the question.

Loading page image...

CHAPTER 1STUDENT'S SURVIVAL AND SOLUTION MANUAL FORMathematics Its Power and Utility, Ninth EditionPage237.This sign means that a stop sign is ahead.39. This sign means that there is a roundabout ahead.41. This sign is used to mean a kangaroo crossing.43. This sign is used to designate a woman's rest room.45. This sign is used to designate a currency exchange service.47. This sign is used to designate a restaurant.49. Choice B, employment51. Choice A, announcements53.Choice E, recreation1.2 Formulating the Problem, page 11SURVIVALHINT:It is important that you pay attention to theagreement.Thisorder of operationsprocedure is used almost every day in this course. There are four main algebraic processes; these aresimplify evaluate, solve,factor.,andIn this section, we state, “Toa numerical expression meanssimplifyto carry out all the operations, according to the order of operations, and to write the answer as a singlenumber.”New Terms Introduced in this SectionAdditionCounting numberDifferenceDistributive propertyElementary operationsEstimationJuxtapositionNatural numberProductQuotientSimplify a numerical expressionNumerical expressionSumTranslationWhole numberProblem Setpage 181.2,1.a.b. Display:3.(1) Parentheses first(2) Multiplication and division, reading from left to right(3) Addition and subtraction, reading from left to right4.Distributive Property:(+) =+a bcabacSURVIVAL HINT:Take a look at the essential ideas of this section. There are two:1.State the order of operations.2.Explain the distributive property in your own words.Because these items are essential to your understanding of the material, we give the answer to all ofthe essential ideas in this.Your instructor may or may not assign theseproblems, butSurvival Manualit would be a good idea to designate a section of your notebookand then put intoESSENTIAL IDEASthis sectionof the essential ideas.all

Loading page image...

STUDENT'S SURVIVAL AND SOLUTION MANUAL FORSECTION 1.2Mathematics Its Power and Utility, Ninth EditionPage35. False; the error was to add first.7.2(3 + 4)23 + 24 is an example of the distributive property; what is shown here issimplification, so the statement is wrong.9.False; it is a whole number.11.a. Since the last operation was addition, we call this a.sumb. Since the last operation was addition, we call this a.sum13.a.126 + 32 + 35 Since the last operation was addition, we call this a.sumb. 5Since the last operation was division, we call this aquotient.15a..153+ Since the last operation was addition, we call this a.sumb. 3 Since the last operation was subtraction, we call this a.difference17 a..32 Since the last operation was addition, we call this a.sumb.8286456 Since the last operation was addition, we call this a.sum19 a..555 Since the last operation was addition, we call this a.sum

Loading page image...

CHAPTER 1STUDENT'S SURVIVAL AND SOLUTION MANUAL FORMathematics Its Power and Utility, Ninth EditionPage4b. 13Since the last operation was addition, we call this a.sum21 a. Since the last operation was addition, we call this a.sumb.19 Since the last operation was addition, we call this a.sum23 a..218 + 935236 + 310 Since the last operation was subtraction, we call this a.differenceb.2(18 + 9)352227352543 Since the last operation was subtraction, we call this a.difference25 a.b..3(4 + 8)34 + 387(9 + 4)79 + 7427 a..4(300 + 20 + 7) = 4300 + 420 + 47b.6(500 + 30 + 3) = 6500 + 630 + 6329 “The sum” means “” and “the product” means “”: 3 + 24. Parentheses are notnecessary because the order of operations requires that the product be done before the addition.31. “Times” means “” and “sum” means “”: 10(5 + 6)The parentheses are used to indicate the order of operations and they are also used toindicate multiplication.33. 85 + 10; if we wanted 8(5 + 10) we would need to say “Eight times the quantityfive plus ten.”35. 8(119); the difference requires parentheses for the correct order of operations.37. Press::716Display261Since the last operation was subtraction, we call this a.difference39. Press::Display800

Loading page image...

STUDENT'S SURVIVAL AND SOLUTION MANUAL FORSECTION 1.3Mathematics Its Power and Utility, Ninth EditionPage5Since the last operation was subtraction, we call this a.sum41. Press::Display1,080Since the last operation was subtraction, we call this a.sum43. Press:Don't forget the times sign for the indicated multiplication.:Display1,600Since the last operation was multiplication, we call this a.product45. Press::Display59Since the last operation was subtraction, we call this a.difference47. Press::Display2,700Since the last operation was subtraction, we call this a.difference49. Press::Display285,197Since the last operation was subtraction, we call this a.sum51. Press::since the last operation was subtraction, we call this a.Displaysum2,323;Estimates for Problems 53-60 may vary.53. Each day has 24 hours so we estimate8,000 We estimate this time to be 8,000 hours. The exact answer is 8,640 hours.55. We estimate,, We estimate the deduction to be $. The exact answer is $. 57. We estimate by assuming a 40 hour work week for 50 weeks a year:,00036,000 We estimate the annual salary to be $36,000. The exact answer is $37,440.59. We estimate00 We estimate we can drive 300 miles. The exact answer is 345 miles.1.3 Fractions and Decimals, page 19SURVIVALHINT:A fraction is an indicated division.For example,is one unit (the proverbial pie)12divided into two parts, so it isThis section is devoted to developing your number sense regarding .fractions.You may or may not have developed this number sense in previous arithmetic classes, butnow is a good time for a refresher.

Loading page image...

CHAPTER 1STUDENT'S SURVIVAL AND SOLUTION MANUAL FORMathematics Its Power and Utility, Ninth EditionPage6New Terms Introduced in this SectionApproximately equal to symbolColumn namesCommon fractionDecimalDecimal fractionDecimal pointDenominatorDivision by zeroFractionHundredImproper fractionMixed numberNumeratorPlace-value namesProper fractionRemainderRepeating decimalTenRational numberTerminating decimalTrailing zerosProblem Setpage 261.3,3.A fraction is a quotient of a whole number divided by a counting number.4a.b.c.d.e..110100100010000The answers are getting larger. Answers vary; it looks like the closer the divisor is to 0 thelarger the answer.5.The place value names (in decreasing order) are: trillions, hundred billions, ten billions,billions, hundred millions, ten millions, millions, hundred thousands, ten thousands,thousands, hundreds, tens, units, decimal point, tenths, hundredths, thousandths, ten-thousandths, hundred-thousandths, and millionths.SURVIVALHINT:Did you remember to look at theEven if they were not assigned,ESSENTIAL IDEAS?you should add these terms to your notebook:1. Fraction2. Common fraction/decimal fraction3. Division by 0 is not permitted.4. Place value names7.False; can't divide by 0.9.True; we can affix any number of trailing zeros.11. False; 0. 13. False; by calculator, the answer is appoximately 27.96709753.15.ab. proper;. proper;813172117ab...4219 a..= 516133Divideintoto obtain, with a remainder of.b.= 625144Divideintoto obtain, with a remainder of.c.= 1414111010Divideintoto obtain, with a remainder of. d.= 3Divideintoto obtain, with a remainder of.

Loading page image...

STUDENT'S SURVIVAL AND SOLUTION MANUAL FORSECTION 1.3Mathematics Its Power and Utility, Ninth EditionPage721 a..= 11Divideintoto obtain, with a remainder of.b.=1010Divideintoto obtain, with a remainder of.c.331=Divideintoto obtain, with a remainder of.d.=Divideintoto obtain, with a remainder of.23 a..=Divideintoto obtain, with a remainder of.b.=Divideintoto obtain c.=18Divideintoto obtaind.=Divideintoto obtain, with a remainder of.25 a.. b. 27 a.. b.512 29 a..= =b. 25531 a..= b. =33 a..1= b.2=1 35 a..= b.= 7SURVIVAL HINT:36-47In Problems, do not round the decimal representations. For example,13= 0.3_Note the bar over the three; this shows that the three repeats. It is NOT correct to write1133= 0.33333 or= 0.33or any other such representation.The three repeats and does not terminate.That is, in doing the longdivision, there is never a remainder of zero.37 a..= Long division;by calculator:5Continue with the division until you see the digits repeat. There is one repeating digit.b.=Long division;by calculator:Continue with the division until you see the digits repeat. There is one repeating digit.

Loading page image...

CHAPTER 1STUDENT'S SURVIVAL AND SOLUTION MANUAL FORMathematics Its Power and Utility, Ninth EditionPage839 a..= Long division;by calculator:Continue with the division until the remainder is zero.b.= Long division;by calculator:Continue with the division until you see the digits repeat. There is one repeating digit.41 a..= Long division;by calculator:Continue with the division until you see the digits repeat. There is one repeating digit.b.= Long division;by calculator:Continue with the division until you see the digits repeat. There is one repeating digit.43 a..= Long division;by calculator:5Continue with the division until you see the digits repeat. There is one repeating digit.b.= Long division;by calculator:Continue with the division until you see the digits repeat. There is one repeating digit.45 a..= Long division;by calculator:Continue with the division until you see the digits repeat. There is one repeating digit.b.=Long division;by calculator:Continue with the division until you see the digits repeat. There is one repeating digit.47 a..=Long division;by calculator:Continue with the division until the remainder is zero.b.3= 3 199Long division;by calculator:9Continue with the division until you see the digits repeat. There is one repeating digit.49 a..The square is divided into one hundred small parts, and we see 82 of them are shaded,soorof the square is shaded..The circle is divided into 8 parts and 5 parts are shaded;.b58SURVIVAL HINT:Your answers to Problems 50-51 may vary. Estimating is not an easy skill to learn,sorelax and do the best you can.51 a..The square is divided into one hundred small parts, and we see 63 of them are shaded,so 0.63 of the square is shaded.b.The square is divide into one hundred small parts and there are four small triangles,each pair of which can form a square so there is a total ofof those squares are not shared. Thus, the shaded portion isor 0.82 of the large square. SURVIVALHINT:Do not round the answers to Problem 53, but use the overbar to indicate therepeating decimals. If your calculator does not show a pattern, you must approximate the answer.

Loading page image...

STUDENT'S SURVIVAL AND SOLUTION MANUAL FORSECTION 1.4Mathematics Its Power and Utility, Ninth EditionPage953 a..Press::Answer: 0.715Display.466666666666.Press::Answer: 0.318b722Display.318181818181855. First, note that= 0.5:$52$52.5$5,25012 To multiply by 100, move the decimal point two places to the right.57. First, note that= 0.25:$ 2$ 2. 5$42.25$ 4$8,45014 To multiply by 100, move the decimal point two places to the right.59. First, note that= 0.125:$63$63.1258$6,312.5018 To multiply by 100, move the decimal point two places to the right.1.4 Rounding and Estimation, page 28SURVIVAL HINT:Take a look at the essential ideas. Add these ideas to your journal.New Terms Introduced in this SectionRounding moneyRounding numbersProblem Setpage 311.4,3.The rounding place digit is the name of the positional column to which the number is beingrounded.4.Estimation is making a reasonably accurate guess. It is important in everyday life in manysituations in which an exact answers is not needed. For example, when making a purchase,deciding on which route to take, how long a task may take to complete, or tipping at arestaurant.5. 30. 0 5 rounded to the nearest tenth is 30.1, so the statement is false. The error is that thenumber was rounded to the nearest unit, rather than the nearest tenth.7. 3,6 8 4,999 rounded to the nearest ten thousand is 3,680,000, so the statement is false. Theerror is that one was added to the rounding place digit and it should not have been.

Loading page image...

CHAPTER 1STUDENT'S SURVIVAL AND SOLUTION MANUAL FORMathematics Its Power and Utility, Ninth EditionPage109.23122510 = 250; estimate is correct.11. 2. 3 12 Rounding place digit is marked.2.3Digit to the right is a 1, so delete the “12”.13. 6,287.4 5 13Rounding place digit is marked.6,287.45Digit to the right is a 1, so delete the “13”.15. 5. 2 91Digit to the right is a 9, so add one5.3to the rounding place digit and delete the “91”.17. 6, 2 87.4513Digit to the right is an 8, so add6,300one to the rounding place digit and change the digits to the rightto zeros. Drop the zeros to the right of the decimal point.19. 12.8 1 97Digit to the right is a 9, so12.82add one to the rounding place digit and delete the “97”.21. 4.81 7 92Digit to the right is a 9, so4.818add one to the rounding place digit and delete the “92”.23. 4 .8199Digit to the right is a 8, so5add one to the rounding place digit and delete the “.8199”.25. $12.9 9 3Digit to the right is a 3, so$12.99delete the “3”.27. $14.9 9 8Digit to the right is a 8, so$15.00add one to the rounding place digit and delete the “8”. Note thatadding 1 to 9 causes a carry into the next column. That is,$14.99 + $0.01 = $15.00.29. 6 9 4.3814 Digit to the right is an 4, so690change the numerals to the right of the rounding place digit to zeros; thendelete those to the right of the decimal point.31. $8 6 ,125Digit to the right is an 1, so$86,000change the digits to the right of the rounding place digit to zeros.33. From the calculator display, we see 2/3 is represented as 0.66 6 6666667. The digit to theright is a 6, so add 1 to the rounding place digit and drop the digits to the right to obtain:0.667.35. From the calculator display, we see 2/17 is represented as 0.11 7 6470588. The digit to theright is a 6, so add 1 to the rounding place digit and drop the digits to the right to obtain:0.118.37. From the calculator display, we see 7/51 is represented as 0.13 7 254902. The digit to theright is a 2, so do not change the rounding place digit but drop the digits to the right toobtain: 0.137.39.260.3333333333; rounded answer: 0.333; by calculator:26

Loading page image...

STUDENT'S SURVIVAL AND SOLUTION MANUAL FORSECTION 1.5Mathematics Its Power and Utility, Ninth EditionPage1141.0.41666666666; rounded answer: 0.417; by calculator:51251243.0.3179916318; rounded answer: 0.318; by calculator:15247815247845. B: 4.825 mi, so it is about 10 miles round trip; 510 = 50.Think47. C: $35,000$36,000 and $36,00012 = $3,000.Think49. B: $1,000$1,200 and $1,20012 = $100.Think51. $15,00012= $1,250 ; by calculator:150001253.= $12.125 ; rounded answer: $12.13; by calculator:$1,818.751501818.7515055.$70.8333333 ; rounded answer: $70.83by calculator:$850128501257.$112.333333 ; rounded answer $112.33; by calculator:$674667461.5 Exponents and Prime Factorization, page 33SURVIVAL HINT:There are many ideas in this section which you will use daily in your future math work.Be sure you understand the concept of an exponent, and that of a prime factorization.New Terms Introduced in this SectionBaseCompositeCubedExponentExponential notationFactorFactoringFactorizationFactor treeGoogolPowerPowers of tenPrime factorizationPrime numberScientific notationSquaredProblem Setpage 391.5,3.An exponent is a number used to indicate repeated multiplication. In other words, it is thenumber of repeated factors. Init is the number.bnn4.A number is in scientific notation when that number is written as a power of 10 or as adecimal number between 1 and 10 times a power of 10.5.An excellent way to find the prime factorization is to use factor trees.6.Theis an exponent key and EE is used for scientific notation.yxSURVIVAL HINT:Take a look at the four preceding essential ideas. Add these ideas to your journal.7.ab.c.d.. one million1061010101010108.ab.c.d.. one thousand1031010109.a.b.c.d.one-tenth1010.110.ab.c.d.. one-hundredth10

Loading page image...

CHAPTER 1STUDENT'S SURVIVAL AND SOLUTION MANUAL FORMathematics Its Power and Utility, Ninth EditionPage1211. False;means.13. False;there are two multiplications (not three).15.a.In scientific notation, the decimal point goes after the first nonzero digit:3.210= 3,200Decide on the exponent by counting the number of decimal places necessary towrite this number, 3.2, as the given number. We see it is three places.Move the decimal point 3 places to the right.b.2.510= 25,000Move the decimal point 4 places to the right.c.1.810= 18,000,000Move the decimal point 7 places to the right.d.6.410= 640Move the decimal point 2 places to the right.17.a.4.2110= 0.0000Move the decimal point 6 places to the left.b.9.210= 92,000,000Move the decimal point 7 places to the right.c.110=Don't move the decimal point.d.1.510=Don't move the decimal point.19 a..“E9” means “10 ”, so 6.34E9 = 6.3410b.5.2019E11 = 5.201910c.“08” means “10 ”, so 4.093745 08 = 4.09374510d.8.291029292 128.2910292921021 a..7.210= 72,000,000,000Move the decimal pointplaces to the right.10b.4.510= 4,500Move the decimal pointplaces to the right.323 a..2.110= 0.Move the decimal pointplaces to the left.3b.4.610= 0. Move the decimal pointplaces to the left.725 a...10= Move the decimal pointplaces.b..10= Move the decimal pointplaces to the left.4

Loading page image...

STUDENT'S SURVIVAL AND SOLUTION MANUAL FORSECTION 1.5Mathematics Its Power and Utility, Ninth EditionPage1327 a.b.. 29 a..2.189282711021,892,827,100 b.0.0000329 070.000032910329 31. 33. 35.7 37 ab...(22)525 39 ab...2264222322222162222282222224222222222 41 ab...,2225252525252525101025 43 a..See which prime divides evenly into the given number. If it does not divide evenly,move to the next prime. If it does divide evenly, try that same number again.

Loading page image...

CHAPTER 1STUDENT'S SURVIVAL AND SOLUTION MANUAL FORMathematics Its Power and Utility, Ninth EditionPage14,7637779177713713 b.,1317,64113131,35713132359132359 45 a..Use your calculator and the list of primes to see which prime divides evenly into thegiven number. If it does not divide evenly, move to the next prime. If it does divideevenly, try that same number again.,192,407192983 b.,3196131313131 47. First estimate the number of seconds in a year:6060365246106103.651024663.6510Now multiply this number by your age (in years) to see that the most reasonable exponentis the one shown in choice A.49. Choice A is a penny, choice B is a dime, and choice C is a dollar; the best choice is C.51. Choice B is a very small number (and not even a possibility), and choice C is too large, sothe best choice must be A.53. 41,840,000 = 4.1841055. 3.3310= 333,00057 a..,,,,,,, By calculator,b. 59. NOTE: no calculator; this is an estimation problem.$$$$$$$$$$ $$$$+ $+ $+ $+ $1 + $$$$$$1 $$2$20 (Actual, with calculator is $

Loading page image...

STUDENT'S SURVIVAL AND SOLUTION MANUAL FORSECTION 1.6Mathematics Its Power and Utility, Ninth EditionPage151.6 Common Fractions, page 42SURVIVALHINT:You may have had problems with fractions in the past, but the emphasis here is onunderstanding fractions and learning how to use a calculator to help you with calculation involvingfractions.If you are feeling anxious about this topic, it may be time to take a break with some of theanxiety reducing techniques introduced in the first section of this book. Relax.... ask questions, and youwill succeed!New Terms Introduced in this SectionCancelingCompletely reduce fractionComplex decimalDivide fractionsFundamental property of fractionsInvertMultiply fractionsReciprocalReduced fractionReducing fractionsSimplify a fractional expressionProblem Setpage 481.6,3.Use the fundamental property of fractions (see the answer to Problem 1) to eliminate allcommon factors (other than 1 or1).4.A fraction is reduced when there is no number (except 1) that divides into both thenumerator and denominator.5.To multiply fractions, multiply numerators and multiply denominators.6.To divide fractions, invert and multiply.7.A terminating decimal is a fraction whose decimal representation ends.8.(1) Multiply the given number without its decimal point by the decimal name of the last digit.(2) By the decimal name of the last digit, we mean: one place is tenth, or; two places is110hundredth, or; three places is thousandth, or;.111001,0009. A reduced fraction is one in which there is no common factor (other thanand)between the numerator and denominator; this is true.11. F; 13.butThese results are different, so the statement isfalse.15.abcd....

Loading page image...

CHAPTER 1STUDENT'S SURVIVAL AND SOLUTION MANUAL FORMathematics Its Power and Utility, Ninth EditionPage1617 abcd.....3423141628531414243824523 19 abcd.....405485,6706721448,15051 21. Shade two of the five rows and three of the four columns.There are 6 of the 20 squaresthat are double shaded. This can also be stated as three-tenths of the large square.23. Shade four of the five rows and one of the three columns.There are 4 of the 15 squaresthat are double shaded.25. Divide the side into six parts and the top into three parts.Then, shade one of the six rowsand two of the three columns.There are 2 of the 18 squares that are double shaded. Thiscan also be stated as one-ninth of the large square.27. In this problem, you are verifying for yourself that division gives the same result as “invertand multiply.”a.The divisor is 5, and the answer is 3. Also, 15 b.The divisor is 3, the answer is 2. Also, 29. In this problem, you are verifying for yourself that division gives the same result as “invertand multiply.”a.The divisor is, and the answer is. Also, The divisor is, the answer is. Also,b. 31 a.b.. c.d. 71002014SURVIVAL HINT:Noteis reduced. You do not need to write this answer as the mixed number2e.f.

Loading page image...

STUDENT'S SURVIVAL AND SOLUTION MANUAL FORSECTION 1.6Mathematics Its Power and Utility, Ninth EditionPage1733 a.b.c.. d.e.f. 35 a.b.c.. d.e.f. SURVIVAL HINT:You may be able to do these mentally, any number divided by itself is.37 a.b.c.. d.e.f. 39 a.b.. c.d. e.f.

Loading page image...

CHAPTER 1STUDENT'S SURVIVAL AND SOLUTION MANUAL FORMathematics Its Power and Utility, Ninth EditionPage1841 a.b..1829 c.d. e.f. 43.abc. 0... ,45.a.bc ..,47.a.b.c. 161775016SURVIVAL HINT:You may know these answers from memory.49.a.b.c. 151.$$111010$, AGESALARY

Loading page image...

STUDENT'S SURVIVAL AND SOLUTION MANUAL FORSECTION 1.7Mathematics Its Power and Utility, Ninth EditionPage1953.$,$,111010$, AGESALARYSURVIVAL HINT:Translate the word “ofto mean multiply.”55.316$12,512 = $2,346By calculator:3 57. $227.00$ By calculator:59. $,$44,0002215$44,0005122$2,00022522$10,000 1.7 Adding and Subtracting Fractions, page 50SURVIVAL HINT:Thein the first two problems summarize what you need toESSENTIAL IDEASremember from this section.New Terms Introduced in this SectionCommon denominatorExtended order of operationsLCDLowest common denominatorSubtraction of fractionsProblem Setpage 561.7,1.Step 1Find the LCD.Step 2Change the forms of the fractions to obtain forms with common denominators.Step 3Add the numerators of the fractions with common denominators.3.This job would require at least two cuts, so the total is:2+ 5+ 7+ 5+ 5+ 7+ 5111324831642161616161617 171618 116

Loading page image...

CHAPTER 1STUDENT'S SURVIVAL AND SOLUTION MANUAL FORMathematics Its Power and Utility, Ninth EditionPage20The smallest single length is 18inches.5.(1) First, perform any operations enclosed in parentheses.(2) Next, perform any operations that involve raising to a power.(3) Perform multiplication and division, reading from left to right.(4) Do addition and subtraction, reading from left to right.6.Step 1Factor all given denominators into prime factors; write this factorization usingexponents.Step 2List each different prime factor you found in the prime factorization of thedenominators.Step 3On each prime in the list from Step 2, place the largest exponent that appears onthat prime factor anywhere in the factorization of the denominators.Step 4The LCD is the product of the prime factors with the exponents found in Step 3.7.False; do not add the denominators; the correct answer is+=.3478889.This problem and solution have no errors.11. This problem and solution have no errors.13. 1920140402=The correct response is A.15. 193201240104040 The correct response is D.17. If I multiply a number by a number larger than 1, the result is larger, but if I multiply anumber by a number smaller than 1, the result is smaller. The correct response is B.19. If I divide a number by a number larger than 1 the result is smaller, but if I divide a numberby a number smaller than 1, then the result is larger. The correct response is A.21 abc..+.+.+213358538555777111111SURVIVALHINT:A number isif there is no number other than 1 that divides into both thereducednumerator and denominator. This means, for example, the result in Problem 21b is reduced.d.ef3551299..+

Loading page image...

STUDENT'S SURVIVAL AND SOLUTION MANUAL FORSECTION 1.7Mathematics Its Power and Utility, Ninth EditionPage2123 a.b.c.. d.e.f. 525. Pick larger exponents for LCD. These are shown in boldface.LCDLCDa.b. c.d.LCDLCD2357 = 630 27. Pick larger exponents for LCD. These are shown in boldface.,LCD,LCD,a.b. c.d.LCD,LCD235, 29 ab..LCD is 6;.LCD is 24;++51525520156366682424

Loading page image...

CHAPTER 1STUDENT'S SURVIVAL AND SOLUTION MANUAL FORMathematics Its Power and Utility, Ninth EditionPage22.LCD is 24;LCD is 12;cd. .LCD is 30;. LCD is 12;ef 31 ab.c... 33 a..LCD23 LCDb.

Loading page image...

STUDENT'S SURVIVAL AND SOLUTION MANUAL FORSECTION 1.7Mathematics Its Power and Utility, Ninth EditionPage2335 a..LCD23 b. LCD37 a.. b. 39 a.b..

Loading page image...

CHAPTER 1STUDENT'S SURVIVAL AND SOLUTION MANUAL FORMathematics Its Power and Utility, Ninth EditionPage2441. Multiplication before addition:++4174784177859559559595145By calculator:Display:0.8Answer is 0.8 or.4543. Parentheses first:++ 2++ 24211210153515155225151 + 222633+283By calculator:Display:9.333333333Answer is 9.or.45. By calculator: Display:(This is an approximate answer.).448711614547. First find the regions labeled “B” and add up their areas: The first one at the left isof;1124The second one is at the right and isof:1132++11111124328613148364+342424+724 49. For this one, we find the portion that is not C. The C portion at the left isand the C14portion at the right isofor:++111312464362321212+512111326

Loading page image...

STUDENT'S SURVIVAL AND SOLUTION MANUAL FORSECTION 1.7Mathematics Its Power and Utility, Ninth EditionPage25Thus, the portion that is not C is: 1=57121251. This is the portion that is not B. From Problem 47, the portion that is B is. Thus, we724find1=717242453. We see the square is divided into three columns of equal size. We are looking for the partslabeled K: in the first column K isoforof that column; in the second column it is111323of that column; there is no K in the third column. Thus,111111163333189++ 0+121818+3181655. We see the square is divided into three columns of equal size. We are looking for the partslabeled Y: in the first column Y isof that column; in the second column it isof that1123column; there is no Y in the third column. Thus,11111112333369++ 0+321818+51857. R or G or Y is everything that is not K:1=1566The fact that K isof the square was found in Problem 53.16

Loading page image...

CHAPTER 1STUDENT'S SURVIVAL AND SOLUTION MANUAL FORMathematics Its Power and Utility, Ninth EditionPage2659 1+ 2+ 31+ 2+ 31213864321212126 17127 512The total weight is 7pounds.1.8 Hindu-Arabic Numeration System, page 58SURVIVALHINT:Thein the first three problems summarize what you need toESSENTIAL IDEASremember from this section.New Terms Introduced in this SectionAbacusExpanded notationHindu-Arabic numeralsNumberNumberNumeralNumeration systemProblem Setpage 611.8,1.A decimal numeration system refers to a numeration system with 10 symbols and rules forcombining those symbols to represent all numbers. If we refer to the decimal numerationsystem we use everyday then (1) there are ten symbols, (2) larger numbers are expressed interms of powers of 10, and (3) it is positional.3.A Hindu-Arabic numeral is one of the decimal numerals we use everyday: and.5.Ais an expression of quantity whereas ais a symbol used to represent anumbernumeralnumber.6.Expanded notation is writing a number by showing the meaning of each digit in thatnumber.78 a.b...ab. 100.6429.

Preview Mode

This document has 832 pages. Sign in to access the full document!

Report

Study Now!

Document Details

Related Documents

AP Calculus AB Scoring Guide Unit 6 Progress Check

Clinical Psychologist

Module 4 Matrices

MATH 1324 Homework 5 Answers

Ap progress 1 5 all 5

The Fundamental Theorem of Calculus and Definite I

AP Calculus AB Scoring Guide

Investigating the Rising Cost of MTA Transit Fare

Module 11 Geometry

AP Calculus AB Unit 5 Progress Check Scoring Guide

Company

Explore

Study Tools