Solution Manual for Basic College Mathematics, 10th Edition

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SOLUTIONSMANUALBEVERLYFUSFIELDBASICCOLLEGEMATHEMATICSTENTHEDITIONMargaret L. LialAmerican River CollegeStanley A. SalzmanAmerican River CollegeDiana L. HestwoodMinneapolis Community and Technical College

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Table of Contents1Whole Numbers.............................................................................................................................11.1Reading and Writing Whole Numbers • .........................................................11.2Adding Whole Numbers • ..............................................................................21.3Subtracting Whole Numbers • ........................................................................91.4Multiplying Whole Numbers • .......................................................................161.5Dividing Whole Numbers • ............................................................................241.6Long Division • ..............................................................................................30Summary Exercises• ......................................36Whole Numbers Computation1.7Rounding Whole Numbers • ...........................................................................381.8Exponents, Roots, and Order of Operations • .................................................461.9Reading Pictographs, Bar Graphs, and Line Graphs • ....................................501.10Solving Application Problems • .....................................................................52Chapter 1 Review Exercises • .........................................................................63Chapter 1 Mixed Review Exercises • .............................................................71Chapter 1 Test • ...............................................................................................732Multiplying and Dividing Fractions.......................................................................................... 762.1Basics of Fractions • .......................................................................................762.2Mixed Numbers • ............................................................................................772.3Factors • ..........................................................................................................842.4Writing a Fraction in Lowest Terms • ............................................................91Summary Exercises• ............................................................95Fraction Basics2.5Multiplying Fractions • ...................................................................................972.6Applications of Multiplication • ..................................................................... 1012.7Dividing Fractions • ........................................................................................ 1052.8Multiplying and Dividing Mixed Numbers • .................................................. 110Chapter 2 Review Exercises • ......................................................................... 116Chapter 2 Mixed Review Exercises • ............................................................. 119Chapter 2 Test • .............................................................................................. 120Cumulative Review Exercises (Chapters 1–2) • ............................................. 1223Adding and Subtracting Fractions.......................................................................................... 1253.1Adding and Subtracting Like Fractions • ....................................................... 1253.2Least Common Multiples • ............................................................................. 1273.3Adding and Subtracting Unlike Fractions • .................................................... 1333.4Adding and Subtracting Mixed Numbers • ..................................................... 138Summary Exercises• ........................................... 148Operations with Fractions3.5Order Relations and the Order of Operations • ............................................... 151Chapter 3 Review Exercises • ......................................................................... 157Chapter 3 Mixed Review Exercises • .............................................................. 161Chapter 3 Test • .............................................................................................. 163Cumulative Review Exercises (Chapters 1–3) • ............................................. 165

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4Decimals.....................................................................................................................................1684.1Reading and Writing Decimal Numbers • ...................................................... 1684.2Rounding Decimal Numbers • ........................................................................ 1714.3Adding and Subtracting Decimal Numbers • ................................................. 1764.4Multiplying Decimal Numbers • ..................................................................... 182Summary Exercises• ............................ 188Adding, Subtracting, and Multiplying Decimal Numbers4.5Dividing Decimal Numbers • ......................................................................... 1904.6Fractions and Decimals • ................................................................................ 200Chapter 4 Review Exercises • ......................................................................... 206Chapter 4 Mixed Review Exercises • .............................................................. 210Chapter 4 Test • .............................................................................................. 212Cumulative Review Exercises (Chapters 1–4) • ............................................. 2135Ratio and Proportion................................................................................................................2175.1Ratios • ........................................................................................................... 2175.2Rates • ............................................................................................................. 2215.3Proportions • ................................................................................................... 2255.4Solving Proportions • ...................................................................................... 229Summary Exercises• .................................... 234Ratios, Rates, and Proportions5.5Solving Application Problems with Proportions • .......................................... 237Chapter 5 Review Exercises • ......................................................................... 243Chapter 5 Mixed Review Exercises • ............................................................. 247Chapter 5 Test • .............................................................................................. 249Cumulative Review Exercises (Chapters 1–5) • ............................................. 2506Percent....................................................................................................................................... 2546.1Basics of Percent • .......................................................................................... 2546.2Percents and Fractions • .................................................................................. 2586.3Using the Percent Proportion and Identifying the Componentsin a Percent Problem • .................................................................................... 2656.4Using Proportions to Solve Percent Problems • ............................................. 2716.5Using the Percent Equation • .......................................................................... 279Summary Exercises• ....... 284Using Percent Proportion and Percent Equation6.6Solving Application Problems with Percent • ................................................ 2866.7Simple Interest • ............................................................................................. 2936.8Compound Interest • ....................................................................................... 298Chapter 6 Review Exercises • ......................................................................... 303Chapter 6 Mixed Review Exercises • ............................................................. 307Chapter 6 Test • .............................................................................................. 309Cumulative Review Exercises (Chapters 1–6) • ............................................. 311

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7Measurement.............................................................................................................................3157.1Problem Solving with U.S. Measurement Units • .......................................... 3157.2The Metric System—Length • ........................................................................ 3227.3The Metric System—Capacity and Weight (Mass) • ...................................... 325Summary Exercises• .......................... 330U.S. and Metric Measurement Units7.4Problem Solving with Metric Measurement • ................................................ 3317.5Metric–U.S. Measurement Conversions and Temperature • .......................... 334Chapter 7 Review Exercises • ......................................................................... 338Chapter 7 Mixed Review Exercises • ............................................................. 340Chapter 7 Test • .............................................................................................. 342Cumulative Review Exercises (Chapters 1–7) • ............................................. 3438Geometry................................................................................................................................... 3478.1Basic Geometric Terms • ................................................................................ 3478.2Angles and Their Relationships • ................................................................... 3488.3Rectangles and Squares • ................................................................................ 3508.4Parallelograms and Trapezoids • .................................................................... 3558.5Triangles • ....................................................................................................... 3588.6Circles • .......................................................................................................... 361Summary Exercises• ........................... 366Perimeter, Circumference, and Area8.7Volume • ......................................................................................................... 3688.8Pythagorean Theorem • .................................................................................. 3718.9Similar Triangles • .......................................................................................... 375Chapter 8 Review Exercises • ......................................................................... 380Chapter 8 Mixed Review Exercises • ............................................................. 384Chapter 8 Test • .............................................................................................. 386Cumulative Review Exercises (Chapters 1–8) • ............................................. 3889Basic Algebra.............................................................................................................................3919.1Signed Numbers • ........................................................................................... 3919.2Adding and Subtracting Signed Numbers • .................................................... 3939.3Multiplying and Dividing Signed Numbers • ................................................. 4029.4Order of Operations • ..................................................................................... 406Summary Exercises• ................................ 413Operations with Signed Numbers9.5Evaluating Expressions and Formulas • ......................................................... 4159.6Solving Equations • ........................................................................................ 4199.7Solving Equations with Several Steps • .......................................................... 4299.8Using Equations to Solve Application Problems • ......................................... 438Chapter 9 Review Exercises • ......................................................................... 447Chapter 9 Mixed Review Exercises • ............................................................. 453Chapter 9 Test • .............................................................................................. 455Cumulative Review Exercises (Chapters 1–9) • ............................................. 457

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10Statistics..................................................................................................................................... 46110.1Circle Graphs • ............................................................................................... 46110.2Bar Graphs and Line Graphs • ........................................................................ 465Summary Exercises• ......................................................................... 468Graphs10.3Frequency Distributions and Histograms • ..................................................... 46910.4Mean, Median, and Mode • ............................................................................ 470Chapter 10 Review Exercises • .......................................................................4Chapter 10 Review Exercises • ....................................................................... 474Chapter 10 Mixed Review Exercises • ........................................................... 476Chapter 10 Test • ............................................................................................ 477Cumulative Review Exercises (Chapters 1–10) • ........................................... 479Appendix: Inductive and Deductive Reasoning• ......................................................... 483

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1.1Reading and Writing Whole Numbers1CHAPTER 1WHOLE NUMBERS1.1Reading and Writing WholeNumbers1.1Margin Exercises1.(a)$%#is in theplace.%tens(b)("%is in theplace.%ones(c)%(*is in theplace.%hundreds2.The place value of each digit:(a)14,2181: ten-thousands4: thousands2: hundreds1: tens8: ones(b)460,3294: hundred-thousands6: ten-thousands0: thousands3: hundreds2: tens9: ones3.The digits in each period (group) of$ #&" '!* $#),,,:(a)is in the billions period.$is in the millions period.(b)#&"is in the thousands period.(c)'!*is in the ones period.(d)$#)4.(a)is eighteen.")is thirty-six.(b)$'is four hundred eighteen.(c)%")is nine hundred two.(d)*!#5.(a)is three, onefour.$"!%thousandhundred,is ninety-five, three hundred(b)*& $(#thousandseventy-two.,,is one hundred million, seventy-(c)"!! !(& !!#five thousand, two.,,,is eleven(d)"" !## !%! !!!billion, twenty-twomillion, forty thousand.6.thousand, four hundred thirty-seven is(a)One"%$(.hundred seventy-one thousand, six is(b)Nine*(" !!'Þ,hundred twenty-(c)Eighty-two million, threefive is,,.)# !!! $#&7.(a)The U.S. population in the 2015 column is$25 million and is written in digits as$!!! !!!25,,.The estimated U.S. population in the 2020(b)column is41 million and is written in digits as$$!!! !!!41,,.The household income in 2010 was $ 6,326(c)%and is written in words as forty-six thousand,three hundred twenty-six dollars.(d)The estimated average yearly salary in 2020is $ 6,169 and is written in words as thirty-six$thousand, one hundred sixty-nine dollars.1.1Section Exercises1.The digit in the hundreds place in the wholenumberis.$ '&!!(c)2.The digit in the ten-thousands place in the wholenumber,is." % ')"$$(b)3.,; ten-thousands:; hundreds:"!)"&"!4.,:; ones:)#' $$)#; ten-thousands5.,,,;thousands:( '#&*")$#)#millions:;)6.,,,;"!(!##& !"'billions:;"millions:!7.The digits in the thousands period in the wholenumber,,are.&&#$")')(')(8.The digits in the millions period in the wholenumber,,,are.*(%)(' &#)$#"$#"9.thousands:; ones:$ &'" %$&,,; millions:;$&'"%$&10.,,,"!! #&) "!! !!'; billions:;"!!millions:;#&)thousands:; ones:"!!'11.Evidence suggests that this is true. It is commonto count using fingers.

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2Chapter 1Whole Numbers12.No doubt there is a relationship here. Oneanswer might be that people could count usingtheir fingers and toes and, therefore, thought ofthem as numbers or digits.13.,is twenty-three thousand, one hundred#$ ""&fifteen. The statement isfalse(no "and").14.,is thirty-seven thousand, eight hundred$( ))'eighty-six. The statement istrue.15.,is three hundred forty-six,$%' !!*thousandnine.16.,is two hundred eighteen,#") !$$thousandthirty-.three17.,,is twenty-five#& (&' ''&million, seven hundredfifty-six thousand, six hundred sixty-five.18.,,is nine hundred ninety-nine*** **$ !!!million,nine hundred ninety-three thousand.19.Sixty-three thousand, one hundred sixty-three is'"$'$,Þ20.Ninety-five thousand, one hundred eleven is*"Þ& "",21.Tenhundred twenty-three ismillion, two"! !!! ##$,,.22.One hundred millionhundred is, two"!! !!! #!!Þ,,23.Seventy-ninehundred eightymillion, sixthousand in digits is 79,680,000.24.Two hundred-three thousand in digits isforty#%$ !!!Þ,25.Fifty million, fifty-one thousand, five hundredseven in digits is,,.&! !&" &!(26.Fifty-two thousand, eight hundred in digits is52,800.27.Fifty-four million, seven hundred fifty thousandin digits is,,&% (&! !!!Þ28.Two hundred twenty-one thousand in digits is##" !!!Þ,29.Eight hundred trillion, six hundred twenty-onemillion, twenty thousand, two hundred fifteen indigits is,,,,.)!! !!! '#" !#! #"&30.,3,,is twohundred fifty-#&$ )*' %%)billion, threethreehundred ninety-six thousand,million, eightfour hundred forty-eight.31.The least used method of transportation is publictransportation.,,in words is six' !'* &)*million,sixty-nine thousand, five hundred eighty-nine.32.From the table, "drive alone" is the method oftransportation most used.,,written out)% #"& #*)is eighty-fourhundred fifteenmillion, twothousand, two hundred ninety-eight.33.The number of people who walk to work or workat home is,,. In words,,,is( )*% *""( )*% *""written as sevenhundred ninety-million, eightfour thousand, nine hundred eleven.34.From the table, the number of people whocarpool is,,. Written in words,"& $(( '$%"& $(( '$%,,is fifteenhundredmillion, threeseventy-seven thousand, six hundred thirty-four.1.2 Adding Whole Numbers1.2Margin Exercises1.;(a)#  ' œ' œ)#)(b);*  & œ "% &  * œ "%;(c)%  ( œ "" (  % œ ""2.(a)$)$  ) œ ""&""  & œ "'%"'  % œ #! '#!  ' œ #'#'(b)&'&  ' œ ""$""  $ œ "%#"%  # œ "' %"'  % œ #!#!(c)*'*  ' œ "&)"&  ) œ #$(#$  ( œ $! $$!  $ œ $$$$(d)$)$  ) œ ""'""  ' œ "(%"(  % œ #" )#"  ) œ #*#*

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1.2Adding Whole Numbers33.(a)(b)#'&$% ($ #'&**(**,,,(c)%# $!& "" &'$&$ )')4.ones andonesones(a)'' # ( '(œ "$$"*(b)&) $ $ )$œ ""* ""ones andonesonesones andonesones(c)&' $ ( '(œ "$* $"ones andonesones(d)$% % * %*œ "$) $"5.,(a)%" # "" '#% #( "$( # ) *( '"$"(),(b)( ) #"%$ &( #$! & " '* $"! $# '# # "6.(a))"'$'$"(#& ('&%))&(,,,(b)"& )#*('&()"&*( "$ "(*#* ))#7.The shortest route from Lake Buena Vista toConway is as follows:%'$Lake Buena Vista to Resort AreaResort Area to Pine CastlePine Castle to Belle IsleBelle Isle to Conwaymiles'"*8.The next shortest route from Orlando to ClearLake is as follows:&)&'(Orlando to Pine HillsPine Hills to Altamonte SpringsAltamonte Springs to CasselberryCasselberry to BerthaBertha to Winter ParkWinter Park to Clear Lakemiles ($)9.feet&#'###*(&#' #*("'%'The amount of fencing needed isfeet,"'%'which is the perimeter of (distance around) theproject.10.correct(a)'$%* #)"!%correct(b)*#($*&'% #&""'$(

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4Chapter 1Whole Numbers(is incorrect.)(c)(*#")( '$**%$*&$,,,,(,is incorrect.)(d)#" )*#"" (%' %$ *#&(( &'$(* &'$1.2Section Exercises1.%$ &%*(2.") ""#*3.&' $$)*4.)$ "&*)5.$"( &(#))*6.&(% $#&)**7.$")"&" %#!))*8."$&#&$ %"!(*)9.'$"!#&# "##$(()&10."#"&(!& $"'$)*)*11.Line up the numbers in columns. Then start at theright and add the ones digits. Add the ten digitsnext, and, finally, the hundreds digits.correct*$#%% '"$"&)*12.Line up:(is incorrect.)&"("$" #&!)*)"!*)13.Line up:(is incorrect.)"#&"%$"" #""%('('(')'14.Line up:correct$#%""&"$ #!"%'(')15.Line up:,,,,"# "%#%$ #!" #$ "!$() %%'16.Line up:,,,,%" "#%"# $!# #$ &!!(' *#'17.Line up:$#"$ &("&)*#)18.Line up:'$%% "'&&(***19.Line up:,,,$) #!% #" !#!&* ##%20.Line up:,,,'$ #&" $' $!&** &&'

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1.2Adding Whole Numbers521.correct)( ' $"& !"22.(is incorrect.)"* *#""""!""23.correct)' ' *"& &"24.(is incorrect.)$( ) &"# #"$#"25.(is incorrect.)%( ( %"# """""26.*( ( *"( '"27.'( ( )"% &"28.*' % ("% $"29.($ #*"!#"30.') $ ("! &"31.( %' *! &"'& ""32.' #" $& **) !"33.$ !' )% )""& %"34.( *) #! '"!! %" "35.#() " $&% "$" "36."(# "&'$#)"37.* #) )% $"(( ""38.' )' ( # '"% " #" "39.& #' ) ) %"% " !" "40.""' )*("!"$" "41.$&(% # )"(' $*"""42.,' )(" ( &#)"% $**"43.,( ) *'$ (# )"" '# %" " "44.,* $)#( &)'"' *')"45.,* ' #&( *) '"( '" "" " "

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6Chapter 1Whole Numbers46.,& (")& '#$( %$'") (((""47.,* ! &'( )' !) *($ ""& *& %# #48.,% ! ##(! *) '# "$ ("$ $) *""49.Step 1: Add the digits in the ones column.Add the digits in the tens column,Step 2:including the regrouped.#Add the hundreds column, including theStep 3:regrouped."Add the thousands column, including theStep 4:regrouped.",*!" " #")(!)* #)''$'"! '%)50.," ( !)$# "' ") *# '"" !" '#""51.,*"""% ##' !( %%$ &) '' $"& &* %52.,' & !&"( $( !% %"' )"$ )* !" #53.,*""$ #"* '! $)# "" '! %"" && (54.,( ' $"& *) $($ '&! &"% "' ## " #55.,# " !*' $" '$* )) ("# !( )" " #56.#" " $$ ##' &! )* $(% &" ) # !! &* '* "57.*# $ $& &$* (# (( #%$ (' $$# )% #& !58.$" )()" !&# (( '# '' &$" (( &) ## # $

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1.2Adding Whole Numbers759.,*##"%"$)&* *"*'!#$"" #")"# #')60.,*$ $ #&('( *$%'!()"& *')$(""& '*!61.Add up to check addition.correct#!*")$#%') (*"#!*"62.Add up to check addition.incorrect; should be('*"(*#"% $('(&*('*63.Add up to check addition.correct")&($#')&# '(*")&(64.Add up to check addition.incorrect; should be""#!"(#*'("$ *%"##!""#!65.Add up to check addition.correct&%#!%("$#)'"& '%&%#!66.Add up to check addition.,,correct"" &)$$ '#)(#&'% ( $"*"" &)$67.Add up to check addition.,,incorrect; should be,"" &(('()( *&#&'(") # "($"" $(("" &((68.Add up to check addition.,,correct"" #"#&"') ('!#%")* " (#$"" #"#69.Add up to check addition.,,correct"% $$#%("%#((())() '$'"% $$#

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8Chapter 1Whole Numbers70.Add up to check addition.,,incorrect; should be,"' (!*' ("&#)$* '"("$ )""' ("*"' (!*71.Changing the order in which two numbers areadded does not change the sum. You can addtwo numbers from bottom to top when checkingaddition.72.Changing the grouping of the addends in anaddition problem does not change the sum. Forexample, you can add pairs of numbers that addto."!73.The shortest route between Southtown and Renais through Thomasville.#" "#$$Southtown to ThomasvilleThomasville to Renamiles74.The shortest route from Elk Hill to Oakton isthrough Thomasville.") "($&Elk Hill to ThomasvilleThomasville to Oaktonmiles75.The shortest route between Thomasville andMurphy is through Rena and Austin."#"& ""$)Thomasville to RenaRena to AustinAustin to Murphymiles76.The shortest route from Murphy to Thomasvilleis through Austin and Rena."""& "$)Murphy to AustinAustin to RenaRena to Thomasvillemiles277.To find the total amount raised, add the amountsraised at each event.$,$,$ %)# "# )'!"' $%#flea marketannual auctiontotal amount raised78.")& "#*$"%hot dogshamburgerstotal items sold79.%"$ #)''**womenmentotal people80.#)$ #")&!"employeesemployeestotal employees81.,,"$ ()'$ %*( # )(%#! "&(on-campus dayon-campus nighton-linetotal students82.))(##$%'&')$&*(#"% ")"(%))'$ $total tornadoes83.To find the perimeter, add the lengths of the%sides in any order.feet$#&"'!$#& "'!*(!feet is the total distance around the lot.*(!84.To find the perimeter, add the lengths of the%sides in any order.feet%)$#%) $#"'!Maria will needfeet of gutters."'!85.To find the perimeter, add the lengths of the$sides in any order.feet$!#% ")(#Martin will needfeet of lumber.(#

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1.3Subtracting Whole Numbers986.To find the perimeter, add the lengths of the%sides in any order.meters%'&&($%*) &($#"!*meters of fencing will be needed.#"!*87.The largest four-digit number possible, using thedigits,,, andeach once, will begin with the% " *#largest digit in the thousands place and theremaining digits will descend in size until thesmallest digit is in the ones place. Therefore, thelargest four-digit number possible is.*%#"88.The smallest four-digit number possible, usingthe digits,,, andeach once, will begin with% " *#the smallest digit in the thousands place and theremaining digits will ascend in size until thelargest digit is in the ones place. Therefore, thesmallest four-digit number possible is."#%*89.The largest five-digit number possible, using thedigits,, andat least once, will use the largest' #(digit in the ten-thousands, thousands, andhundreds place and the remaining digits willdescend in size until the smallest digit is in theones place.Therefore, the largest five-digitnumber possible is,.(( ('#90.The smallest five-digit number possible, usingthe digits,, andat least once, will use the' #(smallest digit in the ten-thousands, thousands,and hundreds place and the remaining digits willascend in size until the largest digit is in the onesplace.Therefore, the smallest five-digit numberpossible is,.## #'(91.The largest seven-digit number possible is* **% %$$,,.92.The smallest seven-digit number possible is$ $$% %**,,.93.To write the largest seven-digit number possible,using the digits,, and, and using each digit% $*at least twice, write the largest digits on the left,and use the smaller digits as you move right.94.To write the smallest seven-digit numberpossible, using the digits,, and, and using% $*each digit at least twice, write the smallest digitson the left, and use the larger digits as you moveright.1.3 Subtracting Whole Numbers1.3Margin Exercises1.(a):)  # œ "!"! œ )"! œ#)#or:(b)(  % œ """"  ( œ %""  % œ (or:(c)"&  ## œ $($(  "& œ ##$(  ## œ "&or:(d)#$  && œ ()()  && œ #$()  #$ œ &&or2.:(a)(  & œ #( œ & ( œ #  &#or(b):*  % œ &* œ %  &* œ &  %or:(c)#"  "& œ '#" œ "&  '#" œ '  "&or:(d)&)  %# œ "'&) œ %#  "'&) œ "'  %#or3.onesonesonetenstenstens(a)(%% $œ " %$( %œ $$"onesonesonestenstenstens(b)')) %œ % #%' #œ %%%(c)%#* $")"""(d)$*#( #'"%"$"$4.(a)('%& %&$"SubtractionAdditionproblemproblem$"('is correct.Match:$"(b)&$## ## #"#"%$SubtractionAdditionproblemproblemis incorrect.Not a match:#"(continued)

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10Chapter 1Whole NumbersRework.&$## ## $"$"&$SubtractionAdditionproblemproblemis correct.Match:$"(c)$(%#&" #&" ""$""$$'%SubtractionAdditionproblemproblemis incorrect.Not a match:""$Rework.$(%#&" #&" "#$"#$$(%SubtractionAdditionproblemproblemis correct.Match:"#$(d)(&$" %$!"$#$!Subtractionproblem%$!" $#$!(&$"Additionproblemis correct.Match:$#$!5./ /(a)& ) " *$ *%")/ /(b)) ' $ )% )("'/ /(c)% " # (" %$""/ /(d)) ' $% ()" '&"$/ /(e)( ' # "& ('! &&"#6./ /(a)* # (% $%)"#) )///(b)' ( &) '& ) *& "'"&/ //(c)% ( ( $ ) *) )$ "'"(/// /(d)" % " (* ) )% # *! "$"!"(8 7/ //(e)7"'$ * $ ) * #% ) % ("$7./ ///(a)# ! ' " ( (# *" *"!"'/ ///(b)( ! $ % " &# ) )' *"!"$/ ///(c)( ! # % # ' $ #% $ * #' *"!"#8./ ///(a)$ ! ) " & **# *"!")" %/ /(b)& ( ! $ ' )# ! #' "!/ ///(c)" & ( !* ) $& ) (! "%"'"!/ /////(d)( ! ! " & " * $" ) ! )' * *"!"!""4/ /////(e)$ * *! ! ! " ( ) ## # " )"!"!"!

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