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76PRACTICETEST1ANSWERSANDEXPLANATIONS = 4 3 π 64 27 = 256 81 π Recallthat π = approx.3.14,so 256 81 (3.14) isabout9.92,or10whenroundedtothenearest cubicinch. 12.ThecorrectanswerisF. Theprobabilitythatthe gumballchosenwillNOTbegreenwhenthereare 6yellowgumballs,5greengumballs,and4red gumballsisthenumberoffavorableoutcomes(the numberoftimesayelloworredgumballcanbe chosen)dividedbythenumberoftotaloutcomes (thetotalnumberofgumballs).Thenumberof favorableoutcomesis10becausethereare6yel- lowgumballsand4redgumballs.Thetotalnumber ofoutcomesis6 5 4,or15.Thustheprobability ofthegumballNOTbeinggreenis 10 15 ,whichcan bereducedto 2 3 . AnswerchoiceGisincorrectbecauseitisthe probabilitythatachosengumball will begreen. 13.ThecorrectanswerisD. Tondthenumberof sportsawardsearned,multiplythenumberofpar- ticipantsineachsportbytheratioforthatsport, andthenaddthese4products.Thisisamatrix multiplication,asshownbelow: [ 25305080 ] 0.2 0.5 0.3 0.4 = 25(0.2) 30(0.5) 50(0.3) 80(0.4) = 5 15 15 32 = 67 14.ThecorrectanswerisG. Tondtheaveragenum- berofstudentspersectionenrolledinUSHistory, ndthetotalnumberofstudentsinallsectionsand dividebythenumberofsections.Add25 29 24 toget78,thendivideby3.Thisresultsinan averageof26studentsenrolledpersectioninUS History. IfyouselectedanswerchoiceF,youfoundthe median,ormiddlenumber(whichisnotalwaysthe average),of24,25,and29. 15.ThecorrectanswerisB. Thetotalnumberof booksavailableis(30 − 3) (30 − 5),or27 25, whichis52.Tondtheclassperiodsforwhich therearenotenoughbooks,ndthetotalnumber ofbooksneededforeachperiod,asgiveninthe tablebelow. PERIOD 1 2 3 4 5 BOOKSNEEDED 23 49 56 50 27 Theonlyentryinthetablewithmorethan52 is56forperiod3. IfyouselectedanswerchoiceE,youprobably used60asthenumberofavailablebooksanddid nottakeintoaccountthe8missingbooks. 16.ThecorrectanswerisG. Becausethesumofeach rowisequivalent,thesumofrow1isthesameas thesumofrow2. Row1:( − 4 x ) 9 x 2 x = 7 x Row2:7 x ? ( − 3 x ) = 4 x ? Thequestionmarkmustrepresent3 x ,because 7 x = 4 x 3 x .Youcouldalsoperformthesecal- culationsusingthesumvaluesincolumn1and column2. IfyouselectedanswerchoiceK,youmayhave thoughtthateachsummustbe0andfoundthat − 4 x wouldmakethesumsofrow2andcolumn2 equal0. 17.ThecorrectanswerisE. The x -coordinateis positiveif A istotherightofthe y -axis.The y -coordinateispositiveif y isabovethe x -axis. Thetablebelowshowsthesignof x andthesign of y inthefourquadrants. QUADRANT SIGNOF x y I II − III − − IV − ThusthesignsarethesameinQuadrantsIand IIIonly. 18.ThecorrectanswerisJ. Tondthenumberof distinctcompletemealsthatReggiecanmakefrom 5differententrees,4differentsides,and6different desserts,multiplythequantitiesinthe3different groupstogether.Thus,thereare(5)(4)(6),or120 distinctmealsthatReggiecanmake.Thegure belowshowsthatforeachmeal,thereare4sides, andforeachsidethereare6desserts.
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