• lJCket lhar. aAowsyou 10 00 3 of these 1ICIivities. III howmanydifferenl ways C8fl you go103 of these adMties?
.. Shawn, $con. Rip. Trish. and Yoshi 8fe
finalists in • drawing lor e trip 10Weier Wond. TwowOneI1i wi. be picked at I1l1ldom.. How many different pairscoold go to WaterWoOd?
Chapter 20 Lesson 4 537
Mixed Problem Solving
SOl.... ShoWyour work.Tell what slral"SlYyou
.-1. wendy. Barbarll.HoYiard.and Marvin are the
lOP lour finishers in a lace. Barbaol is not flf$l or second.MaMn flflishes afterBarbara.Howatd finishes before Wendy. wtXIis ineactl of thetop lour places?
.. Numbercards for the numbers 3. 4, S. 6, 7.8.
9.and 10lifeplaced facedown on • table.
Suppose you wm up hWIcards. Howm8l1)'
different pairsof numbers are possibk?
8. Mr. Willard has 8 bills in his wallet. The bib are $10.$5, and$1. IfMr. Winard has $29.
what bills does he have in his wallet?
'bIlhoose
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1i!!I Data UHthe graph to solve Problem, 10-13.
Tile graph shows the number of game tickets
lhal ellch of lour students sold.
10. How many mOl"etickets did Daisy sell than Evan?
11. A game ticket sells for$2_95. About how many cloIlafsworth of gametickets did MyrIsell?
12. How many game Iickets did the four Slooenls sell in811 How many dollars 'Mll1h oIlickets is this?
11 lasl: year.Geofge'slicket sales¥IIIefe 20"4 greater then lis IotaI $hooMl in the graph.
How manytickets did Geotge seI lastyear?
-
Game Tickets Sold
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14. Sieml. GaWI.Kayla,.Jacob. and Amanda can tutortome thin:l-grade students in math. Only
2 tulOBare needed. Howmanydifferent pairs of lllIOBcan !herebe?Explain how you
found your answer.
538
Problem Solving on Tests
E.tcndcd Re'pon,e ChooMthe letteroIlhe cowtet answer.
" . correct aI"Aer Isno! here,choose NH.
I. What is the missing angle measure?
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A W e 160"
170ã oNH
1 .. M....urem.<1t A rog thaim : ores 2 j yards by 3 yardsmsts S540. Another
; lUll Ihat measures5 leet by8 feet costs
l $360. Whicto I\l{I has • tligher price pel"
1 square fOOl. of area?
i expl.ln How did you lind your 8nswe(;'
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Chapter 20 LIl$$Ofl 4 539
&-18: ~ inctI. 10!MI
• What are me actualdimenIiomDIme
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b You need toincludea aqu.lIIr, planting area whose actual sides measure 30 leet.
What will be the dimensionsof the square inthe drawing?
~ Suppose you have10deti(jn • new
~rd&n whose dimenslons are 75% 01 me Ieogth and75%ofmewidlhDI !he
garden pictunld.What wiI bra the aetuaJ dimensoons01 me ~ ~rden?
d W. me poItOO" definingthe Ihape Dllhe
~ ~rden[In pII<lcl and thaI Dllhe origi1eII garden besimilaI'? ~
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5. You ereusing the plan below todesign a
~rdef1. Usean inchrulertomeasure me scaledrawingand helpyou ~te this
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Open Response
3. A restaurant has 3 tables. Each table can seat 1 person on each end and 3 people alongeach of the othersides.
Theends ofthe !abies are pushed togetherto make one long table. How
many peop6ecan sit at thelong table?
Represent Supportyoursolution'NittI a
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2. In a survey of 200 students at Warrel1 HighSchool. 88 Sl!I'J!hey favor year- round sctlools.Warren High School has
a IOta!of 950 students. Based on the survey. how many students are~kefyto
flM:)r year-roundsctlOOb?
SOlyc Clt(:h problem.
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Experimental Probability
Object iva Determine ltIe e.~1probability10<a gMloset01dala.
Vocabulary
exper!...,tll p<obllbility
Work Together
When you perfonn an experimenL you may get resulls Ihal differ from the resullS predicted by theoretical probability.
To find the experimental probability of an event. compare lhe number of favorable oulcomes with lhe 10lal number of completed trials or experiments.
Work with a partner to find experimental probability of lossing each Jlumber on a number cube.
MaterialS
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Learning TOO! 56 'ed. blue. andyelow connectingcubes
.'" On lhe recording sheet. list all the
Pndktioo
0 possible outcomes lor tossing a number
-- ? liJTJf:SIn
cubtl 0fICIl. Then wrile lhe lheoretical
Ennt Probability ? trials
probability for each outcome. , , ,
• How many possible outcomes are , , , - ~
there? ,
• How can you find the theoreticalprobability ot each oulcome? ,
I
L
.l~ Use theorebcal probability 10 predict
o Iha numbtl. 01 limes 6ach oulcoma shotJld occur in an experiment with 30 trials. Write your predictioos on Iha .acording sheet.
• How d~ you make your predictioos?
540
..'TEA> Perform the experiment. TOSS the number cube 30
0 times. Rewrd each outcome. Then find the total number of times each ootcome occurred.
• Find the experimental probability 01 each ootoome and reoord it in the last columnon the sheet.
• How dose are the experimental probabilities to the theorefical probabHities?
~lENT RESULTS
Numberol'
~a,-onoble ~rimenllll
E...,llt Outcon""" Probability
, , ,,
, , , • ,
, , ~" • , ,
, , , • ,
, , ," • , ,
b , ~, • , ,
Repeatt!le experiment. Toss 1tle cube ano1tler 30 fimes. COmbine your resuks with the results 01 1tle original experiment.
• How did including the additional 30 tlials affect the ,esults of the entire experiment?
On Your Own
Use the recording sheet to complete eKh probability experiment.
Re<:ord eKh probability as aIractlon In simplest form.
,. Toss a number cube and get an even number.
Complete 20 tosses.
EXPERL\tENT RESULTS I'rediction Tallyol' Numberol'
-- ?limfSin ~a.-orable h"Ottble ~rimenllll
E...,llt Probability ?triab
""-~ ""-~ Probability
,- .l=.!. 1=~
(2.4.b) , ,
Chapter 20 Lesson 5 541
For Problems 2-5, select 2 blue tubes, 5 yellow tubes, and 3 red tubes--a tolal of 10 tubes. Place them In a bag. Then use tile recording sheet to tomplete each probability uperiment.
2. Find the theoretical probability of selecting a blue cube. Then pick acube. tally the result. and retum the cube to the bag.
Repeat 20 times Then find the experimental probablility.
3. Find the theoretical probability of selecting a yellowcube.
Then pick acube. tally the resulL and return the cube to the bag. Repeat 20times. Then find the experimental probablility.
... Find the theoretical probability of selecting a red cube. Thell pick a cube. tally the result, and return the cube to the bag.
Repeat 20 times. Then find the experimental probablility.
$. Do the experiment in Problem 4 of selecting a redcube. but repeat 50limes. Then find the experimental probablility.
EXPERL'U:NTRESULTS Prediction TaUyof Number of
-- 1timesIn Fa.'Orable Fa,'Orable Experimental E'fflt Probability 1 trials ,,",~ ,,",~ Probabi~ty
, , , ,
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You learned the difference between uperimental probability and theoretical probability.
8. Suppose you spin this spinner 20 times and find the experimental probability of spinning red iS~. Is this close to wtJat you would have predicted? Explain.
1. Use your results from Problems 4 and S.
Does the experimental probability get closer to or farther from the theoretical probability as the number of trials increases?
542
Suppose you choose one of the 50 sUItes at random.