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Resources

Find probabilities using combinations and permutations

At the annual Haunted Harvest Festival, Nolan is running a spinner game. The spinner is divided into five unequal parts. Depending on where the spinner lands, guests can win one of these small toys: spider, skull, bat, monster, or skeleton. Before the guests arrive, Nolan spins the spinner

12

times to try it out. Here are his results:

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bat, spider, skull, bat, skeleton, monster, spider, bat, skull, bat, monster, skull

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Based on the data, what is the probability of the spinner landing on bat?

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Write your answer as a fraction or whole number.

Hamid is playing a trivia game with multiple choice questions. Each question has

2

correct answers among

5

answer choices.

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Hamid has no idea what the answers to a certain question are, so he needs to choose two different answers at random.

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What is the probability that Hamid guesses both answers correctly?

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Round your answer to two decimal places.

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\square

3

batches of cookies with

c

cookies in each batch. She then ate

8

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How many cookies does Anna have left?

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Write your answer as an expression.

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\square

\text{cookies}

The library is trying to decide which book to feature in next month's young adult book club, Salt to the Sea or The Sun is Also a Star.

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Which of the following survey methods will allow the library to make a valid conclusion about which book the young adults who use their library would prefer?

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1

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120

randomly selected people from a list of all young adults registered to the library.

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120

randomly selected people from a list of all people registered to the library.

City Councilwoman Kelly wants to know whether the residents of her district support a proposed school redistricting plan.

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Which of the following survey methods will allow Councilwoman Kelly to make a valid conclusion about whether residents of her district support the proposed plan?

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1

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200

residents of her district whose names are chosen at random.

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200

parents at the local playground.

Bella wants to conduct a survey to determine how many of the residents of Forks believe in supernatural creatures.

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Which of the following survey methods will allow Bella to make a valid conclusion about the percentage of residents of Forks that believe in supernatural creatures?

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1

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(A) Ask a randomly selected sample of residents to answer the question anonymously.

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(B) Ask a randomly selected sample of high school students to answer the question anonymously.

You're having dinner at a restaurant that serves

5

kinds of pasta (spaghetti, bow ties, fettuccine, ravioli, and macaroni) in

4

different flavors (tomato sauce, cheese sauce, meat sauce, and olive oil).

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If you randomly pick your kind of pasta and flavor, what is the probability that you'll end up with bow ties, cheese sauce, or both?

Chef Lloyd's fridge is filled with

7

5

of which contain whole milk. Before he begins to bake, he examines the cartons' expiration dates. If Chef Lloyd checks the expiration dates on

4

randomly selected cartons, what is the probability that all of them contain whole milk?

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Write your answer as a decimal rounded to four decimal places.._________

Every attendant at a town's Chili Cook-off received a raffle ticket. There were

8

raffle prizes, including

5

that were cooking utensils. If

4

prizes were randomly raffled away in the first hour of the cook-off, what is the probability that all of them are cooking utensils?

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Write your answer as a decimal rounded to four decimal places.._________

Mr. Shen brought in

8

solid colored eggs for his Physics classes.

5

of the eggs were blue. If Mr. Shen randomly chose

4

eggs for his first class to use in an egg drop experiment, what is the probability that all of them are blue? Write your answer as a decimal rounded to four decimal places.._________

Every attendant at a town's Chili Cook-off received a raffle ticket. There were

8

raffle prizes, including

6

that were gift certificates to restaurants.

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4

prizes were randomly raffled away in the first hour of the cook-off, what is the probability that all of them are gift certificates to restaurants?

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Write your answer as a decimal rounded to four decimal places.._________

An English teacher gave his class a choice of

8

6

of which are contemporary novels. If a student randomly picks

5

books, what is the probability that all of them are contemporary novels?

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Write your answer as a decimal rounded to four decimal places.___

As Student Council President, Marcy organized a school-wide scavenger hunt. She hid

8

6

of which were hidden in the main office. If

5

goody bags were randomly discovered during first period, what is the probability that all of them were hidden in the main office?

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Write your answer as a decimal rounded to four decimal places._____

9

exercises over the span of a week.

7

of his exercises involve biking.

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If he randomly chose

6

exercises to do on Monday, what is the probability that all of them involve biking?

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Write your answer as a decimal rounded to four decimal places.

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An English teacher gave his class a choice of

8

6

of which are contemporary novels. If a student randomly picks

4

books, what is the probability that all of them are contemporary novels? Write your answer as a decimal rounded to four decimal places. ____

Erica and her stepmother wanted to start volunteering together. They found

7

opportunities online,

5

of which involved working with the elderly.

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If they randomly chose to apply to

4

of the opportunities, what is the probability that all of them involve working with the elderly?

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Write your answer as a decimal rounded to four decimal places.

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Tucker is filling out summer job applications, so that he can earn money to buy a car. Of the

9

jobs he's applying for,

7

are tutoring jobs.

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If Tucker randomly picks

6

applications to submit today, what is the probability that all of them are for tutoring jobs?

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Write your answer as a decimal rounded to four decimal places.

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7

5

of which are blue.

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If John randomly picks

4

buttons, what is the probability that all of them are blue?

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Write your answer as a decimal rounded to four decimal places.

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Audrey and her best friend wanted to paint their apartment. In their storage closet, they found

8

cans of paint. Audrey remembered that

5

of the cans contained beige paint, but none of the cans had labels.

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If Audrey randomly opened

4

cans, what is the probability that all of them contain beige paint?

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Write your answer as a decimal rounded to four decimal places.

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9

seeds in order to plant an herb garden for her grandma. Of the seeds she bought,

7

were dill seeds.

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If Erin chooses to plant

6

random seeds on the east side of the garden, what is the probability that all of them are dill seeds?

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Write your answer as a decimal rounded to four decimal places.

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After touring a coffee bean farm, Lily impulsively bought

8

bags of coffee beans. Of the bags she bought,

6

were filled with caramel flavored coffee beans.

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If Lily randomly selects

5

of the bags to send to family members, what is the probability that all of them are caramel flavored?

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Write your answer as a decimal rounded to four decimal places.

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Kelly teaches a ceramics class on the weekends. In Sunday's class, the students created

8

6

of which were plates. After each class, Kelly bakes the clay objects in a hot kiln to harden them. Students pick up their finished pieces later in the week.

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If Kelly randomly chose

5

clay objects to bake in the kiln Sunday night, what is the probability that all of them are plates?

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Write your answer as a decimal rounded to four decimal places.

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The Danville High School Speech and Debate Club hosted its annual car wash fundraiser. Each club member brought a bottle of car wash soap, so there were

8

6

of the bottles contained green soap.

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If a club member randomly selects

5

bottles to pour into the first soap bucket, what is the probability that all of them contain green soap?

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Write your answer as a decimal rounded to four decimal places.._________

Dana is shopping for a costume at a thrift store. There are

8

costumes hanging on the rack, including

6

food-shaped costumes. If the costumes all look like the right size, and Dana randomly selects

5

to try on, what is the probability that all of them are food-shaped costumes? Write your answer as a decimal rounded to four decimal places.._________

Brenna is handing out

8

invitations to her New Year's Eve party,

5

of which are printed on green paper. If Brenna randomly hands out

4

invitations before lunch, what is the probability that all of them are printed on green paper?

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Write your answer as a decimal rounded to four decimal places.._________

Mr. Lynch brought in

8

solid colored eggs for his Physics classes.

6

of the eggs were green. If Mr. Lynch randomly chose

5

eggs for his first class to use in an egg drop experiment, what is the probability that all of them are green?

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Write your answer as a decimal rounded to four decimal places.._________

Lucy and her dad went ice-fishing this winter. They caught

8

total fish, including

6

arctic char. If on the last day of the trip, Lucy randomly selected

4

fish to donate to fishermen who hadn't caught any fish that day, what is the probability that all of them are arctic char?

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Write your answer as a decimal rounded to four decimal places.______

Annie and her best friend wanted to paint their apartment. In their storage closet, they found

8

cans of paint. Annie remembered that

6

of the cans contained beige paint, but none of the cans had labels.

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If Annie randomly opened

5

cans, what is the probability that all of them contain beige paint?

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Write your answer as a decimal rounded to four decimal places.

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Water is drained out of a tank at a rate of

r(t)=20 e^{-0,1 t^{2}}

liters per minute, where

t

is the time in minutes,

0 \leq t \leq 10

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How much water is drained between times

t=3

t=9

minutes? Use a graphing calculator and round your answer to three decimal places.

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Emily volunteers on the weekend at the Central Library. As a school project, she decides to record how many people visit the library, and where they go. On Saturday,

416

people went to The Youth Wing,

448

people went to Social Issues, and

341

went to Fiction and Literature.

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On Sunday, the library had

500

total visitors. Based on what Emily had recorded on Saturday, about how many people should be expected to go to Social Issues? Round your answer to the nearest whole number.

Zachary has a bag that contains strawberry chews, cherry chews, and peach chews. He performs an experiment. Zachary randomly removes a chew from the bag, records the result, and returns the chew to the bag. Zachary performs the experiment

66

times. The results are shown below:

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A strawberry chew was selected

61

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A cherry chew was selected

3

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A peach chew was selected

2

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If the experiment is repeated

200

more times, about how many times would you expect Zachary to remove a peach chew from the bag? Round your answer to the nearest whole number.

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The first three terms of a sequence are given. Write your answer as a decimal or whole number. Round to the nearest thousandth (if necessary).

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452,443,434, \ldots

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32

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The first three terms of a sequence are given. Write your answer as a decimal or whole number. Round to the nearest thousandth (if necessary).

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461,452,443, \ldots

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39

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Mekala has an MP

3

player called the Jumble. The Jumble randomly selects a song for the user to listen to. Mekala's Jumble has

4

2

country songs, and

3

jazz songs on it. Mekala plans to listen to

270

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Complete the following statement with the best prediction.

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Mekala will listen to...

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1

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60

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60

country songs but probably not exactly

60

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210

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210

country songs but probably not exactly

210

Jose is going to use a random number generator

500

times. Each time he uses it, he will get a

1,2,3

4

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Complete the following statement with the best prediction.

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Jose will get something other than a

2

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1

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250

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250

times but probably not exactly

250

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375

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375

times but probably not exactly

375

Shun is going to flip a fair coin

450

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Complete the following statement with the best prediction.

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The coin will land tails up...

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1

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175

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175

times but probably not exactly

175

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225

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225

times but probably not exactly

225

Ramkin is going to flip a fair coin

1200

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What is the best prediction for the number of times that the coin will land heads up?

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1

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50

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50

times but probably not exactly

50

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600

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600

times but probably not exactly

600

Jeremy is going to roll a fair

6

180

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What is the best prediction for the number of times that Jeremy will roll a number greater than

4

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1

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30

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30

times but probably not exactly

30

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60

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60

times but probably not exactly

60

Elizabeth is going to roll a fair

6-

600

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Complete the following statement with the best prediction.

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Elizabeth will roll an even number...

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1

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100

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100

times but probably not exactly

100

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300

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300

times but probably not exactly

300

Cam is going to roll a fair

6

2400

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What is the best prediction for the number of times that Cam will roll the number

4

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1

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400

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400

times but probably not exactly

400

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600

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600

times but probably not exactly

600

Ellen has a bag with

3

red marbles and

2

blue marbles in it. She is going to randomly draw a marble from the bag

300

times, putting the marble back in the bag after each draw.

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What is the best prediction for the number of times that Ellen will draw a blue marble?

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1

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120

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120

times but probably not exactly

120

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150

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150

times but probably not exactly

150

Saqui buys streamers for

\$ 0.09

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What is the price, in dollars, of

300

centimeters of streamers?

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100

centimeters in a meter.

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1

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\$ 0.03

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\$ 0.27

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\$ 27

Maya is playing a trivia game with multiple choice questions. Each question has

2

correct answers among

5

answer choices.

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Maya has no idea what the answers to a certain question are, so she needs to choose two different answers at random.

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What is the probability that Maya's first guess is CORRECT and her second guess is INCORRECT?

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Round your answer to two decimal places.

50

workers onsite at a large construction project. Six of them are left-handed, and the rest are not. Suppose that the project manager randomly selects

2

workers (without replacement).

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What is the probability that NEITHER of the workers selected are left-handed?

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Round your answer to two decimal places.

Hamid is playing a trivia game with multiple choice questions. Each question has

2

correct answers among

5

answer choices.

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Hamid has no idea what the answers to a certain question are, so he needs to choose two different answers at random.

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What is the probability that Hamid guesses both answers correctly? Round your answer to two decimal places.

Corey and Yin are trying to decide who will get to choose where they go for lunch. They decide to flip a coin until it lands showing heads. If the first flip shows heads, then Corey gets to choose. If heads shows on the second flip or later, then Yin gets to choose.

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Is this a fair way to decide who chooses where they go lunch? Why or why not?

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1

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(A) No, Corey is most likely to get to choose.

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(B) No, Yin is most likely to get to choose.

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(C) Yes, they both have an equal probability of choosing.

An accountant for a certain state models the sales tax revenue that the state has earned over several years. The model shows that sales tax revenue grew by

15 \%

2

years ago, when it started to grow by

\$ 179.5

million per year. If the sales tax revenue

2

\$ 2.1

billion, approximately how much lower is the sales tax revenue this year than it would be if it had continued growing by

15 \%

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1

=1,000

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1

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\$ 136

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\$ 318

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\$ 2.05

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\$ 5.24

Tritium, a radioactive isotope of hydrogen, is often used in emergency EXIT signs. Because of the radioactive substance present in these signs, proper disposal is a matter of concern to the Environmental Protection Agency. The half-life of tritium is approximately

12

years. That is, every

12

years, the amount of tritium decreases by

50 \%

. If a new tritium EXIT sign contains

25

curies of tritium, approximately how many curies of tritium will remain after

24

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1

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6

25

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\mathbf{1 2 . 5}

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25

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30

Wendy thinks the perfect chocolate chip cookie has

35

chocolate chips for every

5

cookies. Cookie Club makes cookies with

100

chocolate chips for every

15

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What will Wendy think about the chocolate in Cookie Club's cookies?

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1

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(A) Cookie Club's cookies have too much chocolate.

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(B) Cookie Club's cookies have too little chocolate.

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(C) Cookie Club's cookies are just right.

The property taxes in a town decrease as the distance from the local elementary school increases. The greatest property taxes are

4.5 \%

, and for every

10

miles from the school, property taxes decrease by

0

5

percentage points. If a house's property taxes are

3 \%

, what is the distance of that house from the school?

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1

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\mathbf{1 0}

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20

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30

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40