Resources

Resources

Interpret regression lines

Read the following description of a data set.

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Lucy is a professional dancer booked for a major event. Although she has a rigorous practice schedule, she sometimes has to end a practice session when she begins to experience stiffness. She wonders if stretching more before starting a session will allow her to practice for a longer time.Over the next few days Lucy varies the number of minutes she stretches before the start of her session,

x

, and notes the number of minutes she can practice before experiencing stiffness,

y

.The least squares regression line of this data set is:

y = 0.549x + 295.628

\newline

Complete the following sentence:

\newline

For each additional minute of stretching, the least squares regression line predicts she will be able to practice

\_

minutes longer.

Read the following description of a data set.

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Grape growers in France think they will have a massive crop this year and want to know how this will influence demand for grape juice.They compared how many grapes were produced (in millions of metric tons),

x

, and the amount of French grape juice that was sold in previous years (in billions of liters),

y

.The least squares regression line of this data set is:

y = 0.143x + 5.363

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Complete the following sentence:

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The least squares regression line predicts the amount of French grape juice sold would increase by ___ billion liters if the amount of grapes produced increased by one million metric tons.

Read the following description of a data set.

\newline

A gym franchise was considering a television marketing campaign to increase its membership. The franchise's market researchers wanted to get a better sense of the television and exercise habits of the gym's target demographic. To begin, the market researchers surveyed some of the current members about how many hours they had spent watching television and exercising last month.Using the survey responses, the researchers compared the number of hours of television watched,

x

, to the number of hours of exercise,

y

, for each member.The least squares regression line of this data set is:

y = -1.636x + 89.046

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Complete the following sentence:

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If a gym member had watched one additional hour of television last month, the least squares regression line predicts that they would have spent ___ hours less exercising that month.

Read the following description of a data set.

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A movie theater manager is studying the snack buying habits of her customers. She expects that when longer movies are shown, people buy more snacks. Each week she calculates the average duration of all movies being shown and the percentage of customers who buy snacks.The manager calculates the average movie duration (in minutes),

x

, and the percentage of the customers who bought snacks,

y

.The least squares regression line of this data set is:

y = 0.262x - 15.968

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Complete the following sentence:

\newline

If the average movie duration increased by one minute, the least squares regression line predicts that the percentage of customers who buy snacks would increase by ___.

Read the following description of a data set.

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A reporter for a college magazine is writing a feature about student participation in on-campus organizations. He wants to see if there is a relationship between student population and the number of on-campus organizations.To begin, he recorded the number of students,

x

, and the number of officially recognized student organizations,

y

, for several colleges.The least squares regression line of this data set is:

y = 0.029x + 31.556

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Complete the following sentence:

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For each additional student, the least squares regression line predicts there would be ___ more student organizations.

Read the following description of a data set.

\newline

A gym franchise was considering a television marketing campaign to increase its membership. The franchise's market researchers wanted to get a better sense of the television and exercise habits of the gym's target demographic. To begin, the market researchers surveyed some of the current members about how many hours they had spent watching television and exercising last month.Using the survey responses, the researchers compared the number of hours of television watched,

x

, to the number of hours of exercise,

y

, for each member.The least squares regression line of this data set is:

y = -0.684x + 58.503

\newline

Complete the following sentence:

\newline

If a gym member had watched one additional hour of television last month, the least squares regression line predicts that they would have spent ___ hours less exercising that month.

Read the following description of a data set.

\newline

Colette is indignant that her favorite author takes too long to write new books. To determine how atypical her favorite author's speed is, Colette looked at how writing speed varies between different active authors.For her favorite novelists, she recorded the number of years they had been actively writing,

x

, and how many novels they had written,

y

.The least squares regression line of this data set is:

y = 0.064x + 5.024

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Complete the following sentence:

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For each additional year, the least squares regression line predicts that an author would have written an additional ___ novels.

Read the following description of a data set.

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The president of a book club is concerned about the low attendance at the club's most recent book discussion. She wonders whether the considerable length of the book is to blame.For each of the last few books that club members chose, the president notes the number of pages,

x

, as well as the number of people who attended the discussion,

y

.The least squares regression line of this data set is:

y = -0.018x + 16.473

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Complete the following sentence:

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If a book has one additional page, the least squares regression line predicts

\_\_

fewer people will attend the discussion.

Read the following description of a data set.

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A botanist at a university is studying oak trees and the acorns they produce. He collected several acorns from the same tree and measured them.For each acorn, he recorded its volume (in cubic centimeters),

x

, and its weight (in grams),

y

.The least squares regression line of this data set is:

y = 2.438x - 2.933

\newline

Complete the following sentence:

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For each additional cubic centimeter of acorn volume, the least squares regression line predicts that it would weigh

\_\_

Read the following description of a data set.

\newline

A state's Department of Education is planning to change some school district boundaries to alleviate overcrowding at certain campuses. As a first step, the department put together a report on a sample of towns in the state.For each town in the sample, the report recorded its population (in thousands),

x

, and its number of schools,

y

.The least squares regression line of this data set is:

y = 0.122x - 3.426

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Complete the following sentence:

\newline

If a town had one thousand more people, the least squares regression line predicts that it would have

\_

Read the following description of a data set.

\newline

Jim is a programmer in Silicon Valley and spends most of his day typing and drinking coffee. He wants to know if drinking coffee makes him type faster.Over the next few days, Jim varies the number of cups of coffee he drinks,

x

, and measures the average number of words typed per minute on each day,

y

.The least squares regression line of this data set is:

y = 0.325x + 105.824

\newline

Complete the following sentence:

\newline

The least squares regression line predicts Jim's average daily typing speed will increase by ___ words per minute for each additional cup of coffee.

Read the following description of a data set.

\newline

The operator of an electric plant was concerned about the performance of some of its wind turbines.She consulted the manuals to find the rotor diameter of each turbine (in meters),

x

. Then, on a day with steady wind, she checked the control panel and noted each turbine's power output (in kilowatts),

y

.The least squares regression line of this data set is:

y = 22.316x - 636.704

\newline

Complete the following sentence:

\newline

For each additional meter of rotor diameter, the least squares regression line predicts the power output of a turbine would increase by ___ kilowatts.

Cara is putting apples from her orchard into

5

-pound bags to sell. The median number of apples in the bags is

15

apples, and the interquartile range is

2

apples. Cara hopes all the bags will sell in the next

4

7

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Which is a measure of how much the number of apples in a bag varies?

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2

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4

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7

\newline

15

A large random sample of American students in seventh grade showed that

20 \%

of them were reading below grade level.

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Based on this data, which of the following conclusions are valid?

\newline

1

\newline

20 \%

of all American students in seventh grade were reading below grade level.

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20 \%

of this sample was reading below grade level, but we cannot conclude anything about the population.

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20 \%

of all American students were reading below grade level.

The Read and Feed restaurant wants to know how satisfied their customers are with their service. They printed an internet link to a survey on every receipt, and

150

of their customers chose to answer the survey. The data showed that

60 \%

of the customers were satisfied with their service.

\newline

Based on this data, which of the following conclusions are valid?

\newline

1

\newline

60 \%

of customers in this sample are satisfied, but we cannot conclude anything about the population.

\newline

60 \%

of all Read and Feed customers are satisfied.

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60 \%

of all Read and Feed customers who have internet access are satisfied.

When Jonas becomes the Receiver of Memory, he gets a rule that he may not tell his dreams. He wants to know how many of his

50

classmates have the same rule. He asks

5

friends from his class whether they may tell their dreams. Of those,

4

say that they may.

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Based on this data, which of the following conclusions are valid?

\newline

1

\newline

80 \%

of all of Jonas's classmates may tell their dreams.

\newline

80 \%

of all people in Jonas's community may tell their dreams.

\newline

80 \%

of the classmates in this sample may tell their dreams, but we cannot conclude anything about the population.

Francis surveyed a random sample of

70

students at Franklin High School about their favorite season. Of the students surveyed,

18

chose fall as their favorite season. There are

1816

students at Franklin High School.

\newline

Based on the data, what is the most reasonable estimate for the number of students at Franklin High School whose favorite season is fall?

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1

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257

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467

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515

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\mathbf{1 3 4 9}

The following list contains the number of movies that a group of

9

students saw in theaters in the past

12

\newline

4,10,10,6,16,15,6,7,4

\newline

Find the median number of movies that the students saw.

\newline

\square

1.32(0.65 p)

represents the amount Cai paid for dinner at a restaurant after he applied a discount coupon and added tip. Which changes to the original price could have resulted in the expression?

\newline

0.65 \%

32 \%

\newline

32 \%

tip and then a discount of

35 \%

\newline

65 \%

0.32 \%

\newline

32 \%

tip and then a discount of

65 \%

1.16(0.75 p)

represents the amount Aubrey paid for dinner at a restaurant after she applied a discount coupon and added tip. Which changes to the original price could have resulted in the expression?

\newline

116 \%

tip and then a discount of

75 \%

\newline

0.16 \%

tip and then a discount of

75 \%

\newline

75 \%

16 \%

\newline

25 \%

16 \%

Read the following description of a data set.

\newline

Fulton County's Parks and Recreation Department is considering establishing a new park. As part of the decision-making process, the department asked an intern to conduct a park usage study.The study considered the area (in square kilometers),

x

, and the number of visitors last year,

y

, of each county park.The least squares regression line of this data set is:

y = 10,637.929x + 134,391.457

\newline

Complete the following sentence:

\newline

If a park's area was one square kilometer larger, the least squares regression line predicts that it would have had

\_\_

more visitors last year.

Read the following description of a data set.

\newline

Leo has trouble getting his math homework done on time, and his mother suspects it is due to lack of sleep.For the next few nights, Leo's mother notes the number of hours he sleeps,

x

, and the number of minutes it takes him to do his math homework the following day,

y

.The least squares regression line of this data set is:

y = -48.057x + 483.245

\newline

Complete the following sentence:

\newline

If Leo sleeps for one extra hour at night, the least squares regression line predicts it will take him

\_\_

fewer minutes to do his math homework the next day.

Read the following description of a data set.

\newline

Kenji wants to ensure that the new board game he's designing is accessible to a wide age range. To test this, he had several children of various ages play the board game against each other. Each child played the game the same number of times.For each child, Kenji recorded his or her age,

x

, and the number of games that child had won,

y

.The least squares regression line of this data set is:

y = 22.284x - 116.736

\newline

Complete the following sentence:

\newline

If a child were one year older, the least squares regression line predicts he or she would have won

\_

Read the following description of a data set.

\newline

A reporter for a college magazine is writing a feature about student participation in on-campus organizations. He wants to see if there is a relationship between student population and the number of on-campus organizations.To begin, he recorded the number of students,

x

, and the number of officially recognized student organizations,

y

, for several colleges.The least squares regression line of this data set is:

y = 0.017x + 176.089

\newline

Complete the following sentence:

\newline

For each additional student, the least squares regression line predicts there would be ___ more student organizations.

Read the following description of a data set.

\newline

Mr. Espinoza wants to demonstrate the importance of proofreading to his English class. He had students read the same passage and mark all the spelling and grammar errors they could find.He recorded how many minutes each student had spent on the exercise,

x

, and how many errors that student had missed,

y

.The least squares regression line of this data set is:

y = -1.332x + 43.879

\newline

Complete the following sentence:

\newline

For each additional minute a student spent proofreading, the least squares regression line predicts that he or she would miss

\_\_

Read the following description of a data set.

\newline

Antonio runs an apple orchard, and his trees did not produce many apples this season. His friends tell him that adding more fertilizer to the soil may help for next season. Since fertilizer is expensive, Antonio decides to test this theory on some small plots of land with equal area.He varies the kilograms of fertilizer used in each plot,

x

, and counts the number of apples produced on each,

y

, at the end of one season.The least squares regression line of this data set is:

y = 1.113x + 331.176

\newline

Complete the following sentence:

\newline

If one additional kilogram of fertilizer was used in a plot, the least squares regression line predicts an additional ___ apples would be produced on it that season.

Read the following description of a data set.

\newline

Jaylen is packing for vacation and is wondering how many books to bring. He wants to make sure he does not run out of reading material, so he looks at his reading journal to see how many books he read on past vacations.For each vacation, he records the vacation's length (in days),

x

, and how many books he read,

y

.The least squares regression line of this data set is:

y = 1.214x - 5.465

\newline

Complete the following sentence:

\newline

If Jaylen stays on vacation for one extra day, the least squares regression line predicts that he would have read ___ additional books.

Read the following description of a data set.

\newline

On most days Isabella takes her lunch break in the park near her office. While sitting on the park bench, she scatters seeds for the pigeons and wonders how many pigeons will come.She decided to keep track of both the number of seed packages she scatters for the pigeons,

x

, and the number of pigeons that come,

y

.The least squares regression line of this data set is:

y = 3.124x - 17.542

\newline

Complete the following sentence:

\newline

If Isabella scattered one additional seed package, the least squares regression line predicts that ___ additional pigeons would come.

Read the following description of a data set.

\newline

A sporting goods chain is planning to open a new store in Putnam County. In order to decide on an optimal location, their market researchers gathered data on sports facilities in towns across the county.The researchers considered the population (in thousands),

x

, and the number of sports facilities,

y

, in each town.The least squares regression line of this data set is:

y = 0.524x - 38.329

\newline

Complete the following sentence:

\newline

If a town had one thousand more people, the least squares regression line predicts that it would have

\_\_

more sports facilities.

Read the following description of a data set.

\newline

A software developer is looking for ways to predict how many bugs will appear in future projects. He used a bug-tracking database to analyze several recent projects.From the database, he recorded the number of lines of code for each project,

x

. He also looked up the number of bugs that had been found in each project's code,

y

.The least squares regression line of this data set is:

y = 0.048x - 460.924

\newline

Complete the following sentence:

\newline

For each additional line of code, the least squares regression line predicts ___ more bugs would be found in that project.

Read the following description of a data set.

\newline

A state's Department of Education is planning to change some school district boundaries to alleviate overcrowding at certain campuses. As a first step, the department put together a report on a sample of towns in the state.For each town in the sample, the report recorded its population (in thousands),

x

, and its number of schools,

y

.The least squares regression line of this data set is:

y = 0.119x - 18.064

\newline

Complete the following sentence:

\newline

If a town had one thousand more people, the least squares regression line predicts that it would have

\_

Read the following description of a data set.

\newline

A state's Department of Education is planning to change some school district boundaries to alleviate overcrowding at certain campuses. As a first step, the department put together a report on a sample of towns in the state.For each town in the sample, the report recorded its population (in thousands),

x

, and its number of schools,

y

.The least squares regression line of this data set is:

y = 0.163x + 30.698

\newline

Complete the following sentence:

\newline

If a town had one thousand more people, the least squares regression line predicts that it would have

\_

Read the following description of a data set.

\newline

Mr. Carter is trying to convince his middle school typing students that it is better to slow down when they are learning to type. He argues that students who type too quickly make too many errors.To prove his point, Mr. Carter has students type a sample paragraph. He records their average typing speed (in words per minute),

x

, and the number of errors they made,

y

.The least squares regression line of this data set is:

y = 0.138x + 10.252

\newline

Complete the following sentence:

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For an increase of one word per minute in typing speed, the least squares regression line predicts an increase of ___ errors while typing the sample paragraph.

Read the following description of a data set.

\newline

A food scientist wants to understand how much sugar children like in their desserts. He sets up a study where children taste cups of vanilla pudding with varying sweetness and rate each cup on a scale of

1

10

10

is excellent.For each tasting, the food scientist writes down the grams of sugar in the pudding cup,

x

, as well as its rating,

y

.The least squares regression line of this data set is:

y = 0.216x - 4.085

\newline

Complete the following sentence:

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For each additional gram of sugar in a pudding cup, the least squares regression line predicts its rating will increase by ___.

29

. Multiple choice - Bushels of corn exported from the U.S., in millions, from

2008

2012

, can be modeled by a quadratic function. In

2008

, the U.S. exported approximately

1849

million bushels of com. In

2009

, the U.S. exported approximately

1979

million bushels of corn, which was a maximum for that time period. According to the above information, which of the following best approximates the U.S. corn exports in

2012

\newline

809

million bushels

\newline

1170

million bushels

\newline

1589

million bushels

\newline

2369

million bushels

Bushels of corn exported from the U.S., in millions, from

2008

2012

, can be modeled by a quadratic function. In

2008

, the U.S. exported approximately

1849

million bushels of corn. In

2009

, the U.S. exported approximately

1979

million bushels of corn, which was a maximum for that time period. According to the above information, which of the following best approximates the U.S. corn exports in

2012

\newline

809

million bushels

\newline

1170

million bushels

\newline

1589

million bushels

\newline

2369

million bushels

A list of positive integers has the following properties:

\newline

- The sum of the items in the list is

30

\newline

- The unique mode of the list is

9

\newline

- The median of the list is a positive integer that does not appear in the list itself.

\newline

Find the sum of the squares of all the items in the list.

Perpetual inventory using LIFO

\newline

Beginning inventory, purchases, and sales data for DVD players are as follows:

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1

\newline

140

\newline

\$29

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10

110

\newline

15

\newline

150

\newline

\$30

\newline

20

\newline

120

\newline

24

35

\newline

30

\newline

140

\newline

\$34

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The business maintains a perpetual inventory system, costing by the last-in, first-out method.

\newline

Determine the cost of goods sold for each sale and the inventory balance after each sale, presenting the data in the form illustrated in Exhibit

4

. Un LIFO, if units are in inventory at two different costs, enter the units with the HIGHER unit cost first in the cost of Goods Sold Unit cost column and LOWER unit cost first in the Inventory Unit cost column.

\newline

The following data points represent the number of chicken nuggets on each family member's plate.

\newline

1,3,0,6, ?

\newline

If the mean of the data set is

3

chicken nuggets, find the missing number of chicken nuggets.

\newline

Diego is a wildlife researcher. They were analyzing the mean and median lengths of

9

whales their team had observed. The whales all had different lengths between

23 \mathrm{~m}

27 \mathrm{~m}

\newline

Diego found out that they were misreading the shortest length. It was actually

20 \mathrm{~m}

23 \mathrm{~m}

\newline

How will this length decreasing affect the mean and median?

\newline

1

\newline

(A) Both the mean and median will decrease.

\newline

(B) The mean will decrease, and the median will increase.

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(C) The mean will decrease, and the median will stay the same.

\newline

(D) The mean will stay the same, and the median will decrease.

11

items in the grocery store. Each item had a different price, and the mean was about

\$ 4.44

. On his way to the register, he added a

12^{\text {th }}

item: a jug of olive oil for

\$ 39.99

\newline

How will adding the jug of olive oil affect the mean and median?

\newline

1

\newline

(A) Both the mean and median will increase, but the median will increase by more than the mean.

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(B) Both the mean and median will increase, but the mean will increase by more than the median.

\newline

(C) The mean will increase, and the median will decrease.

\newline

(D) The median will increase, and the mean will decrease.

A small accounting firm has

4

accountants who each earn a different salary between

52

000

58

000

dollars. For extra help during tax season, they hire a

5^{\text {th }}

accountant who earns

10

000

dollars. [Show data].

\newline

How will hiring the

5^{\text {th }}

accountant affect the mean and median?

\newline

1

\newline

(A) Both the mean and median will decrease, but the median will decrease by more than the mean.

\newline

(B) Both the mean and median will decrease, but the mean will decrease by more than the median.

\newline

(C) The mean will decrease, and the median will increase.

\newline

(D) The mean will increase, and the median will decrease.

A zookeeper weighs her animals once a month and compares their weights to the previous month.

\newline

3 \mathrm{~kg}

between January and February.

\newline

The rhino gained

12 \mathrm{~kg}

between January and February.

\newline

2 \mathrm{~kg}

between January and February.

\newline

The penguin gained

4 \mathrm{~kg}

between January and February.

\newline

Which animal had the least amount of change in weight?

\newline

1

\newline

\newline

\newline

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Based on her research, Aria estimates that

75 \%

of the students at her college work while they're in school. The margin of error of her estimation is

5 \%

. Based on her estimate and margin of error, Aria would most likely agree with which of the following statements?

\newline

1

\newline

70 \%

80 \%

of the students at Aria's college work while they're in school.

\newline

70 \%

75 \%

of the students at Aria's college work while they're in school.

\newline

72.5 \%

77.5 \%

of the students at Aria's college work while they're in school.

\newline

74.5 \%

75.5 \%

of the students at Aria's college work while they're in school.

In which of the following scenarios can the decline of Littleroot Town's population be described as linear?

\newline

1

\newline

2.5 \%

of the current population leaves Littleroot Town.

\newline

(B) Each year, an increasing number of people leave Littleroot Town.

\newline

(C) Each year, a decreasing number of people leave Littleroot Town.

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(D) Each year, a constant number of people leave Littleroot Town.

A writer for a high school newspaper is conducting a survey to estimate the number of students that will vote for a particular candidate in an upcoming student government election. All students at the high school are eligible to vote in the election, and the writer decides to select a sample of students to take the survey. Which of the following sampling methods is most likely to produce valid results?

\newline

1

\newline

(A) Survey every fifth student to enter the school library.

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(B) Survey every fifth student to arrive at school one morning.

\newline

(C) Survey every fifth senior to arrive at school one morning.

\newline

(D) Survey every fifth student to enter the school stadium for a football game

Vicente surveyed a random sample of New Mexico residents ages

18

24

about how much they typically tip at a restaurant. The results of the survey are most representative of which of the following populations?

\newline

1

\newline

(A) New Mexico residents

\newline

(B) Albuquerque, New Mexico residents

\newline

(C) New Mexico residents ages

18

24

\newline

(D) Albuquerque, New Mexico residents ages

18

24

Phytoremediation is the use of plant growth to purify pollutants from soil, water, or air. Suppose that a crop of brake ferns can remove

15

(\mathrm{mg})

per square meter of a particular pollutant from the soil in

20

20

weeks, the ferns are harvested and a new crop is planted. If

c

represents the number of crops of brake ferns needed to phytoremediate soil contaminated with

170 \mathrm{mg}

per square meter of the pollutant down to healthy levels of

5 \mathrm{mg}

per square meter, which equation best models the situation?

\newline

1

\newline

170-20 c=5

\newline

170+20 c=5

\newline

170-15 c=5

\newline

170+15 c=5

A large truck, traveling

30

miles per hour, carries a letter from the central post office to the local post office. The letter is then loaded onto a local vehicle, which travels at an average speed of

10

miles per hour, until the letter reaches its destination. The large truck carried the letter for

a

minutes and the local vehicle carried the letter for

b

minutes. If the total distance that the letter travelled from the central post office to its destination was

24

miles, which of the following equations correctly relates

a

b

\newline

1

\newline

\frac{30}{60} a+\frac{10}{60} b=24

\newline

\frac{60}{30} a+\frac{60}{10} b=24

\newline

30 a+10 b=24

\newline

60 \cdot 30 a+60 \cdot 10 b=24

Read the following description of a data set. Rod Diamond is a singer who appeals to an older demographic. For a comedy segment on a late night show, he asked random people on the street how old they were and how many of his songs they could name, if any. Rod noted the age of each person he spoke with,

x

, and the number of songs each could name,

y

. The least squares regression line of this data set is:

y = 0.886x - 23.764

Complete the following sentence: The least squares regression line predicts that if a person is one year older, they will be able to name

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