Question: Every summer, Josiah goes on a week-long canoe trip with his childhood camp friends. After the trip, he usually purchases some oars from the destination city. His collection of oars is organized by year and type of wood. What is the probability that a randomly selected oar was made from spruce wood and was purchased in 2010? Simplify any fractions.

Answer: 1/6

Solution:
Let A be the event "the oar was made from spruce wood" and B be the event "the oar was purchased in 2010".
To find the probability that a oar was made from spruce wood and was purchased in 2010, first identify the sample space and the event.
The outcomes in the sample space are the different oars. Each oar is equally likely to be selected, so this is a uniform probability model.
The event is A and B, "the oar was made from spruce wood and was purchased in 2010".
Since this is a uniform probability model, count the number of outcomes in the event A and B and count the total number of outcomes. Then, divide them to compute the probability.

Find the number of outcomes in the event A and B.
A and B is the event "the oar was made from spruce wood and was purchased in 2010", so look at the table to see how many oars were made from spruce wood and were purchased in 2010.
The number of oars that were made from spruce wood and were purchased in 2010 is 3.

Find the total number of outcomes.
Add all the numbers in the table to find the total number of oars.
3 + 3 + 6 + 6 = 18

Find P(A and B).
Since all outcomes are equally likely, the probability of event A and B is the number of outcomes in event A and B divided by the total number of outcomes.
P(A and B) = \frac{# of outcomes in A and B}{total # of outcomes}
 = \frac{3}{18}
 = \frac{1}{6}
The probability that a oar was made from spruce wood and was purchased in 2010 is \frac{1}{6}.


Question: An administrator at the Department of Motor Vehicles (DMV) tracked the average wait time from month to month. According to the table, what was the rate of change between July and August?

Answer: -7

Month | Waiting time (minutes)
June | 36
July | 41
August | 34
September | 28
October | 36

Solution:
Plug the numbers into the formula for rate of change and simplify.
Rate of change
 = \frac{change in value}{change in time}
 = \frac{34 minutes - 41 minutes}{1 month}
 = \frac{-7 minutes}{1 month}
 = -7 minutes per month
The rate of change between July and August was - 7 minutes per month.


Question: Look at the following schedule. Which game ends at 11.30 A.M.?

Choices:
- Waves versus Alligators game
- Fire versus Blizzard game
- Thunder versus Eagles game
- Dolphins versus Bears game

Answer: Waves versus Alligators game

Game | Begin | End
Waves versus Alligators | 10:00 A.M. | 11:30 A.M.
Dolphins versus Bears | 10:40 A.M. | 12:10 P.M.
Thunder versus Eagles | 11:15 A.M. | 12:45 P.M.
Sharks versus Storm | 11:30 A.M. | 1:00 P.M.
Lions versus Blue Jays | 11:45 A.M. | 1:15 P.M.
Lightning versus Coyotes | 12:10 P.M. | 1:40 P.M.
Fire versus Blizzard | 1:05 P.M. | 2:35 P.M.
Hawks versus Jaguars | 1:30 P.M. | 3:00 P.M.
Cardinals versus Cobras | 2:25 P.M. | 3:55 P.M.

Waves versus Alligators
Dolphins versus Bears
Thunder versus Eagles
Sharks versus Storm
Lions versus Blue Jays
Lightning versus Coyotes
Fire versus Blizzard
Hawks versus Jaguars
Cardinals versus Cobras

Solution: Find 11:30 A. M. on the schedule. The Waves versus Alligators game ends at 11:30 A. M.


Question: Each branch has 5 flowers. How many flowers are on 6 branches?

Answer: 30

Number of branches | Number of flowers
1 | 5
2 | 10
3 | 15
4 | 20
5 | 25
6 | ?

Solution: Count by fives. Use the chart: there are 30 flowers on 6 branches.


Question: Liz's Treats counted how many times its most frequent customers ate ice cream last month. How many customers are there in all?

Answer: 54

Times eaten | Frequency
0 | 8
1 | 17
2 | 9
3 | 20
4 | 0

Solution:
Add the frequencies for each row.

Add:

8 + 17 + 9 + 20 + 0 = 54

There are 54 customers in all.


Question: Valeria buys 3.2 pounds of African rice. What is the total cost?

Answer: 12.80

African rice | $4/lb
basmati rice | $5/lb
white rice | $7/lb
brown rice | $8/lb
sticky rice | $5/lb

African rice
basmati rice
white rice
brown rice
sticky rice

Solution:
Find the cost of the African rice. Multiply the price per pound by the number of pounds.
$4 × 3.2 = $12.80
The total cost is $12.80.


Question: Josie, a fantasy football fan, carefully studied the number of touchdowns completed by her favorite players last season. How many players scored at least 1 touchdown last season?

Answer: 46

Touchdowns scored | Frequency
0 | 8
1 | 20
2 | 15
3 | 10
4 | 0
5 | 1

Solution:
Find the rows for 1, 2, 3, 4, and 5 touchdowns last season. Add the frequencies for these rows.

Add:

20 + 15 + 10 + 0 + 1 = 46

46 players scored at least 1 touchdown last season.


Question: Lola buys 1.4 pounds of lace scraps. What is the total cost?

Answer: 16.80

silk scraps | $8 per lb
lace scraps | $12 per lb
denim scraps | $9 per lb
felt scraps | $10 per lb
canvas scraps | $10 per lb

silk scraps
lace scraps
denim scraps
felt scraps
canvas scraps

$8 per lb
$12 per lb
$9 per lb
$10 per lb
$10 per lb

Solution:
Find the cost of the lace scraps. Multiply the price per pound by the number of pounds.
$12 × 1.4 = $16.80
The total cost is $16.80.


Question: Hunter counted the number of pairs of shoes for sale at each of the shoe stores in the mall. How many stores have exactly 90 pairs of shoes?

Answer: 4

Solution:
For the number 90, the stem is 9, and the leaf is 0. Find the row where the stem is 9. In that row, count all the leaves equal to 0.

You counted 4 leaves, which are blue in the stem-and-leaf plot above. 4 stores have exactly 90 pairs of shoes.


Question: As part of a math lab, Darell tracked the number of times his classmates drew a number between 2 and 8. Which number was drawn the fewest times?

Answer: 4

Solution: Look at the frequency column. Find the least frequency. The least frequency is 0, which is in the row for 4. 4 was drawn the fewest times.


Question: Look at the following schedule. Which class ends at 5.45 P.M.?

Choices:
- Plant Biology class
- Russian class
- Japanese class
- European History class

Answer: European History class

Subject | Begin | End
Russian | 8:10 A.M. | 9:40 A.M.
Ancient Civilizations | 10:20 A.M. | 11:45 A.M.
Plant Biology | 12:20 P.M. | 1:45 P.M.
Advanced Algebra | 2:10 P.M. | 3:00 P.M.
Japanese | 3:40 P.M. | 5:00 P.M.
European History | 5:10 P.M. | 5:45 P.M.

Russian
Ancient Civilizations
Plant Biology
Advanced Algebra
Japanese
European History

Solution: Find 5:45 P. M. on the schedule. European History class ends at 5:45 P. M.


Question: The local high school found out how many members each club had. What is the mode of the numbers?

Answer: 9

Club | Number of members
Japanese club | 9
film club | 9
history club | 8
speech club | 9
French club | 8

Japanese club
film club
history club
speech club
French club

Solution:
Read the numbers from the table.

9, 9, 8, 9, 8

First, arrange the numbers from least to greatest:

8, 8, 9, 9, 9

Now count how many times each number appears.

8 appears 2 times.
9 appears 3 times.

The number that appears most often is 9.

The mode is 9.


Question: How much money does Brenda need to buy 7 hang gliders?

Answer: 63,553

hovercraft | $2,810
golf cart | $9,384
trailer | $6,652
hang glider | $9,079
canoe | $2,511
speedboat | $9,880

hovercraft
golf cart
trailer
hang glider
canoe
speedboat

Solution:
Find the total cost of 7 hang gliders by multiplying 7 times the price of a hang glider.

$9,079 × 7 = $63,553

Brenda needs $63,553.


Question: A pair of Franklin High School hockey fans counted the number of games won by the school each year. According to the table, what was the rate of change between 2015 and 2016?

Answer: 0

Solution:
Plug the numbers into the formula for rate of change and simplify.
Rate of change
 = \frac{change in value}{change in time}
 = \frac{12 games - 12 games}{2016 - 2015}
 = \frac{12 games - 12 games}{1 year}
 = \frac{0 games}{1 year}
 = 0 games per year
The rate of change between 2015 and 2016 was 0 games per year.


Question: How much more does a Jamaican vacation package cost than a Caribbean vacation package?

Answer: 5,349

African safari vacation package | $8,630.00
Caribbean vacation package | $3,920.00
Hawaiian vacation package | $6,637.00
Jamaican vacation package | $9,269.00
European vacation package | $8,988.00

African safari vacation package
Caribbean vacation package
Hawaiian vacation package
Jamaican vacation package
European vacation package

Solution:
Subtract the price of a Caribbean vacation package from the price of a Jamaican vacation package.

$9,269.00 - $3,920.00 = $5,349.00

A Jamaican vacation package costs $5,349.00 more than a Caribbean vacation package.


Question: The members of the local garden club tallied the number of plants in each person's garden. How many gardens have at least 30 plants?

Answer: 6

Solution:
Count all the leaves in the rows with stems 3, 4, 5, 6, and 7.

You counted 6 leaves, which are blue in the stem-and-leaf plot above. 6 gardens have at least 30 plants.


Question: How much money does Lauren need to buy a boxcar and a jet ski?

Answer: 13,802

Solution:
Add the price of a boxcar and the price of a jet ski:

$7,900 + $5,902 = $13,802

Lauren needs $13,802.


Question: Danny's classmates revealed how many science articles they read. Together, how many science articles did Danny and Lisa read?

Answer: 808

Name | Number of science articles
Karen | 173
Danny | 682
Lisa | 126
Alan | 130

Solution:
Find the numbers in the table.

Danny: 682
Lisa: 126

Now add: 682 + 126 = 808.

Danny and Lisa read 808 science articles.


Question: How much would it cost to buy 3 pounds of gummy bears, 3 pounds of yogurt-covered peanuts, and 2 pounds of licorice?

Answer: 17

lemon sours | $1 per pound
yogurt-covered peanuts | $1 per pound
gummy bears | $2 per pound
licorice | $4 per pound

lemon sours
yogurt-covered peanuts
gummy bears
licorice

$1 per pound
$1 per pound
$2 per pound
$4 per pound

Solution:
Find the cost of the gummy bears. Multiply:

$2 × 3 = $6

Find the cost of the yogurt-covered peanuts. Multiply:

$1 × 3 = $3

Find the cost of the licorice. Multiply:

$4 × 2 = $8

Now find the total cost by adding:

$6 + $3 + $8 = $17

It would cost $17.


Question: A flight attendant was counting the number of passengers present to see if any upgrades could be offered. The flight attendant's list contained passengers' Frequent Flyer status as well as number of bags checked. What is the probability that a randomly selected passenger has 1 checked bag and silver status? Simplify any fractions.

Answer: 1/5

 | Bronze status | Silver status
0 checked bags | 4 | 4
1 checked bag | 8 | 4

Solution:
Let A be the event "the passenger has 1 checked bag" and B be the event "the passenger has silver status".
To find the probability that a passenger has 1 checked bag and silver status, first identify the sample space and the event.
The outcomes in the sample space are the different passengers. Each passenger is equally likely to be selected, so this is a uniform probability model.
The event is A and B, "the passenger has 1 checked bag and silver status".
Since this is a uniform probability model, count the number of outcomes in the event A and B and count the total number of outcomes. Then, divide them to compute the probability.

Find the number of outcomes in the event A and B.
A and B is the event "the passenger has 1 checked bag and silver status", so look at the table to see how many passengers have 1 checked bag and silver status.
The number of passengers who have 1 checked bag and silver status is 4.

Find the total number of outcomes.
Add all the numbers in the table to find the total number of passengers.
4 + 8 + 4 + 4 = 20

Find P(A and B).
Since all outcomes are equally likely, the probability of event A and B is the number of outcomes in event A and B divided by the total number of outcomes.
P(A and B) = \frac{# of outcomes in A and B}{total # of outcomes}
 = \frac{4}{20}
 = \frac{1}{5}
The probability that a passenger has 1 checked bag and silver status is \frac{1}{5}.


Question: The coach of the Academic Bowl recorded the scores in a trivia game to determine who would represent the school at the regional competition. How many people scored more than 9?

Answer: 14

Solution:
Find the row for 10 and read the frequency. The frequency is 14.

14 people scored more than 9.


Question: Dylan's classmates revealed how many science articles they read. What is the mean of the numbers?

Answer: 8

Name | Number of science articles
Dylan | 7
Kenji | 5
Nellie | 8
Braden | 9
Tisha | 10
Maureen | 9

Solution:
Read the numbers from the table.

7, 5, 8, 9, 10, 9

First, count how many numbers are in the group.

There are 6 numbers.

Now add all the numbers together:

7 + 5 + 8 + 9 + 10 + 9 = 48

Now divide the sum by the number of numbers:

48 ÷ 6 = 8

The mean is 8.


Question: A food industry researcher compiled the revenues of several pizzerias. Which restaurant made more from pizzas, New York Slice or The Real Chicago?

Choices:
- The Real Chicago
- New York Slice

Answer: The Real Chicago

Restaurant | Cheese pizzas | Vegetarian pizzas
New York Slice | $10 | $19
The Real Chicago | $17 | $19
Dan's Deep Dish | $6 | $12
The Big Cheese | $6 | $16

New York Slice
The Real Chicago
Dan's Deep Dish
The Big Cheese

Solution:
Add the numbers in the New York Slice row. Then, add the numbers in the The Real Chicago row.

New York Slice: $10.00 + $19.00 = $29.00
The Real Chicago: $17.00 + $19.00 = $36.00

$36.00 is more than $29.00. The Real Chicago made more from pizzas.


Question: An architecture student measured the heights of all the buildings downtown. How many buildings are at least 27 meters tall?

Answer: 12

Solution:
Find the row with stem 2. Count all the leaves greater than or equal to 7.

Count all the leaves in the rows with stems 3, 4, 5, 6, 7, and 8.

You counted 12 leaves, which are blue in the stem-and-leaf plots above. 12 buildings are at least 27 meters tall.


Question: Perry's Treats counted how many times its most frequent customers ate ice cream last month. How many customers ate ice cream at least 1 time?

Answer: 29

Solution:
Find the rows for 1, 2, 3, 4, and 5 times. Add the frequencies for these rows.

Add:

4 + 17 + 7 + 0 + 1 = 29

29 customers ate ice cream at least 1 time.


Question: A pet store owner had his staff count the number of fish in each tank. What is the largest number of fish per tank?

Answer: 68

Solution:
Look at the last row of the stem-and-leaf plot. The last row has the highest stem. The stem for the last row is 6.

Now find the highest leaf in the last row. The highest leaf is 8.

The largest number of fish per tank has a stem of 6 and a leaf of 8. Write the stem first, then the leaf: 68.

The largest number of fish per tank is 68 fish.


Question: Look at the following schedule. When does Ms. Hampton's class begin?

Choices:
- 2:50 P.M.
- 1:55 P.M.
- 9:50 A.M.
- 2:00 P.M.

Answer: 2:00 P.M.

Class | Begin | End
Mr. Harper's class | 7:25 A.M. | 8:20 A.M.
Mrs. Suzuki's class | 8:25 A.M. | 9:30 A.M.
Mrs. Carlson's class | 9:50 A.M. | 10:20 A.M.
Ms. Dyer's class | 10:30 A.M. | 11:10 A.M.
Mr. Mason's class | 11:20 A.M. | 11:55 A.M.
Mrs. McCoy's class | 12:00 P.M. | 12:45 P.M.
Ms. Mueller's class | 1:05 P.M. | 1:55 P.M.
Ms. Hampton's class | 2:00 P.M. | 2:50 P.M.

Mr. Harper's class
Mrs. Suzuki's class
Mrs. Carlson's class
Ms. Dyer's class
Mr. Mason's class
Mrs. McCoy's class
Ms. Mueller's class
Ms. Hampton's class

Solution:
Find Ms. Hampton's class on the schedule. Find the beginning time for Ms. Hampton's class.

Ms. Hampton's class: 2:00 P. M.


Question: For an economics project, Jim determined the cost of ferry rides for bicycles and cars. How much higher is the fare for a car on the Seattle-Bremerton ferry than on the Mukilteu-Clinton ferry?

Answer: 5

Ferry | Car | Bicycle
Southport-Fort Fisher | $5 | $2
Mukilteu-Clinton | $7 | $5
Ocracoke | $15 | $3
Fauntleroy-Vashon | $15 | $5
Seattle-Bremerton | $12 | $8

Southport-Fort Fisher
Mukilteu-Clinton
Ocracoke
Fauntleroy-Vashon
Seattle-Bremerton

Solution:
Find the Car column. Find the numbers in this column for Seattle-Bremerton and Mukilteu-Clinton.

Seattle-Bremerton: $12.00
Mukilteu-Clinton: $7.00

Now subtract:

$12.00 − $7.00 = $5.00

The fare for a car is $5 more on the Seattle-Bremerton ferry than on the Mukilteu-Clinton ferry.


Question: Danny has $103.16. How much money will Danny have left if he buys a model airplane and a mystery game?

Answer: 49.93

toy guitar | $25.03
remote control car | $16.92
mystery game | $14.34
model airplane | $38.89
chess board | $12.98
trivia game | $31.99

toy guitar
remote control car
mystery game
model airplane
chess board
trivia game

Solution:
Find the total cost of a model airplane and a mystery game.

$38.89 + $14.34 = $53.23

Now subtract the total cost from the starting amount.

$103.16 - $53.23 = $49.93

Danny will have $49.93 left.


Question: After a field trip to the park, students in Mrs. Garcia's art class counted the number of leaf rubbings they had made. How many students made at least 2 leaf rubbings?

Answer: 14

Leaf rubbings made | Frequency
0 | 20
1 | 13
2 | 3
3 | 11

Solution:
Find the rows for 2 and 3 leaf rubbings. Add the frequencies for these rows.

Add:

3 + 11 = 14

14 students made at least 2 leaf rubbings.


Question: Each toy bin has 2 red blocks. How many red blocks are in 5 toy bins?

Answer: 10

Number of toy bins | Number of red blocks
1 | 2
2 | 4
3 | 6
4 | 8
5 | ?

Solution: Count by twos. Use the chart: there are 10 red blocks in 5 toy bins.


Question: Look at the table. Then answer the question. At a price of $65, is there a shortage or a surplus?

Choices:
- shortage
- surplus

Answer: surplus

Solution: At the price of $65, the quantity demanded is less than the quantity supplied. There is too much of the good or service for sale at that price. So, there is a surplus.


Question: The players on a quiz show received the following scores. Who had the highest score?

Choices:
- Vince
- Herman
- Tom
- Wesley

Answer: Wesley

Name | Score
Vince | 445
Herman | 425
Tom | 422
Wesley | 452

Solution:
Find the greatest number in the table. Remember to compare the numbers starting with the highest place value. The greatest number is 452.

Now find the corresponding name. Wesley corresponds to 452.


Question: An environmental agency examined how many trees were planted by different organizations. In all, how many trees were planted by New Planet and Plant It?

Answer: 578

Organization | Number of trees planted
Make it Green | 270
Dreaming Green | 454
New Planet | 207
Plant It | 371

Make it Green
Dreaming Green
New Planet
Plant It

Solution:
Find the numbers in the table.

New Planet: 207
Plant It: 371

Now add: 207 + 371 = 578.

In all, 578 trees were planted by New Planet and Plant It.


Question: Castroville University offers four applied majors and monitors the number of students in each. What fraction of the students in applied majors are majoring in mechanical engineering? Simplify your answer.

Answer: 5/28

School | Intake
Electronics | 170
Architecture | 470
Civil engineering | 280
Mechanical engineering | 200

Electronics
Architecture
Civil engineering
Mechanical engineering

Solution:
Find how many students are majoring in mechanical engineering.

200

Find how many total students are in all the applied majors.

170 + 470 + 280 + 200 = 1,120

Divide 200 by1,120.

\frac{200}{1,120}

Reduce the fraction.

\frac{200}{1,120} → \frac{5}{28}

\frac{5}{28} of students are majoring in mechanical engineering.


Question: Look at this table. Is this relation a function?

Choices:
- yes
- no

Answer: yes

Solution:
Look at the x-values in the table.

Each of the x-values is paired with only one y-value, so the relation is a function.


Question: Look at this table. Is this relation a function?

Choices:
- yes
- no

Answer: yes


Question: If Edwin buys 4 kilograms of chestnuts, 5 kilograms of peanuts, and 5 kilograms of macadamia nuts, how much will he spend?

Answer: 50.31

pine nuts | $5.43 per kilogram
Brazil nuts | $3.93 per kilogram
chestnuts | $5.14 per kilogram
macadamia nuts | $4.00 per kilogram
pistachios | $2.86 per kilogram
peanuts | $1.95 per kilogram

pine nuts
Brazil nuts
chestnuts
macadamia nuts
pistachios
peanuts

$5.43 per kilogram
$3.93 per kilogram
$5.14 per kilogram
$4.00 per kilogram
$2.86 per kilogram
$1.95 per kilogram

Solution:
Find the cost of the chestnuts. Multiply:

$5.14 × 4 = $20.56

Find the cost of the peanuts. Multiply:

$1.95 × 5 = $9.75

Find the cost of the macadamia nuts. Multiply:

$4 × 5 = $20

Now find the total cost by adding:

$20.56 + $9.75 + $20 = $50.31

He will spend $50.31.


Question: In considering whether to open a new branch, the city council examined the number of times some typical residents went to the library last month. How many people went to the library at least 3 times last month?

Answer: 44

Number of trips | Frequency
1 | 1
2 | 12
3 | 6
4 | 9
5 | 13
6 | 16

Solution:
Find the rows for 3, 4, 5, and 6 times last month. Add the frequencies for these rows.

Add:

6 + 9 + 13 + 16 = 44

44 people went to the library at least 3 times last month.


Question: Nora has $11. Does she have enough to buy fried eggs and a breakfast burrito?

Choices:
- yes
- no

Answer: no

breakfast burrito | $9
fried eggs | $3
bowl of melon | $1
waffle with berries | $1

breakfast burrito
fried eggs
bowl of melon
waffle with berries

Solution:
Add the price of fried eggs and the price of a breakfast burrito:

$3 + $9 = $12

$12 is more than $11. Nora does not have enough money.


Question: The table shows a function. Is the function linear or nonlinear?

Choices:
- linear
- nonlinear

Answer: linear

Solution:
To determine whether the function is linear or nonlinear, see whether it has a constant rate of change.
Pick the points in any two rows of the table and calculate the rate of change between them. The first two rows are a good place to start.
Call the values in the first row x1 and y1. Call the values in the second row x2 and y2.
Rate of change = \frac{y2 - y1}{x2 - x1}
 = \frac{10 - 7}{13 - 12}
 = \frac{3}{1}
 = 3
Now pick any other two rows and calculate the rate of change between them.
Call the values in the second row x1 and y1. Call the values in the third row x2 and y2.
Rate of change = \frac{y2 - y1}{x2 - x1}
 = \frac{13 - 10}{14 - 13}
 = \frac{3}{1}
 = 3
The two rates of change are the same.
If you checked the rate of change between rows 1 and 3, you would find that it is also 3.
This means the rate of change is the same for each pair of points. So, the function has a constant rate of change.
The function is linear.


Question: While hanging Christmas lights for neighbors, Kelsey counted the number of broken lights on each string. How many strings had at least 50 broken lights?

Answer: 4

Solution:
Count all the leaves in the rows with stems 5, 6, 7, 8, and 9.

You counted 4 leaves, which are blue in the stem-and-leaf plot above. 4 strings had at least 50 broken lights.


Question: A car dealership tracked the number of cars sold each month. In which month did the dealership sell the most cars?

Choices:
- November
- December
- January
- February

Answer: January

Month | Number of cars
November | 268
December | 286
January | 289
February | 226

Solution:
Find the greatest number in the table. Remember to compare the numbers starting with the highest place value. The greatest number is 289.

Now find the corresponding month. January corresponds to 289.


Question: An administrator at the Department of Motor Vehicles (DMV) tracked the average wait time from month to month. According to the table, what was the rate of change between May and June?

Answer: -34

Month | Waiting time (minutes)
March | 10
April | 7
May | 40
June | 6
July | 50

Solution:
Plug the numbers into the formula for rate of change and simplify.
Rate of change
 = \frac{change in value}{change in time}
 = \frac{6 minutes - 40 minutes}{1 month}
 = \frac{-34 minutes}{1 month}
 = -34 minutes per month
The rate of change between May and June was - 34 minutes per month.


Question: Seth went to the store. He bought 1+3/10 pounds of lentils. How much did he spend?

Answer: 3.90

lentils | $3/pound
sunflower seeds | $3/pound
soybeans | $1/pound
pumpkin seeds | $3/pound
flax seeds | $8/pound
sesame seeds | $5/pound

lentils
sunflower seeds
soybeans
pumpkin seeds
flax seeds
sesame seeds

Solution:
Find the cost of the lentils. Multiply the price per pound by the number of pounds.
$3 × 1\frac{3}{10} = $3 × 1.3 = $3.90
He spent $3.90.


Question: The table shows a function. Is the function linear or nonlinear?

Choices:
- linear
- nonlinear

Answer: linear

Solution:
To determine whether the function is linear or nonlinear, see whether it has a constant rate of change.
Pick the points in any two rows of the table and calculate the rate of change between them. The first two rows are a good place to start.
Call the values in the first row x1 and y1. Call the values in the second row x2 and y2.
Rate of change = \frac{y2 - y1}{x2 - x1}
 = \frac{12 - 20}{1 - 0}
 = \frac{-8}{1}
 = -8
Now pick any other two rows and calculate the rate of change between them.
Call the values in the second row x1 and y1. Call the values in the third row x2 and y2.
Rate of change = \frac{y2 - y1}{x2 - x1}
 = \frac{4 - 12}{2 - 1}
 = \frac{-8}{1}
 = -8
The two rates of change are the same.
8.
This means the rate of change is the same for each pair of points. So, the function has a constant rate of change.
The function is linear.


Question: Eddie has $9.50. Does he have enough to buy a coffee mug and a glass bowl?

Choices:
- yes
- no

Answer: no

coffee mug | $2.93
glass measuring cup | $5.81
cookie jar | $5.92
serving platter | $8.06
glass bowl | $6.97

coffee mug
glass measuring cup
cookie jar
serving platter
glass bowl

Solution:
Add the price of a coffee mug and the price of a glass bowl:

$2.93 + $6.97 = $9.90

$9.90 is more than $9.50. Eddie does not have enough money.


Question: The table shows a function. Is the function linear or nonlinear?

Choices:
- linear
- nonlinear

Answer: nonlinear

Solution:
To determine whether the function is linear or nonlinear, see whether it has a constant rate of change.
Pick the points in any two rows of the table and calculate the rate of change between them. The first two rows are a good place to start.
Call the values in the first row x1 and y1. Call the values in the second row x2 and y2.
Rate of change = \frac{y2 - y1}{x2 - x1}
 = \frac{1 - 0}{6 - 5}
 = \frac{1}{1}
 = 1
Now pick any other two rows and calculate the rate of change between them.
Call the values in the second row x1 and y1. Call the values in the third row x2 and y2.
Rate of change = \frac{y2 - y1}{x2 - x1}
 = \frac{4 - 1}{7 - 6}
 = \frac{3}{1}
 = 3
The rate of change is not the same for each pair of points. So, the function does not have a constant rate of change.
The function is nonlinear.


Question: Look at the following schedule. Nina just missed the 12.15 P.M. train at Ashland. What time is the next train?

Choices:
- 3:15 A.M.
- 12:45 A.M.
- 10:15 P.M.
- 7:30 P.M.

Answer: 7:30 P.M.

Springfield Ashland Lexington Burlington Newberry Lancaster Cedarburg Morristown Newberg

Solution:
Find 12:15 P. M. in the row for Ashland.

Look for the next train in that row.

The next train is at 7:30 P. M.


Question: Josh looked over his calendar to see how many times he had soccer practice each month. In which month did Josh have the most soccer practices?

Choices:
- November
- March
- April
- May

Answer: April

Month | Number of practices
November | 24
March | 23
April | 28
May | 22

Solution:
Find the greatest number in the table. Remember to compare the numbers starting with the highest place value. The greatest number is 28.

Now find the corresponding month. April corresponds to 28.


Question: Look at the table. Then answer the question. At a price of $960, is there a shortage or a surplus?

Choices:
- shortage
- surplus

Answer: shortage

Solution: At the price of $960, the quantity demanded is greater than the quantity supplied. There is not enough of the good or service for sale at that price. So, there is a shortage.


Question: An economics student recorded the amount of per-capita aid that the U.S. gave to various countries during the 1900s. Per capita, how much more aid did Pakistan receive in 1980 than in 1990?

Answer: 4

Country | 1980 | 1990
Algeria | $9 | $10
Afghanistan | $2 | $7
Libya | $5 | $5
Pakistan | $14 | $10

Country Algeria Afghanistan Libya Pakistan

Solution:
Find the Pakistan row. Find the numbers in this row for 1980 and 1990.

1980: $14.00
1990: $10.00

Now subtract:

$14.00 − $10.00 = $4.00

Per capita, Pakistan received $4 more in aid in 1980 than in 1990.


Question: A law firm in Weston kept track of how many hours were billed by each partner last year. What fraction of the hours were billed by Jamie? Simplify your answer.

Answer: 100/533

Partner | Hours billed
Jenna | 690
Maddie | 950
Jamie | 1,000
Grayson | 910
Sidney | 890
Mitchell | 890

Jenna Maddie Jamie Grayson Sidney Mitchell

Solution:
Find how many hours were billed by Jamie.

1,000

Find how many hours were billed in total.

690 + 950 + 1,000 + 910 + 890 + 890 = 5,330

Divide 1,000 by 5,330.

\frac{1,000}{5,330}

Reduce the fraction.

\frac{1,000}{5,330} → \frac{100}{533}

\frac{100}{533} of hours were billed by Jamie.


Question: Elena has $0.74. Does she have enough to buy a shiny metal bead and a thick gray bead?

Choices:
- yes
- no

Answer: yes

bead with green and blue swirls | $0.52
star-shaped silver bead | $0.47
shiny metal bead | $0.28
long red bead | $0.72
thick gray bead | $0.44
white bead with black spots | $0.27

bead with green and blue swirls
star-shaped silver bead
shiny metal bead
long red bead
thick gray bead
white bead with black spots

Solution:
Add the price of a shiny metal bead and the price of a thick gray bead:

$0.28 + $0.44 = $0.72

$0.72 is less than $0.74. Elena does have enough money.


Question: Kamal kept track of the number of characters in each book he read. How many books had at least 30 characters but fewer than 50 characters?

Answer: 8

Solution:
Count all the leaves in the rows with stems 3 and 4.

You counted 8 leaves, which are blue in the stem-and-leaf plot above. 8 books had at least 30 characters but fewer than 50 characters.


Question: Tyler went on a bird watching trip and jotted down the number of birds he saw each day. What is the mode of the numbers?

Answer: 6

Day | Number of birds
Friday | 2
Saturday | 6
Sunday | 6
Monday | 2
Tuesday | 6

Solution:
Read the numbers from the table.

2, 6, 6, 2, 6

First, arrange the numbers from least to greatest:

2, 2, 6, 6, 6

Now count how many times each number appears.

2 appears 2 times.
6 appears 3 times.

The number that appears most often is 6.

The mode is 6.


Question: Tammy has $1.06. Does she have enough to buy a tangerine and a nectarine?

Choices:
- yes
- no

Answer: yes

apricot | $0.40
nectarine | $0.33
tangerine | $0.69
pear | $0.51

Solution:
Add the price of a tangerine and the price of a nectarine:

$0.69 + $0.33 = $1.02

$1.02 is less than $1.06. Tammy does have enough money.


Question: Cody's Candies has been studying how much chocolate people have been eating in different countries. In 2002, how much more chocolate did Denmark consume per capita than Australia?

Answer: 5

Country | 2002 | 2005
Australia | 4 | 5
Germany | 10 | 11
Denmark | 9 | 8
Belgium | 8 | 11

Country Australia Germany Denmark Belgium

Solution:
Find the 2002 column. Find the numbers in this column for Denmark and Australia.

Denmark: 9
Australia: 4

Now subtract:

9 − 4 = 5

In 2002, Denmark consumed 5 kilograms more chocolate per capita than Australia.


Question: Damon counted the number of ducks at each pond in the city. How many ponds had at least 50 ducks but fewer than 68 ducks?

Answer: 5

Solution:
Count all the leaves in the row with stem 5.

In the row with stem 6, count all the leaves less than 8.

You counted 5 leaves, which are blue in the stem-and-leaf plots above. 5 ponds had at least 50 ducks but fewer than 68 ducks.


Question: Mr. Kerr recorded the scores of his students on the most recent math quiz. How many students scored more than 9?

Answer: 13

Solution:
Find the row for 10 and read the frequency. The frequency is 13.

13 students scored more than 9.


Question: How much money does Ernest need to buy a baking dish and a mixing bowl?

Answer: 15

cookbook | $3
baking dish | $6
cutting board | $9
mixing bowl | $9

cookbook
baking dish
cutting board
mixing bowl

Solution:
Add the price of a baking dish and the price of a mixing bowl:

$6 + $9 = $15

Ernest needs $15.


Question: The players on a quiz show received the following scores. What is the mode of the numbers?

Answer: 69

Name | Score
Isaac | 65
Mitchell | 69
Charlie | 71
Roger | 69
Haley | 65
Tara | 71
Steven | 69
Dominic | 69

Isaac Mitchell Charlie Roger Haley Tara Steven Dominic

Solution:
Read the numbers from the table.

65, 69, 71, 69, 65, 71, 69, 69

First, arrange the numbers from least to greatest:

65, 65, 69, 69, 69, 69, 71, 71

Now count how many times each number appears.

65 appears 2 times.
69 appears 4 times.
71 appears 2 times.

The number that appears most often is 69.

The mode is 69.


Question: On a camping trip, Clara kept a log of the types of snakes she saw. She noted their colors and approximate lengths. What is the probability that a randomly selected snake is red and 1 foot long? Simplify any fractions.

Answer: 4/17

 | 1 foot long | 2 feet long
Red | 4 | 3
Bright orange | 5 | 5

Solution:
Let A be the event "the snake is red" and B be the event "the snake is 1 foot long".
To find the probability that a snake is red and 1 foot long, first identify the sample space and the event.
The outcomes in the sample space are the different snakes. Each snake is equally likely to be selected, so this is a uniform probability model.
The event is A and B, "the snake is red and 1 foot long".
Since this is a uniform probability model, count the number of outcomes in the event A and B and count the total number of outcomes. Then, divide them to compute the probability.

Find the number of outcomes in the event A and B.
A and B is the event "the snake is red and 1 foot long", so look at the table to see how many snakes are red and 1 foot long.
The number of snakes that are red and 1 foot long is 4.

Find the total number of outcomes.
Add all the numbers in the table to find the total number of snakes.
4 + 5 + 3 + 5 = 17

Find P(A and B).
Since all outcomes are equally likely, the probability of event A and B is the number of outcomes in event A and B divided by the total number of outcomes.
P(A and B) = \frac{# of outcomes in A and B}{total # of outcomes}
 = \frac{4}{17}
The probability that a snake is red and 1 foot long is \frac{4}{17}.


Question: Dr. Wagner, a pediatrician, weighed all the children who recently visited his office. How many children weighed at least 60 pounds but less than 70 pounds?

Answer: 2

Solution:
Count all the leaves in the row with stem 6.

You counted 2 leaves, which are blue in the stem-and-leaf plot above. 2 children weighed at least 60 pounds but less than 70 pounds.


Question: Look at the following schedule. When does the unicycle rider's performance begin?

Choices:
- 8:10 P.M.
- 5:00 P.M.
- 8:35 P.M.
- 8:05 P.M.

Answer: 8:10 P.M.

Performer | Begin | End
the jugglers | 4:10 P.M. | 4:15 P.M.
the trapeze artists | 4:25 P.M. | 4:45 P.M.
the strongman | 5:00 P.M. | 5:05 P.M.
the stuntman | 5:15 P.M. | 5:55 P.M.
the tightrope walkers | 6:00 P.M. | 6:35 P.M.
the magician | 6:40 P.M. | 7:20 P.M.
the clowns | 7:35 P.M. | 8:05 P.M.
the unicycle rider | 8:10 P.M. | 8:35 P.M.

the jugglers
the trapeze artists
the strongman
the stuntman
the tightrope walkers
the magician
the clowns
the unicycle rider

Solution:
Find the unicycle rider's performance on the schedule. Find the beginning time for the unicycle rider's performance.

the unicycle rider: 8:10 P. M.


Question: The school district compared how many math teachers each high school has. What is the mean of the numbers?

Answer: 7

High school | Number of math teachers
River High | 6
Thompson High | 8
Lincoln High | 10
Northside High | 9
Washington High | 5
Green High | 6
Cedar High | 5
Hillview High | 7

River High
Thompson High
Lincoln High
Northside High
Washington High
Green High
Cedar High
Hillview High

Solution:
Read the numbers from the table.

6, 8, 10, 9, 5, 6, 5, 7

First, count how many numbers are in the group.

There are 8 numbers.

Now add all the numbers together:

6 + 8 + 10 + 9 + 5 + 6 + 5 + 7 = 56

Now divide the sum by the number of numbers:

56 ÷ 8 = 7

The mean is 7.


Question: This is Duncan's complete financial record for July. On July 5, how much money did Duncan make?

Answer: 15

Date | Description | Received | Expenses | Available Funds
 | Balance: end of June | | | $450.70
7/5 | cleaning the Owens' pool | $15.00 | | $465.70
7/17 | bottle of water | | $1.50 | $464.20
7/29 | swim trunks | | $16.80 | $447.40

Balance: end of June
cleaning the Owens' pool
bottle of water
swim trunks

Solution: Look at the 7/5 row. The amount received was $15.00. So, Duncan made $15.00 on July 5.


Question: How much money does Donald need to buy a fish bowl and a bag of birdseed?

Answer: 14

bag of birdseed | $9
dog bowl | $9
fish bowl | $5
box of dog biscuits | $2
dog leash | $3
hamster wheel | $3

bag of birdseed
dog bowl
fish bowl
box of dog biscuits
dog leash
hamster wheel

Solution:
Add the price of a fish bowl and the price of a bag of birdseed:

$5 + $9 = $14

Donald needs $14.


Question: A taxi cab driver tracked how many miles she drove each month. How many more miles did the taxi cab driver drive in July than in August?

Answer: 2,154

Month | Miles
July | 3,229
August | 1,075
September | 5,242

Solution:
Find the numbers in the table.

July: 3,229
August: 1,075

Now subtract: 3,229 - 1,075 = 2,154.

The taxi cab driver drove 2,154 more miles in July.


Question: Emilia counted the number of pairs of shoes for sale at each of the shoe stores in the mall. How many stores have at least 60 pairs of shoes but fewer than 100 pairs of shoes?

Answer: 4

Solution:
Count all the leaves in the rows with stems 6, 7, 8, and 9.

You counted 4 leaves, which are blue in the stem-and-leaf plot above. 4 stores have at least 60 pairs of shoes but fewer than 100 pairs of shoes.


Question: A math textbook explains probability by showing a set of cards numbered 4 through 9 and showing the number of people who might draw each card. How many people are there in all?

Answer: 57

Solution:
Add the frequencies for each row.

Add:

1 + 9 + 8 + 16 + 11 + 12 = 57

There are 57 people in all.


Question: Brianna conducted a blind taste test on some of her friends in order to determine if organic fruits tasted different than non-organic fruits. Each friend ate one type of fruit. What is the probability that a randomly selected friend preferred non-organic and tasted apples? Simplify any fractions.

Answer: 1/11

 | Apples | Peaches
Organic | 3 | 4
Non-organic | 1 | 3

Solution:
Let A be the event "the friend preferred non-organic" and B be the event "the friend tasted apples".
To find the probability that a friend preferred non-organic and tasted apples, first identify the sample space and the event.
The outcomes in the sample space are the different friends. Each friend is equally likely to be selected, so this is a uniform probability model.
The event is A and B, "the friend preferred non-organic and tasted apples".
Since this is a uniform probability model, count the number of outcomes in the event A and B and count the total number of outcomes. Then, divide them to compute the probability.

Find the number of outcomes in the event A and B.
A and B is the event "the friend preferred non-organic and tasted apples", so look at the table to see how many friends preferred non-organic and tasted apples.
The number of friends who preferred non-organic and tasted apples is 1.

Find the total number of outcomes.
Add all the numbers in the table to find the total number of friends.
3 + 1 + 4 + 3 = 11

Find P(A and B).
Since all outcomes are equally likely, the probability of event A and B is the number of outcomes in event A and B divided by the total number of outcomes.
P(A and B) = \frac{# of outcomes in A and B}{total # of outcomes}
 = \frac{1}{11}
The probability that a friend preferred non-organic and tasted apples is \frac{1}{11}.


Question: Matthew has $428.00. How much money will Matthew have left if he buys a king snake and a bearded dragon?

Answer: 191

king snake | $119.00
chameleon | $277.00
chinchilla | $112.00
bearded dragon | $118.00

king snake
chameleon
chinchilla
bearded dragon

Solution:
Find the total cost of a king snake and a bearded dragon.

$119.00 + $118.00 = $237.00

Now subtract the total cost from the starting amount.

$428.00 - $237.00 = $191.00

Matthew will have $191.00 left.


Question: Each box has 5 yogurt pops. How many yogurt pops are in 6 boxes?

Answer: 30

Number of boxes | Number of yogurt pops
1 | 5
2 | 10
3 | 15
4 | 20
5 | 25
6 | ?

Solution: Count by fives. Use the chart: there are 30 yogurt pops in 6 boxes.


Question: Each shelf has 10 plates. How many plates are on 3 shelves?

Answer: 30

Number of shelves | Number of plates
1 | 10
2 | 20
3 | ?

Solution: Count by tens. Use the chart: there are 30 plates on 3 shelves.


Question: How much money does Lacey need to buy an orange T-shirt, a pair of white socks, and a pair of shorts?

Answer: 16

orange T-shirt | $7
long-sleeved shirt | $4
pair of white socks | $4
pair of shorts | $5

orange T-shirt
long-sleeved shirt
pair of white socks
pair of shorts

Solution:
Find the total cost of an orange T-shirt, a pair of white socks, and a pair of shorts.

$7 + $4 + $5 = $16

Lacey needs $16.


Question: Every year Ashland has a citywide relay and reports the winning times. According to the table, what was the rate of change between 2010 and 2011?

Answer: 3

Solution:
Plug the numbers into the formula for rate of change and simplify.
Rate of change
 = \frac{change in value}{change in time}
 = \frac{33 minutes - 30 minutes}{2011 - 2010}
 = \frac{33 minutes - 30 minutes}{1 year}
 = \frac{3 minutes}{1 year}
 = 3 minutes per year
The rate of change between 2010 and 2011 was 3 minutes per year.


Question: A shipping company keeps track of the number of boxes in each shipment they send out. How many shipments had at least 10 boxes?

Answer: 23

Solution:
Count all the leaves in the rows with stems 1, 2, 3, 4, 5, 6, and 7.

You counted 23 leaves, which are blue in the stem-and-leaf plot above. 23 shipments had at least 10 boxes.


Question: A county agency recorded the money donated to several charitable causes over time. In May, which cause raised the least money?

Choices:
- education
- hunger
- medical research
- parks

Answer: hunger

Cause | April | May
Hunger | $17 | $2
Parks | $17 | $4
Education | $12 | $7
Medical research | $18 | $9

Solution:
Look at the numbers in the May column. Find the least number in this column.

The least number is $2.00, which is in the Hunger row. In May, the least money was raised for hunger.


Question: Ernest designs bow ties for a local boutique store. The store manager counted the ties currently on display, tracking them by material and shape. What is the probability that a randomly selected bow tie is made of suede and is shaped like a butterfly? Simplify any fractions.

Answer: 2/7

 | Butterfly | Batwing
Cotton | 1 | 3
Suede | 4 | 6

Solution:
Let A be the event "the bow tie is made of suede" and B be the event "the bow tie is shaped like a butterfly".
To find the probability that a bow tie is made of suede and is shaped like a butterfly, first identify the sample space and the event.
The outcomes in the sample space are the different bow ties. Each bow tie is equally likely to be selected, so this is a uniform probability model.
The event is A and B, "the bow tie is made of suede and is shaped like a butterfly".
Since this is a uniform probability model, count the number of outcomes in the event A and B and count the total number of outcomes. Then, divide them to compute the probability.

Find the number of outcomes in the event A and B.
A and B is the event "the bow tie is made of suede and is shaped like a butterfly", so look at the table to see how many bow ties are made of suede and are shaped like a butterfly.
The number of bow ties that are made of suede and are shaped like a butterfly is 4.

Find the total number of outcomes.
Add all the numbers in the table to find the total number of bow ties.
1 + 4 + 3 + 6 = 14

Find P(A and B).
Since all outcomes are equally likely, the probability of event A and B is the number of outcomes in event A and B divided by the total number of outcomes.
P(A and B) = \frac{# of outcomes in A and B}{total # of outcomes}
 = \frac{4}{14}
 = \frac{2}{7}
The probability that a bow tie is made of suede and is shaped like a butterfly is \frac{2}{7}.


Question: As part of a statistics project, a math class weighed all the children who were willing to participate. What is the weight of the lightest child?

Answer: 10

Solution:
Look at the first row of the stem-and-leaf plot. The first row has the lowest stem. The stem for the first row is 1.

Now find the lowest leaf in the first row. The lowest leaf is 0.

The weight of the lightest child has a stem of 1 and a leaf of 0. Write the stem first, then the leaf: 10.

The weight of the lightest child is 10 pounds.


Question: A business magazine surveyed its readers about their commute times. How many commutes are less than 51 minutes?

Answer: 6

Solution:
Count all the leaves in the rows with stems 3 and 4.

In the row with stem 5, count all the leaves less than 1.

You counted 6 leaves, which are blue in the stem-and-leaf plots above. 6 commutes are less than 51 minutes.


Question: At a candy factory, butterscotch candies were packaged into bags of different sizes. How many bags had at least 29 butterscotch candies but fewer than 77 butterscotch candies?

Answer: 16

Solution:
Find the row with stem 2. Count all the leaves greater than or equal to 9.

Count all the leaves in the rows with stems 3, 4, 5, and 6.

In the row with stem 7, count all the leaves less than 7.

You counted 16 leaves, which are blue in the stem-and-leaf plots above. 16 bags had at least 29 butterscotch candies but fewer than 77 butterscotch candies.


Question: Gabrielle purchased 2 pounds of blueberries, 1 pound of raspberries, and 5 pounds of loganberries. What was the total cost?

Answer: 36.18

loganberries | $5.88 per lb
blueberries | $2.35 per lb
strawberries | $4.04 per lb
raspberries | $2.08 per lb

loganberries blueberries strawberries raspberries

$5.88 per lb
$2.35 per lb
$4.04 per lb
$2.08 per lb

Solution:
Find the cost of the blueberries. Multiply:

$2.35 × 2 = $4.70

Find the cost of the raspberries. Multiply:

$2.08 × 1 = $2.08

Find the cost of the loganberries. Multiply:

$5.88 × 5 = $29.40

Now find the total cost by adding:

$4.70 + $2.08 + $29.40 = $36.18

The total cost was $36.18.


Question: Ms. Cline reported her students' scores on the most recent quiz. How many students scored fewer than 80 points?

Answer: 23

Solution:
Count all the leaves in the rows with stems 4, 5, 6, and 7.

You counted 23 leaves, which are blue in the stem-and-leaf plot above. 23 students scored fewer than 80 points.


Question: Mr. Christensen, a track coach, recorded the sizes of all the nearby track teams. How many teams have fewer than 50 members?

Answer: 12

Solution:
Count all the leaves in the rows with stems 2, 3, and 4.

You counted 12 leaves, which are blue in the stem-and-leaf plot above. 12 teams have fewer than 50 members.


Question: How much money does Lester need to buy 8 chocolate cheesecakes?

Answer: 70.80

pecan pie | $6.38
pumpkin pie | $9.74
chocolate cheesecake | $8.85
almond tart | $9.79

pecan pie
pumpkin pie
chocolate cheesecake
almond tart

Solution:
Find the total cost of 8 chocolate cheesecakes by multiplying 8 times the price of a chocolate cheesecake.

$8.85 × 8 = $70.80

Lester needs $70.80.


Question: The bird-watching club recorded how many birds its members saw each month. In which month did the club see the most birds?

Choices:
- October
- November
- December
- January

Answer: December

Month | Number of birds
October | 125
November | 115
December | 152
January | 121

Solution:
Find the greatest number in the table. Remember to compare the numbers starting with the highest place value. The greatest number is 152.

Now find the corresponding month. December corresponds to 152.


Question: After a spelling bee, some students compared how many words they spelled correctly. What is the range of the numbers?

Answer: 18

Name | Number of words spelled correctly
Tucker | 56
Ann | 54
Denise | 54
Nate | 57
Omar | 54
Malik | 65
Kimi | 72

Solution:
Read the numbers from the table.

56, 54, 54, 57, 54, 65, 72

First, find the greatest number. The greatest number is 72.

Next, find the least number. The least number is 54.

Subtract the least number from the greatest number:

72 − 54 = 18

The range is 18.


Question: The players on a quiz show received the following scores. What is the mean of the numbers?

Answer: 7

Name | Score
Mitch | 9
Gina | 9
Riley | 4
Anthony | 7
Betty | 3
Elise | 8
Jada | 9

Mitch Gina Riley Anthony Betty Elise Jada

Solution:
Read the numbers from the table.

9, 9, 4, 7, 3, 8, 9

First, count how many numbers are in the group.

There are 7 numbers.

Now add all the numbers together:

9 + 9 + 4 + 7 + 3 + 8 + 9 = 49

Now divide the sum by the number of numbers:

49 ÷ 7 = 7

The mean is 7.


Question: The city recorded how many fire hydrants there are on each street. What is the mode of the numbers?

Answer: 3

Street | Number of hydrants
Oak Street | 3
Lemon Street | 6
Maple Street | 3
Pine Street | 3
Cedar Street | 7
Fir Street | 6
Elm Street | 1
Aspen Street | 7

Oak Street
Lemon Street
Maple Street
Pine Street
Cedar Street
Fir Street
Elm Street
Aspen Street

Solution:
Read the numbers from the table.

3, 6, 3, 3, 7, 6, 1, 7

First, arrange the numbers from least to greatest:

1, 3, 3, 3, 6, 6, 7, 7

Now count how many times each number appears.

1 appears 1 time.
3 appears 3 times.
6 appears 2 times.
7 appears 2 times.

The number that appears most often is 3.

The mode is 3.


Question: How much money does Tina need to buy 5 denim skirts and 4 purple dresses?

Answer: 65.63

denim skirt | $8.47
pair of shoes | $6.12
orange T-shirt | $7.50
pair of sweat pants | $6.93
purple dress | $5.82

denim skirt
pair of shoes
orange T-shirt
pair of sweat pants
purple dress

Solution:
Find the cost of 5 denim skirts.

$8.47 × 5 = $42.35

Find the cost of 4 purple dresses.

$5.82 × 4 = $23.28

Now find the total cost.

$42.35 + $23.28 = $65.63

Tina needs $65.63.


Question: Look at the following schedule. When does lap swim end?

Choices:
- 10:25 A.M.
- 8:50 A.M.
- 2:25 P.M.
- 3:35 P.M.

Answer: 3:35 P.M.

Activity | Begin | End
family swim | 6:45 A.M. | 7:15 A.M.
swim team practice | 7:25 A.M. | 8:50 A.M.
intermediate swimming class | 9:00 A.M. | 9:40 A.M.
beginning swimming class | 9:50 A.M. | 10:25 A.M.
diving club practice | 10:30 A.M. | 11:00 A.M.
water polo practice | 11:15 A.M. | 12:50 P.M.
advanced swimming class | 1:00 P.M. | 2:20 P.M.
lap swim | 2:25 P.M. | 3:35 P.M.

family swim
swim team practice
intermediate swimming class
beginning swimming class
diving club practice
water polo practice
advanced swimming class
lap swim

Solution:
Find lap swim on the schedule. Find the end time for lap swim.

lap swim: 3:35 P. M.


Question: Winchester Flooring tracked the number of broken tiles in each shipment it received last year. What is the largest number of broken tiles?

Answer: 90

Solution:
Look at the last row of the stem-and-leaf plot. The last row has the highest stem. The stem for the last row is 9.

Now find the highest leaf in the last row. The highest leaf is 0.

The largest number of broken tiles has a stem of 9 and a leaf of 0. Write the stem first, then the leaf: 90.

The largest number of broken tiles is 90 broken tiles.


Question: For a science fair project, Oliver tracked the temperature each day. How many temperature readings were exactly 19°C?

Answer: 4

Solution:
For the number 19, the stem is 1, and the leaf is 9. Find the row where the stem is 1. In that row, count all the leaves equal to 9.

You counted 4 leaves, which are blue in the stem-and-leaf plot above. 4 temperature readings were exactly19°C.


Question: A farmer counted the number of apples on each tree in her orchard. How many trees have at least 80 apples?

Answer: 5

Solution:
Count all the leaves in the rows with stems 8 and 9.

You counted 5 leaves, which are blue in the stem-and-leaf plot above. 5 trees have at least 80 apples.


Question: A pet store owner had his staff count the number of fish in each tank. What is the smallest number of fish per tank?

Answer: 11

Solution:
Look at the first row of the stem-and-leaf plot. The first row has the lowest stem. The stem for the first row is 1.

Now find the lowest leaf in the first row. The lowest leaf is 1.

The smallest number of fish per tank has a stem of 1 and a leaf of 1. Write the stem first, then the leaf: 11.

The smallest number of fish per tank is 11 fish.


Question: Eliana is looking at the price of new cell phones online. Her favorite company, OrangeTech, has a special this weekend. Eliana can add an upgrade to a phone for an additional cost, or she can buy a used phone to get a discount. The change in price for each option is shown in the table. Which option results in a greater change in price?

Choices:
- adding an upgrade
- buying a used phone

Answer: buying a used phone

Option | Change in phone price
Add an upgrade | $60
Buy a used phone | -$75

Solution:
To find the option that results in a greater change in price, use absolute value. Absolute value tells you how much the price changes.
Add an upgrade: |$60| = $60
Buy a used phone: |-$75| = $75
Buying a used phone results in a greater change in price. It reduces the price by $75.


Question: Justine's P.E. class participated in a push-up competition, and Justine wrote down how many push-ups each person could do. How many people did at least 60 push-ups?

Answer: 11

Push-up competition (number of push-ups)

Solution:
Count all the leaves in the rows with stems 6 and 7.

You counted 11 leaves, which are blue in the stem-and-leaf plot above. 11 people did at least 60 push-ups.


Question: After growing tired of squinting while driving, Erik went shopping for a pair of sunglasses. He tried on glasses with different frames and lenses. What is the probability that a randomly selected pair of sunglasses has browline frames and polarized lenses? Simplify any fractions.

Answer: 4/15

 | Polarized lenses | Regular lenses
Cat eye frames | 2 | 5
Browline frames | 4 | 4

Solution:
Let A be the event "the pair of sunglasses has browline frames" and B be the event "the pair of sunglasses has polarized lenses".
To find the probability that a pair of sunglasses has browline frames and polarized lenses, first identify the sample space and the event.
The outcomes in the sample space are the different pairs of sunglasses. Each pair of sunglasses is equally likely to be selected, so this is a uniform probability model.
The event is A and B, "the pair of sunglasses has browline frames and polarized lenses".
Since this is a uniform probability model, count the number of outcomes in the event A and B and count the total number of outcomes. Then, divide them to compute the probability.

Find the number of outcomes in the event A and B.
A and B is the event "the pair of sunglasses has browline frames and polarized lenses", so look at the table to see how many pairs of sunglasses have browline frames and polarized lenses.
The number of pairs of sunglasses that have browline frames and polarized lenses is 4.

Find the total number of outcomes.
Add all the numbers in the table to find the total number of pairs of sunglasses.
2 + 4 + 5 + 4 = 15

Find P(A and B).
Since all outcomes are equally likely, the probability of event A and B is the number of outcomes in event A and B divided by the total number of outcomes.
P(A and B) = \frac{# of outcomes in A and B}{total # of outcomes}
 = \frac{4}{15}
The probability that a pair of sunglasses has browline frames and polarized lenses is \frac{4}{15}.


Question: The Lexington Soup Company recorded the number of rotten tomatoes in each barrel it received. How many barrels had at least 20 rotten tomatoes?

Answer: 5

Solution:
Count all the leaves in the rows with stems 2, 3, 4, 5, 6, 7, 8, and 9.

You counted 5 leaves, which are blue in the stem-and-leaf plot above. 5 barrels had at least 20 rotten tomatoes.


Question: Christina has $0.21. How much money will Christina have left if she buys an orange ribbon and a shiny red button?

Answer: 0.08

green pipe cleaner | $0.03
shiny red button | $0.07
silver bow | $0.01
orange ribbon | $0.06

green pipe cleaner
shiny red button
silver bow
orange ribbon

Solution:
Find the total cost of an orange ribbon and a shiny red button.

$0.06 + $0.07 = $0.13

Now subtract the total cost from the starting amount.

$0.21 - $0.13 = $0.08

Christina will have $0.08 left.


Question: A gymnast jotted down the number of cartwheels she did each day. What is the mean of the numbers?

Answer: 8

Day | Number of cartwheels
Wednesday | 8
Thursday | 6
Friday | 10
Saturday | 7
Sunday | 9

Wednesday Thursday Friday Saturday Sunday

Solution:
Read the numbers from the table.

8, 6, 10, 7, 9

First, count how many numbers are in the group.

There are 5 numbers.

Now add all the numbers together:

8 + 6 + 10 + 7 + 9 = 40

Now divide the sum by the number of numbers:

40 ÷ 5 = 8

The mean is 8.


Question: Dr. Rudd, a pediatrician, weighed all the children who recently visited his office. How many children weighed less than 50 pounds?

Answer: 23

Solution:
Count all the leaves in the rows with stems 1, 2, 3, and 4.

You counted 23 leaves, which are blue in the stem-and-leaf plot above. 23 children weighed less than 50 pounds.


Question: Mona went to the store and bought 3+3/4 pounds of fruit salad. How much did she spend?

Answer: 15

potato salad | $3 per pound
macaroni salad | $3 per pound
fruit salad | $4 per pound
egg salad | $5 per pound
tuna salad | $4 per pound
green salad | $5 per pound

potato salad
macaroni salad
fruit salad
egg salad
tuna salad
green salad

$3 per pound
$3 per pound
$4 per pound
$5 per pound
$4 per pound
$5 per pound

Solution:
Find the cost of the fruit salad. Multiply the price per pound by the number of pounds.
$4 × 3\frac{3}{4} = $4 × 3.75 = $15
She spent $15.


Question: An Idaho farmer has been monitoring crop prices over time. Per cwt, how much did Timothy seed cost in 2005?

Answer: 7

Crop
Canola
Timothy seed
Apples
Peas
Potatoes

Solution:
First, find the row for Timothy seed. Then find the number in the 2005 column.

This number is $7.00. In 2005, Timothy seed cost $7 per cwt.


Question: To figure out how many vacation days she had left to use, Erin looked over her old calendars to figure out how many days of vacation she had taken each year. According to the table, what was the rate of change between 2017 and 2018?

Answer: 8

Solution:
Plug the numbers into the formula for rate of change and simplify.
Rate of change
 = \frac{change in value}{change in time}
 = \frac{34 vacation days - 26 vacation days}{2018 - 2017}
 = \frac{34 vacation days - 26 vacation days}{1 year}
 = \frac{8 vacation days}{1 year}
 = 8 vacation days per year
The rate of change between 2017 and 2018 was 8 vacation days per year.


Question: Arlington will decide whether to extend its public pool's hours by looking at the number of times its residents visited the pool last month. How many people went swimming at least 2 times?

Answer: 34

Number of times | Frequency
1 | 4
2 | 8
3 | 3
4 | 16
5 | 7

Solution:
Find the rows for 2, 3, 4, and 5 times. Add the frequencies for these rows.

Add:

8 + 3 + 16 + 7 = 34

34 people went swimming at least 2 times.


Question: A farm equipment company kept a record of the number of tractors made each month. In which month did the company make the most tractors?

Choices:
- July
- August
- September
- October

Answer: September

Month | Number of tractors
July | 353
August | 332
September | 375
October | 357

Solution:
Find the greatest number in the table. Remember to compare the numbers starting with the highest place value. The greatest number is 375.

Now find the corresponding month. September corresponds to 375.


Question: Mrs. Freeman kept track of her students' scores on last year's final exam. What is the highest score?

Answer: 90

Solution:
Look at the last row of the stem-and-leaf plot. The last row has the highest stem. The stem for the last row is 9.

Now find the highest leaf in the last row. The highest leaf is 0.

The highest score has a stem of 9 and a leaf of 0. Write the stem first, then the leaf: 90.

The highest score is 90 points.


Question: While hanging Christmas lights for neighbors, Paul counted the number of broken lights on each string. How many strings had at least 10 broken lights but less than 20 broken lights?

Answer: 3

Solution:
Count all the leaves in the row with stem 1.

You counted 3 leaves, which are blue in the stem-and-leaf plot above. 3 strings had at least 10 broken lights but less than 20 broken lights.


Question: Look at this table. Is this relation a function?

Choices:
- yes
- no

Answer: yes

Solution:
Look at the x-values in the table.

Each of the x-values is paired with only one y-value, so the relation is a function.


Question: What is the total cost for 5 pounds of hazelnuts?

Answer: 51.45

almonds | $7.23 per lb
hazelnuts | $10.29 per lb
pecans | $4.77 per lb
peanuts | $2.41 per lb

Solution:
Find the cost of the hazelnuts. Multiply the price per pound by the number of pounds.

$10.29 × 5 = $51.45

The total cost is $51.45.


Question: Robert, who just won the election for student body president at Lakeside Middle School, tallied how many votes he received from each grade. What fraction of his votes were from the eighth grade? Simplify your answer.

Answer: 20/179

Grade | Number of votes
Sixth grade | 810
Seventh grade | 780
Eighth grade | 200

Solution:
Find how many of his votes came from the eighth grade.

200

Find how many students voted for him in total.

810 + 780 + 200 = 1,790

Divide 200 by1,790.

\frac{200}{1,790}

Reduce the fraction.

\frac{200}{1,790} → \frac{20}{179}

\frac{20}{179} of of his votes came from the eighth grade.


Question: The players on a quiz show received the following scores. What is the mode of the numbers?

Answer: 2

Name | Score
Malik | 2
Duncan | 2
Grace | 6
Nate | 6
Ian | 2

Solution:
Read the numbers from the table.

2, 2, 6, 6, 2

First, arrange the numbers from least to greatest:

2, 2, 2, 6, 6

Now count how many times each number appears.

2 appears 3 times.
6 appears 2 times.

The number that appears most often is 2.

The mode is 2.


Question: A technical support line tracked how many calls it received each day. On which day did the support line receive the fewest calls?

Choices:
- Monday
- Tuesday
- Wednesday
- Thursday

Answer: Thursday

Day | Number of calls
Monday | 454
Tuesday | 442
Wednesday | 452
Thursday | 425

Solution:
Find the least number in the table. Remember to compare the numbers starting with the highest place value. The least number is 425.

Now find the corresponding day. Thursday corresponds to 425.


Question: Amy surveyed people at the amusement park where she works and asked them how many times they visited last year. How many people went to an amusement park fewer than 2 times?

Answer: 6

Number of trips | Frequency
1 | 6
2 | 3
3 | 9
4 | 12

Solution:
Find the row for 1 time and read the frequency. The frequency is 6.

6 people went to an amusement park fewer than 2 times.


Question: Eli counted the number of problems on each of his tests. What is the largest number of problems?

Answer: 48

Solution:
Look at the last row of the stem-and-leaf plot. The last row has the highest stem. The stem for the last row is 4.

Now find the highest leaf in the last row. The highest leaf is 8.

The largest number of problems has a stem of 4 and a leaf of 8. Write the stem first, then the leaf: 48.

The largest number of problems is 48 problems.


Question: Look at the table. Then answer the question. At a price of $160, is there a shortage or a surplus?

Choices:
- shortage
- surplus

Answer: shortage

Solution: At the price of $160, the quantity demanded is greater than the quantity supplied. There is not enough of the good or service for sale at that price. So, there is a shortage.


Question: As part of a statistics project, a math class weighed all the children who were willing to participate. How many children weighed at least 19 pounds but less than 35 pounds?

Answer: 9

Solution:
Find the row with stem 1. Count all the leaves greater than or equal to 9.

Count all the leaves in the row with stem 2.

In the row with stem 3, count all the leaves less than 5.

You counted 9 leaves, which are blue in the stem-and-leaf plots above. 9 children weighed at least 19 pounds but less than 35 pounds.


Question: The Fairview Art Museum recorded how many finger puppets the children made at last Sunday's art workshop. How many children made more than 5 finger puppets?

Answer: 1

Finger puppets made | Frequency
0 | 5
1 | 10
2 | 0
3 | 13
4 | 16
5 | 18
6 | 1

Solution:
Find the row for 6 finger puppets and read the frequency. The frequency is 1.

1 child made more than 5 finger puppets.


Question: Sue has $54.00. Does she have enough to buy a bicycle and a swimsuit?

Choices:
- yes
- no

Answer: no

softball glove | $21.00
swimsuit | $15.00
bowling ball | $40.00
bicycle helmet | $16.00
bicycle | $43.00

softball glove
swimsuit
bowling ball
bicycle helmet
bicycle

Solution:
Add the price of a bicycle and the price of a swimsuit:

$43.00 + $15.00 = $58.00

$58.00 is more than $54.00. Sue does not have enough money.


Question: Megan counted the number of peanuts in each bag of trail mix. What is the largest number of peanuts?

Answer: 58

Solution:
Look at the last row of the stem-and-leaf plot. The last row has the highest stem. The stem for the last row is 5.

Now find the highest leaf in the last row. The highest leaf is 8.

The largest number of peanuts has a stem of 5 and a leaf of 8. Write the stem first, then the leaf: 58.

The largest number of peanuts is 58 peanuts.


Question: Look at the table. Then answer the question. At a price of $20, is there a shortage or a surplus?

Choices:
- shortage
- surplus

Answer: shortage

Solution: At the price of $20, the quantity demanded is greater than the quantity supplied. There is not enough of the good or service for sale at that price. So, there is a shortage.


Question: A video store clerk looked up the number of movies checked out each day. What is the mean of the numbers?

Answer: 94

Day | Number of movies
Sunday | 96
Monday | 93
Tuesday | 95
Wednesday | 92
Thursday | 94

Sunday Monday Tuesday Wednesday Thursday

Solution:
Read the numbers from the table.

96, 93, 95, 92, 94

First, count how many numbers are in the group.

There are 5 numbers.

Now add all the numbers together:

96 + 93 + 95 + 92 + 94 = 470

Now divide the sum by the number of numbers:

470 ÷ 5 = 94

The mean is 94.


Question: A band from Arlington went on tour over the summer, and each member chipped in for the cost of gas. What fraction of the gas money came from Devon? Simplify your answer.

Answer: 69/127

Band member | Contribution ($)
Vince | 480
Devon | 690
Tara | 100

Solution:
Find how much money Devon contributed for gas.

690

Find how much money was contributed for gas in total.

480 + 690 + 100 = 1,270

Divide 690 by1,270.

\frac{690}{1,270}

Reduce the fraction.

\frac{690}{1,270} → \frac{69}{127}

\frac{69}{127} of Find how much money Devon contributed for gas.


Question: Several people compared how many Web pages they had visited. What is the mean of the numbers?

Answer: 7

Person | Number of Web pages
Nellie | 5
Louis | 8
Grayson | 9
Zack | 8
Jasmine | 4
Perry | 8

Solution:
Read the numbers from the table.

5, 8, 9, 8, 4, 8

First, count how many numbers are in the group.

There are 6 numbers.

Now add all the numbers together:

5 + 8 + 9 + 8 + 4 + 8 = 42

Now divide the sum by the number of numbers:

42 ÷ 6 = 7

The mean is 7.


Question: Helen looked at her calendar to figure out how much time she spent babysitting each month. In which month did Helen babysit the most?

Choices:
- December
- January
- February
- March

Answer: February

Month | Hours
December | 23
January | 22
February | 29
March | 26

Solution:
Find the greatest number in the table. Remember to compare the numbers starting with the highest place value. The greatest number is 29.

Now find the corresponding month. February corresponds to 29.


Question: How much more does baked chicken cost than a pepperoni pizza?

Answer: 7

pepperoni pizza | $13
baked ziti | $14
pasta with pesto sauce | $13
baked chicken | $20

pepperoni pizza
baked ziti
pasta with pesto sauce
baked chicken

Solution:
Subtract the price of a pepperoni pizza from the price of baked chicken.

$20 - $13 = $7

Baked chicken costs $7 more than a pepperoni pizza.


Question: Look at the table. Then answer the question. At a price of $840, is there a shortage or a surplus?

Choices:
- shortage
- surplus

Answer: surplus

Solution: At the price of $840, the quantity demanded is less than the quantity supplied. There is too much of the good or service for sale at that price. So, there is a surplus.


Question: At their family reunion, the Stanley family recorded everyone's age. How many people are exactly 33 years old?

Answer: 1

Solution:
For the number 33, the stem is 3, and the leaf is 3. Find the row where the stem is 3. In that row, count all the leaves equal to 3.

You counted 1 leaf, which is blue in the stem-and-leaf plot above. 1 person is exactly 33 years old.


Question: Look at the following schedule. How long does it take to get from the pizza place to the train station?

Choices:
- 2 hours and 15 minutes
- 2 hours
- 1 hour and 45 minutes
- 1 hour and 30 minutes

Answer: 2 hours and 15 minutes

airport
boat docks
pizza place
amusement park
college campus
football stadium
softball field
train station
bus station

Solution:
Read the times in the first column for the pizza place and the train station.

Find the elapsed time between 11:15 A. M. and 1:30 P. M. The elapsed time is 2 hours and 15 minutes.

No matter which column of times you look at, the elapsed time is always 2 hours and 15 minutes.


Question: Jaylen counted the number of pairs of shoes for sale at each of the shoe stores in the mall. What is the smallest number of pairs of shoes?

Answer: 34

Solution:
Look at the first row of the stem-and-leaf plot. The first row has the lowest stem. The stem for the first row is 3.

Now find the lowest leaf in the first row. The lowest leaf is 4.

The smallest number of pairs of shoes has a stem of 3 and a leaf of 4. Write the stem first, then the leaf: 34.

The smallest number of pairs of shoes is 34 pairs of shoes.


Question: Compare pattern A to pattern B. Which statement is true?

Choices:
- Each term in pattern B is 27 more than the corresponding term in pattern A.
- Each term in pattern B is 10 times the corresponding term in pattern A.

Answer: Each term in pattern B is 10 times the corresponding term in pattern A.

Solution:
Look at the corresponding terms in the table. For example, the first pair of corresponding terms is 3 and 30.
Read the first statement.
Each term in pattern B is 27 more than the corresponding term in pattern A.
This statement is not true for all of the corresponding terms. For example, 60 is not 27 more than 6.
Read the second statement.
Each term in pattern B is 10 times the corresponding term in pattern A.
This statement is true for all of the corresponding terms.
3 × 10 = 30
6 × 10 = 60
9 × 10 = 90
12 × 10 = 120


Question: How much more does a Hawaiian vacation package cost than an Australian vacation package?

Answer: 210

European vacation package | $959.00
Australian vacation package | $531.00
Hawaiian vacation package | $741.00
Jamaican vacation package | $637.00
Caribbean vacation package | $897.00
African safari vacation package | $538.00

European vacation package
Australian vacation package
Hawaiian vacation package
Jamaican vacation package
Caribbean vacation package
African safari vacation package

Solution:
Subtract the price of an Australian vacation package from the price of a Hawaiian vacation package.

$741.00 - $531.00 = $210.00

A Hawaiian vacation package costs $210.00 more than an Australian vacation package.


Question: At a school carnival, a curious student volunteer counted the number of times visitors to her booth spun the numbers 1 through 6. How many people spun a number less than 2?

Answer: 16

Solution:
Find the row for 1 and read the frequency. The frequency is 16.

16 people spun a number less than 2.


Question: An Idaho farmer has been monitoring crop prices over time. Per cwt, how much did Timothy seed cost in 2004?

Answer: 7

Solution:
First, find the row for Timothy seed. Then find the number in the 2004 column.

This number is $7.00. In 2004, Timothy seed cost $7 per cwt.


Question: How much money does Henry need to buy 2 measuring tapes and a rake?

Answer: 16.98

measuring tape | $4.87
padlock | $5.07
hammer | $9.51
rake | $7.24
broom | $4.58
mop | $8.37

measuring tape
padlock
hammer
rake
broom
mop

Solution:
Find the cost of 2 measuring tapes.

$4.87 × 2 = $9.74

Now find the total cost.

$9.74 + $7.24 = $16.98

Henry needs $16.98.


Question: An economist tracked the amount of per-capita aid sent from the U.S. to various countries during the 1900s. Per capita, how much more aid did Libya receive in 1965 than in 1975?

Answer: 2

Country | 1965 | 1975
Nepal | $2 | $3
Libya | $4 | $2
Sri Lanka | $1 | $11
Afghanistan | $5 | $5

Country
Nepal
Libya
Sri Lanka
Afghanistan

Solution:
Find the Libya row. Find the numbers in this row for 1965 and 1975.

1965: $4.00
1975: $2.00

Now subtract:

$4.00 − $2.00 = $2.00

Per capita, Libya received $2 more in aid in 1965 than in 1975.


Question: Several people compared how many Web pages they had visited. Who visited the most Web pages?

Choices:
- Kenji
- Alexis
- Josh
- Sofia

Answer: Sofia

Person | Number of Web pages
Kenji | 141
Alexis | 119
Josh | 147
Sofia | 174

Solution:
Find the greatest number in the table. Remember to compare the numbers starting with the highest place value. The greatest number is 174.

Now find the corresponding person. Sofia corresponds to 174.


Question: How much more does a denim skirt cost than a purple T-shirt?

Answer: 6

long-sleeved shirt | $4.00
denim skirt | $9.00
pink sweater | $5.00
plaid scarf | $3.00
purple T-shirt | $3.00

long-sleeved shirt
denim skirt
pink sweater
plaid scarf
purple T-shirt

Solution:
Subtract the price of a purple T-shirt from the price of a denim skirt.

$9.00 - $3.00 = $6.00

A denim skirt costs $6.00 more than a purple T-shirt.


Question: Josie, an employee at Morgan's Convenience Store, looked at the sales of each of its soda products. On Friday, how much more did the convenience store make from Nature's Nectar sales than from Sweet Sips sales?

Answer: 12

Beverage | Thursday | Friday
Krazy Kola | $7 | $5
Sweet Sips | $17 | $7
Pearl's Soda | $2 | $12
Nature's Nectar | $1 | $19
Fizzy Fun | $14 | $15

Krazy Kola
Sweet Sips
Pearl's Soda
Nature's Nectar
Fizzy Fun

Solution:
Find the Friday column. Find the numbers in this column for Nature's Nectar and Sweet Sips.

Nature's Nectar: $19.00
Sweet Sips: $7.00

Now subtract:

$19.00 − $7.00 = $12.00

On Friday, the convenience store made $12 more from Nature's Nectar sales than from Sweet Sips sales.


Question: A toy store employee counted the number of toys in each bin in the sale section. What is the smallest number of toys?

Answer: 35

Solution:
Look at the first row of the stem-and-leaf plot. The first row has the lowest stem. The stem for the first row is 3.

Now find the lowest leaf in the first row. The lowest leaf is 5.

The smallest number of toys has a stem of 3 and a leaf of 5. Write the stem first, then the leaf: 35.

The smallest number of toys is 35 toys.


Question: How much money does Walter need to buy a football helmet key chain and a puppy key chain?

Answer: 4.59

football helmet key chain | $1.90
piano key chain | $2.19
rainbow key chain | $2.25
globe key chain | $1.70
puppy key chain | $2.69
soccer ball key chain | $1.96

football helmet key chain
piano key chain
rainbow key chain
globe key chain
puppy key chain
soccer ball key chain

Solution:
Add the price of a football helmet key chain and the price of a puppy key chain:

$1.90 + $2.69 = $4.59

Walter needs $4.59.


Question: The school district compared how many math teachers each high school has. What is the mode of the numbers?

Answer: 2

High school | Number of math teachers
Lincoln High | 2
Cedar High | 2
Northside High | 6
Hillview High | 6
River High | 2
Green High | 7
Westside High | 7

Lincoln High
Cedar High
Northside High
Hillview High
River High
Green High
Westside High

Solution:
Read the numbers from the table.

2, 2, 6, 6, 2, 7, 7

First, arrange the numbers from least to greatest:

2, 2, 2, 6, 6, 7, 7

Now count how many times each number appears.

2 appears 3 times.
6 appears 2 times.
7 appears 2 times.

The number that appears most often is 2.

The mode is 2.


Question: A teacher at Mills Middle School studied the absence rates of her students over the course of a few years. In 2006, which student had the most absences?

Choices:
- Preston
- Liz
- Valentina

Answer: Valentina

Student | 2005 | 2006
Valentina | 2 | 18
Preston | 13 | 3
Liz | 14 | 4

Solution:
Look at the numbers in the 2006 column. Find the greatest number in this column.

The greatest number is 18, which is in the Valentina row. Valentina had the most absences in 2006.


Question: A dentist was making note of his upcoming appointments with different aged patients and the reasons for their visits. What is the probability that a randomly selected appointment is for a broken tooth and is with patients 19-60 years old? Simplify any fractions.

Answer: 2/7

 | Patients under 18 years old | Patients 19-60 years old
Regular cleaning | 4 | 2
Broken tooth | 4 | 4

Solution:
Let A be the event "the appointment is for a broken tooth" and B be the event "the appointment is with patients 19-60 years old".
To find the probability that a appointment is for a broken tooth and is with patients 19-60 years old, first identify the sample space and the event.
The outcomes in the sample space are the different appointments. Each appointment is equally likely to be selected, so this is a uniform probability model.
The event is A and B, "the appointment is for a broken tooth and is with patients 19-60 years old".
Since this is a uniform probability model, count the number of outcomes in the event A and B and count the total number of outcomes. Then, divide them to compute the probability.

Find the number of outcomes in the event A and B.
A and B is the event "the appointment is for a broken tooth and is with patients 19-60 years old", so look at the table to see how many appointments are for a broken tooth and are with patients 19-60 years old.
The number of appointments that are for a broken tooth and are with patients 19-60 years old is 4.

Find the total number of outcomes.
Add all the numbers in the table to find the total number of appointments.
4 + 4 + 2 + 4 = 14

Find P(A and B).
Since all outcomes are equally likely, the probability of event A and B is the number of outcomes in event A and B divided by the total number of outcomes.
P(A and B) = \frac{# of outcomes in A and B}{total # of outcomes}
 = \frac{4}{14}
 = \frac{2}{7}
The probability that a appointment is for a broken tooth and is with patients 19-60 years old is \frac{2}{7}.


Question: Each train car has 10 people. How many people are in 6 train cars?

Answer: 60

Number of train cars | Number of people
1 | 10
2 | 20
3 | 30
4 | 40
5 | 50
6 | ?

Solution: Count by tens. Use the chart: there are 60 people in 6 train cars.


Question: How much more does a grandfather clock cost than a crystal vase?

Answer: 164

silver coat rack | $796.00
grandfather clock | $628.00
crystal sculpture | $734.00
rug | $274.00
crystal vase | $464.00
oil painting | $328.00

silver coat rack
grandfather clock
crystal sculpture
rug
crystal vase
oil painting

Solution:
Subtract the price of a crystal vase from the price of a grandfather clock.

$628.00 - $464.00 = $164.00

A grandfather clock costs $164.00 more than a crystal vase.


Question: Megan looked at the dates of the digital photos on her computer to find out how many she had taken in the past 5 days. What is the mean of the numbers?

Answer: 7

Day | Number of photographs
Sunday | 9
Monday | 8
Tuesday | 9
Wednesday | 2
Thursday | 7

Solution:
Read the numbers from the table.

9, 8, 9, 2, 7

First, count how many numbers are in the group.

There are 5 numbers.

Now add all the numbers together:

9 + 8 + 9 + 2 + 7 = 35

Now divide the sum by the number of numbers:

35 ÷ 5 = 7

The mean is 7.


Question: Stamford will decide whether to extend its public pool's hours by looking at the number of times its residents visited the pool last month. How many people went swimming fewer than 2 times?

Answer: 3

Number of times | Frequency
1 | 3
2 | 10
3 | 17
4 | 6

Solution:
Find the row for 1 time and read the frequency. The frequency is 3.

3 people went swimming fewer than 2 times.


Question: A restaurant's average food preparation time was tracked from day to day as part of an efficiency improvement program. According to the table, what was the rate of change between Thursday and Friday?

Answer: -4

Day | Food preparation time (minutes)
Tuesday | 36
Wednesday | 37
Thursday | 37
Friday | 33
Saturday | 32

Tuesday Wednesday Thursday Friday Saturday

Solution:
Plug the numbers into the formula for rate of change and simplify.
Rate of change
 = \frac{change in value}{change in time}
 = \frac{33 minutes - 37 minutes}{1 day}
 = \frac{-4 minutes}{1 day}
 = -4 minutes per day
The rate of change between Thursday and Friday was - 4 minutes per day.


Question: Some students compared how many clubs they belong to. What is the mode of the numbers?

Answer: 7

Name | Number of clubs
Jared | 5
Lee | 7
Reba | 5
Kamal | 10
Sanjay | 7
Aiden | 7

Solution:
Read the numbers from the table.

5, 7, 5, 10, 7, 7

First, arrange the numbers from least to greatest:

5, 5, 7, 7, 7, 10

Now count how many times each number appears.

5 appears 2 times.
7 appears 3 times.
10 appears 1 time.

The number that appears most often is 7.

The mode is 7.


Question: The parks department compared how many basketball hoops there are at each park. What is the range of the numbers?

Answer: 8

Park | Number of basketball hoops
Westfield Park | 10
Riverfront Park | 6
Mooreland Park | 9
Linden Park | 5
Crestview Park | 2
Heron Park | 4
Pinehurst Park | 3
Kelly Park | 8

Westfield Park
Riverfront Park
Mooreland Park
Linden Park
Crestview Park
Heron Park
Pinehurst Park
Kelly Park

Solution:
Read the numbers from the table.

10, 6, 9, 5, 2, 4, 3, 8

First, find the greatest number. The greatest number is 10.

Next, find the least number. The least number is 2.

Subtract the least number from the greatest number:

10 − 2 = 8

The range is 8.


Question: The shop teacher, Mr. Johnston, wrote down how many picture frames the students made last week. How many students made exactly 6 picture frames?

Answer: 19

Solution:
Find the row for 6 picture frames and read the frequency. The frequency is 19.

19 students made exactly 6 picture frames.


Question: Caleb has $0.34. Does he have enough to buy a piece of mint chocolate and a butterscotch candy?

Choices:
- yes
- no

Answer: no

piece of gum | $0.17
piece of mint chocolate | $0.24
gumball | $0.16
peanut butter cup | $0.24
butterscotch candy | $0.13

piece of gum
piece of mint chocolate
gumball
peanut butter cup
butterscotch candy

Solution:
Add the price of a piece of mint chocolate and the price of a butterscotch candy:

$0.24 + $0.13 = $0.37

$0.37 is more than $0.34. Caleb does not have enough money.


Question: Sean paid attention to how many flowers he planted in the garden during the past 5 days. What is the range of the numbers?

Answer: 17

Day | Number of flowers
Tuesday | 22
Wednesday | 39
Thursday | 29
Friday | 35
Saturday | 33

Solution:
Read the numbers from the table.

22, 39, 29, 35, 33

First, find the greatest number. The greatest number is 39.

Next, find the least number. The least number is 22.

Subtract the least number from the greatest number:

39 − 22 = 17

The range is 17.


Question: Trudy and her friends recorded their scores while playing a board game. How many people scored more than 8?

Answer: 23

Solution:
Find the rows for 9 and 10. Add the frequencies for these rows.

Add:

4 + 19 = 23

23 people scored more than 8.


Question: A real estate agent looked into how many houses were sold in different cities. What is the mode of the numbers?

Answer: 71

City | Number of houses sold
Melville | 71
Liberty City | 74
Center City | 71
New Hamburg | 71
Parville | 74
Fremont | 68
Briggs Corner | 68

Melville
Liberty City
Center City
New Hamburg
Parville
Fremont
Briggs Corner

Solution:
Read the numbers from the table.

71, 74, 71, 71, 74, 68, 68

First, arrange the numbers from least to greatest:

68, 68, 71, 71, 71, 74, 74

Now count how many times each number appears.

68 appears 2 times.
71 appears 3 times.
74 appears 2 times.

The number that appears most often is 71.

The mode is 71.


Question: Percy has $49.50. Does he have enough to buy a pair of brown pants and a pair of shorts?

Choices:
- yes
- no

Answer: yes

denim jacket | $17.18
pair of shorts | $27.55
pair of brown pants | $19.92
black jacket | $10.33

denim jacket
pair of shorts
pair of brown pants
black jacket

Solution:
Add the price of a pair of brown pants and the price of a pair of shorts:

$19.92 + $27.55 = $47.47

$47.47 is less than $49.50. Percy does have enough money.


Question: How much more does a roll of packaging tape cost than a large yellow envelope?

Answer: 0.10

butterfly stamp | $0.30
tulip stamp | $0.23
roll of packaging tape | $0.63
large cardboard box | $0.41
bird postcard | $0.61
large yellow envelope | $0.53

butterfly stamp
tulip stamp
roll of packaging tape
large cardboard box
bird postcard
large yellow envelope

Solution:
Subtract the price of a large yellow envelope from the price of a roll of packaging tape.

$0.63 - $0.53 = $0.10

A roll of packaging tape costs $0.10 more than a large yellow envelope.


Question: Ms. Sherman reported her students' scores on the most recent quiz. How many students scored fewer than 58 points?

Answer: 12

Solution:
Count all the leaves in the rows with stems 2, 3, and 4.

In the row with stem 5, count all the leaves less than 8.

You counted 12 leaves, which are blue in the stem-and-leaf plots above. 12 students scored fewer than 58 points.


Question: How much money does Rhianna need to buy a can of fruit cocktail and a jar of pickles?

Answer: 3.78

jar of olives | $3.08
can of mushrooms | $1.37
jar of pickles | $1.55
can of fruit cocktail | $2.23

jar of olives
can of mushrooms
jar of pickles
can of fruit cocktail

Solution:
Add the price of a can of fruit cocktail and the price of a jar of pickles:

$2.23 + $1.55 = $3.78

Rhianna needs $3.78.


Question: Mitchell recalled how many goals he had made in soccer practice each day. What is the median of the numbers?

Answer: 5

Day | Number of goals
Sunday | 5
Monday | 0
Tuesday | 3
Wednesday | 8
Thursday | 4
Friday | 10
Saturday | 9

Sunday Monday Tuesday Wednesday Thursday Friday Saturday

Solution:
Read the numbers from the table.

5, 0, 3, 8, 4, 10, 9

First, arrange the numbers from least to greatest:

0, 3, 4, 5, 8, 9, 10

Now find the number in the middle.

0, 3, 4, 5, 8, 9, 10

The number in the middle is 5.

The median is 5.


Question: A farmer recalled how many watermelons were harvested in the past 4 days. On which day were the fewest watermelons harvested?

Choices:
- Thursday
- Friday
- Saturday
- Sunday

Answer: Thursday

Day | Number of watermelons
Thursday | 40
Friday | 49
Saturday | 42
Sunday | 46

Solution:
Find the least number in the table. Remember to compare the numbers starting with the highest place value. The least number is 40.

Now find the corresponding day. Thursday corresponds to 40.


Question: Each roof has 5 seagulls. How many seagulls are on 3 roofs?

Answer: 15

Number of roofs | Number of seagulls
1 | 5
2 | 10
3 | ?

Solution: Count by fives. Use the chart: there are 15 seagulls on 3 roofs.


Question: The parks department compared how many basketball hoops there are at each park. What is the mode of the numbers?

Answer: 9

Park | Number of basketball hoops
Palm Park | 9
Mooreland Park | 8
Crestview Park | 8
Riverfront Park | 9
Westfield Park | 8
Linden Park | 9
Heron Park | 2
Otter Park | 9

Palm Park
Mooreland Park
Crestview Park
Riverfront Park
Westfield Park
Linden Park
Heron Park
Otter Park

Solution:
Read the numbers from the table.

9, 8, 8, 9, 8, 9, 2, 9

First, arrange the numbers from least to greatest:

2, 8, 8, 8, 9, 9, 9, 9

Now count how many times each number appears.

2 appears 1 time.
8 appears 3 times.
9 appears 4 times.

The number that appears most often is 9.

The mode is 9.


Question: Brianna has two part-time jobs as a children's entertainer. Here are her yearly finances. What is Brianna's gross income for the year?

Answer: 24,850

Earnings from job as a birthday party princess | $11,650
Earnings from acting in children's plays | $13,200
Income tax and other payroll taxes | $3,083

Solution:
Brianna's gross income is her total earnings before taxes are taken out. Add the earnings from Brianna's two part-time jobs to find her gross income.
$11,650 + $13,200 = $24,850
Brianna's gross income for the year is $24,850.
You do not need the information about Brianna's income tax and other payroll taxes to find her gross income.


Question: How much money does Erica need to buy 5 pairs of designer shoes?

Answer: 23,690

designer handbag | $3,238.00
designer watch | $1,024.00
pair of designer shoes | $4,738.00
designer ball gown | $3,907.00

designer handbag
designer watch
pair of designer shoes
designer ball gown

Solution:
Find the total cost of 5 pairs of designer shoes by multiplying 5 times the price of a pair of designer shoes.

$4,738.00 × 5 = $23,690.00

Erica needs $23,690.00.


Question: Addison worked at a water park last summer. Here are Addison's finances for the summer. What was Addison's net income last summer?

Answer: 6,220

Earnings from job at the water park | $6,840
Income tax and other payroll taxes | $620

Earnings from job at the water park
Income tax and other payroll taxes

Solution:
Addison's gross income was $6,840. Her payroll taxes were $620.
Subtract to find Addison's net income.
$6,840 - $620 = $6,220
Addison's net income last summer was $6,220.


Question: Cole graphed the temperature at noon for 6 days. What is the mode of the numbers?

Answer: 6

Day | Temperature (Â°C)
Thursday | 6
Friday | 6
Saturday | 9
Sunday | 6
Monday | 9
Tuesday | 7

Thursday Friday Saturday Sunday Monday Tuesday

Solution:
Read the numbers from the table.

6, 6, 9, 6, 9, 7

First, arrange the numbers from least to greatest:

6, 6, 6, 7, 9, 9

Now count how many times each number appears.

6 appears 3 times.
7 appears 1 time.
9 appears 2 times.

The number that appears most often is 6.

The mode is 6.


Question: How much money does Rudy need to buy 4 whistles?

Answer: 5.68

package of purple streamers | $2.58
birthday balloon | $1.04
greeting card | $3.18
whistle | $1.42

package of purple streamers
birthday balloon
greeting card
whistle

Solution:
Find the total cost of 4 whistles by multiplying 4 times the price of a whistle.

$1.42 × 4 = $5.68

Rudy needs $5.68.


Question: The owner of an orchard kept records about how many apples were picked in the past 5 days. How many apples in total were picked on Friday and Saturday?

Answer: 12,276

Day | Number of apples
Friday | 8,131
Saturday | 4,145
Sunday | 8,137
Monday | 1,569
Tuesday | 2,068

Solution:
Find the numbers in the table.

Friday: 8,131
Saturday: 4,145

Now add: 8,131 + 4,145 = 12,276.

12,276 apples were picked on Friday and Saturday.


Question: A crayon factory monitored the number of broken crayons per box during the past day. What is the smallest number of broken crayons?

Answer: 12

Solution:
Look at the first row of the stem-and-leaf plot. The first row has the lowest stem. The stem for the first row is 1.

Now find the lowest leaf in the first row. The lowest leaf is 2.

The smallest number of broken crayons has a stem of 1 and a leaf of 2. Write the stem first, then the leaf: 12.

The smallest number of broken crayons is 12 broken crayons.


Question: The table shows a function. Is the function linear or nonlinear?

Choices:
- linear
- nonlinear

Answer: nonlinear

Solution:
To determine whether the function is linear or nonlinear, see whether it has a constant rate of change.
Pick the points in any two rows of the table and calculate the rate of change between them. The first two rows are a good place to start.
Call the values in the first row x1 and y1. Call the values in the second row x2 and y2.
Rate of change = \frac{y2 - y1}{x2 - x1}
 = \frac{11 - 2}{17 - 16}
 = \frac{9}{1}
 = 9
Now pick any other two rows and calculate the rate of change between them.
Call the values in the second row x1 and y1. Call the values in the third row x2 and y2.
Rate of change = \frac{y2 - y1}{x2 - x1}
 = \frac{18 - 11}{18 - 17}
 = \frac{7}{1}
 = 7
The rate of change is not the same for each pair of points. So, the function does not have a constant rate of change.
The function is nonlinear.


Question: Ms. McCormick reported her students' scores on the most recent quiz. How many students scored at least 65 points?

Answer: 3

Solution:
Find the row with stem 6. Count all the leaves greater than or equal to 5.

Count all the leaves in the rows with stems 7 and 8.

You counted 3 leaves, which are blue in the stem-and-leaf plots above. 3 students scored at least 65 points.


Question: Each soccer field has 5 sprinklers. How many sprinklers are on 4 soccer fields?

Answer: 20

Number of soccer fields | Number of sprinklers
1 | 5
2 | 10
3 | 15
4 | ?

Solution: Count by fives. Use the chart: there are 20 sprinklers on 4 soccer fields.


Question: This is Sandra's complete financial record for December. How much money did Sandra spend on December 29?

Answer: 7.80

Date | Description | Received | Expenses | Available Funds
 | Balance: end of November | | | $328.20
12/5 | wrapping paper | | $4.95 | $323.25
12/16 | watching Ms. Simon's cat | $15.00 | | $338.25
12/29 | calendar | | $7.80 | $330.45

Balance: end of November
wrapping paper
watching Ms. Simon's cat
calendar

Solution: Look at the 12/29 row. The expenses were $7.80. So, Sandra spent $7.80 on December 29.


Question: How much more does a banana cream pie cost than a pumpkin pie?

Answer: 0.41

pumpkin pie | $10.53
almond tart | $20.72
birthday cake | $28.48
banana cream pie | $10.94

pumpkin pie
almond tart
birthday cake
banana cream pie

Solution:
Subtract the price of a pumpkin pie from the price of a banana cream pie.

$10.94 - $10.53 = $0.41

A banana cream pie costs $0.41 more than a pumpkin pie.


Question: A zoologist counted the number of reptiles at each of the state's zoos. Are there more reptiles at the Eastern Zoo or the Northside Zoo?

Choices:
- Northside Zoo
- Eastern Zoo

Answer: Northside Zoo

Zoo | Turtles | Lizards
Northside Zoo | 8 | 12
Eastern Zoo | 14 | 5
Wilderness Zoo | 13 | 18
South Zoo | 5 | 7
Pacific Zoo | 13 | 15

Northside Zoo
Eastern Zoo
Wilderness Zoo
South Zoo
Pacific Zoo

Solution:
Add the numbers in the Eastern Zoo row. Then, add the numbers in the Northside Zoo row.

Eastern Zoo: 14 + 5 = 19
Northside Zoo: 8 + 12 = 20

20 is more than 19. There are more reptiles at the Northside Zoo.


Question: Anna has $2.00. Does she have enough to buy a jar of tomato sauce and a bottle of hot sauce?

Choices:
- yes
- no

Answer: yes

bottle of vinegar | $0.81
jar of tomato sauce | $0.94
jar of salsa | $0.95
bottle of hot sauce | $0.85
bottle of soy sauce | $0.84
bottle of mustard | $0.79

bottle of vinegar
jar of tomato sauce
jar of salsa
bottle of hot sauce
bottle of soy sauce
bottle of mustard

Solution:
Add the price of a jar of tomato sauce and the price of a bottle of hot sauce:

$0.94 + $0.85 = $1.79

$1.79 is less than $2.00. Anna does have enough money.


Question: This is Sandra's complete financial record for December. How much money did Sandra spend on December 29?

Answer: 7.80

Date | Description | Received | Expenses | Available Funds
 | Balance: end of November | | | $328.20
12/5 | wrapping paper | | $4.95 | $323.25
12/16 | watching Ms. Bowen's cat | $15.00 | | $338.25
12/29 | calendar | | $7.80 | $330.45

Balance: end of November
wrapping paper
watching Ms. Bowen's cat
calendar


Question: A pretzel stand owner kept track of the number of pretzels sold during the past 3 days. How many more pretzels did the stand sell on Friday than on Sunday?

Answer: 202

Day | Number of pretzels
Friday | 678
Saturday | 364
Sunday | 476

Solution:
Find the numbers in the table.

Friday: 678
Sunday: 476

Now subtract: 678 - 476 = 202.

The stand sold 202 more pretzels on Friday.


Question: A marketing research firm asked people how many times they visited the mall last month. How many people went to the mall twice last month?

Answer: 11

Solution:
Find the row for 2 times and read the frequency. The frequency is 11.

11 people went to the mall exactly twice last month.


Question: Justin went to the store. He bought 3.4 pounds of cream cheese. How much did he spend?

Answer: 6.80

cream cheese | $2 per lb
cottage cheese | $5 per lb
butter | $2 per lb
plain yogurt | $4 per lb
Greek yogurt | $2 per lb

cream cheese
cottage cheese
butter
plain yogurt
Greek yogurt

$2 per lb
$5 per lb
$2 per lb
$4 per lb
$2 per lb

Solution:
Find the cost of the cream cheese. Multiply the price per pound by the number of pounds.
$2 × 3.4 = $6.80
He spent $6.80.


Question: A pair of Sullivan High School hockey fans counted the number of games won by the school each year. According to the table, what was the rate of change between 2011 and 2012?

Answer: -2

Solution:
Plug the numbers into the formula for rate of change and simplify.
Rate of change
 = \frac{change in value}{change in time}
 = \frac{5 games - 7 games}{2012 - 2011}
 = \frac{5 games - 7 games}{1 year}
 = \frac{-2 games}{1 year}
 = -2 games per year
The rate of change between 2011 and 2012 was - 2 games per year.