Percent
Unit Conversions
Doubling and Halving Time
Expected Value
Probabilities
Permutations & Combinations
100

A town's population of 1,200 is ___% of a neighboring town's population of 1,800.

66.7%

100

A factory machine uses 2.5 kilowatt-hours (kWh) of electricity per hour. If the machine runs for 18 hours, how much electricity does it consume in a day?

45 kWh

100

The initial population of a city is 50,000, and it grows with a doubling time of 20 years. What will the population be in 5 years?

59,460

100

A lottery has 5,000 tickets. There is one grand prize of $5,000, two second prizes of $500 each, and five third prizes of $100 each. If you buy one ticket, what is your expected winnings?

$1.30

100

The following Venn diagram shows students enrolled in a school band:

 How many students play a woodwind instrument?

20

100

How many 5-letter passwords can be formed from the letters A, B, C, D, and E if no repetition of letters is allowed?

120 passwords

200

There are 180 students in the morning session, which is ___% of the 450 total students enrolled in the course.

40%

200

A store sells coffee beans in two sizes:

  • 24-ounce bag for $8.99
  • 16-ounce bag for $6.49

Which size offers the better price per ounce?

24-ounce bag has the lower price

200

The initial number of trees in a forest is 12,000, and the population doubles every 25 years. What will the tree population be in 10 years?

15,834

200

A game involves rolling a six-sided die. You win $10 if a 6 is rolled, $5 if a 5 is rolled, and $0 otherwise. What is your expected winnings?

$2.50

200

In a survey, 120 respondents were asked if they liked a new product. 75 said they liked it, and 45 said they didn’t. What is the probability that the next respondent will say they like the product?

75/120 or 0.625 or 62.5%

200

How many ways can 4 people be seated in a row of 4 chairs?

24 arrangements

300

The population of a city increased from 45,000 in 2000 to 54,000 in 2020. 

Find the absolute change and the relative change.

Absolute change: 9000

Relative change: 20%

300

A typist can type at an average speed of 85 words per minute. How many words can they type in 2.5 hours?

12,750 words

300

A population grows at an annual rate of 4%. Estimate the doubling time using the rule of 70. 

18 years

300

An investor considers a stock with a 60% chance of gaining $1,000 and a 40% chance of losing $500. What is the expected profit?

$400

300

In a survey of 1,000 people, 450 said they prefer basketball, 350 said they prefer soccer, and 200 said they prefer tennis. What is the probability that a randomly selected individual prefers soccer?

350/1000 or 0.35 or 35%

300

How many different three-number "combinations" are possible on a locker with numbers 1 through 20, assuming no numbers repeat?

6,840 combinations

400

The percentage of households with internet access increased from 45% in 2000 to 85% in 2020. 

Find the absolute and relative change.

Absolute change: 40 percent points

Relative change: 88.9%

400

Two brands of chips are sold in different-sized packs:

  • Six 10-ounce bags for $15.00
  • Eight 8-ounce bags for $16.00

Which option has the lower unit price per ounce?

Both options have the same unit price
400

The population of a village is 2,000 in 2020, and its annual growth rate is 3.5%.
a) Find the doubling time.
b) Predict the population in 2030.

a. 20 years

b. 2,821

400

A contractor considers a job with a 70% chance of earning $50,000 and a 30% chance of losing $10,000. What is the expected profit?

$32,000

400

If two cards are dealt successively from a standard 52-card deck without replacement, what is the probability of getting a king on the first card and a queen on the second?

16/2652 or 0.006 or .6%

400

A basketball coach needs to select 5 players from a roster of 10. How many ways can the coach choose the players if the order does not matter?

252 ways

500

The actual temperature is 72°F, but your thermometer reads 69°F. 

Find the absolute and relative error.

Absolute Error: -3°F 

Relative Error: -4.2%

500

Your car gets 28 miles per gallon of gasoline, and you drive at an average speed of 50 miles per hour. How much gas do you use in 90 minutes? Round to two decimal places as needed.

2.69 gallons

500

The population of a small city is 10,000 in 2020, and the annual growth rate is 2.8%.
a) Find the doubling time using the rule of 70.
b) Predict the population in 2040.

a. 25 years

b. 17,380

500

In a raffle of 1,000 tickets:

  • One prize of $1,000
  • Three prizes of $200 each
  • Ten prizes of $50 each

What is the expected winnings per ticket?

$2.10

500

If two cards are dealt successively from a standard 52-card deck with replacement, what is the probability of getting a spade on the first card and a heart on the second?

169/2704 or 0.0625 or 6.25%

500

A class has 12 students, and 3 are to be chosen as class representatives for president, vice president, and secretary. How many ways can the representatives be selected, assuming the order matters?

1,320 ways

600

The true length of a box is 12.4 inches, but a ruler measurement records it as 12.8 inches. 

Find the absolute and relative errors.

Absolute Error: 0.7 mpg

Relative Error: 2.3%

600

There are approximately 60 million deaths worldwide each year. Express this quantity in deaths per minute. Round to the nearest whole number if needed.

Approximately 1.90 deaths per second

600

A wildlife reserve has 3,000 deer in 2020, and the population grows at an annual rate of 3.6%.
a) Find the doubling time using the rule of 70.
b) Predict the population in 2030.

a. 19.4 years

b. 4,275

600

A card game has the following payouts:

  • Drawing a heart: $100 
  • Drawing a spade: $50 
  • Other suits: $0

What is the expected payout per draw?

$37.50

600

When two balanced dice are rolled, there are 36 possible outcomes. What is the probability that the sum of the dice is 7 or 11?

8/36 or 0.222 or 22.2%

600

A manager must select 4 workers from a team of 8 for a special project. How many ways can the workers be chosen if the order does not matter?

70 ways
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