Mathematical Models with Applications - QCHSMA4072

You currently earn $11.50 per hour. Assuming that you work 40-hour weeks with no raises, what total gross salary will you earn in the next five years? (there are 52 weeks in 1 year)

$119,600

Write the following phrase as an algebraic expression. Use n for "a number." the product of two and the sum of a number and eight

2(n + 8)

Net pay is the difference between a worker's gross income and his or her deductions. A person's gross income for the year was $65,000 and their total deductions were $12,860. What was their net pay for the year? Use the formula P = I - d, where P is the net pay, I is the gross income and d is the deductions.

$52,140 is the net pay

The following places are three of the wettest locations on Earth. For each site, determine the rainfall in centimeters per year and fill in the missing information. Use the conversion equivalency of 2.54 centimeters (cm) = 1 inch.

1186.18 cm, 1177.29 cm, 1041.4 cm

During the past school year, there were 640 students and 52 teachers. What is the ratio of students to each teacher rounded to the nearest tenth?

12.3:1

Determine the next three terms in the following sequence: 1, 8, 27, 64,____, ____, ____,...

125, 216, 343

To estimate the size of the grizzly bear population in a national park, rangers tagged and released 12 grizzly bears into the park. A few months later, 2 out of 21 grizzly bears sighted were tagged. Assuming the population of tagged bears in the population, estimate the number of grizzly bears in the population of this national park.

126 grizzly bears

As part of your job as a quality-control inspector in a factory you can check 16 parts in 3 minutes. How long will it take you to check 80 parts?

15 minutes

The tables in your classroom have square tops. Four students can comfortably sit at each table with ample working space. Putting tables together in clusters as shown will allow students to work in larger groups. There are 24 students in a math course at your school. How many tables must be put together to seat a group of six students? How many six person clusters would be needed for the entire class of 24?

2 tables, 4 clusters

A baseball player made six hits in nine innings. What is the ratio of hits to innings?

2:3

A landscaper is designing a wall made of white bricks. The pattern consists of 130 white bricks in the bottom row, 110 white bricks in the second row, and 90 white bricks in the third row. How many white bricks will the 6th row have?

30

Jeremy's car went 300 miles (highway) on 10 gallons of gasoline. What was the average number of miles per gallon?

30 mpg

Louis has two different job offers for a position in shoe sales. One pays $25 per week plus a $2 commission for each pair of shoes sold. The second job pays $40 per week plus a $1.50 commission for each pair of shoes sold. How many shoes would Louis have to sell to make the same total salary in either job?

30 pairs of shoes

The distance an object travels is determined by how fast it goes and for how long it moves. If an object's speed remains constant, the formula is where d is the distance, r is the speed, and t is the time. A satellite is orbiting the Earth at the rate of 25 kilometers per minute. How far will it travel in two hours?

3000 kilometers

A rectangular garden has a perimeter of 172 feet. The length of the garden is 24 feet more than the width. What are the dimensions of the garden? (Recall the formula P = 2L + 2W.)

31 ft by 55 ft

Use the number line below to determine the ratio of AD to EI.

3:4

Jewelry is commonly weighed in carats. Five carats are equivalent to one gram. How many grams of gold are contained in a 24-carat gold chain?

4.8 g

Find each unit rate. 140 mi in 3.5 h

40 mi per h

There are 84 boys in a freshman class of 146 students. Find the ratio of boys to girls.

42:31

Your high school freshman class consists of 760 students. In recent years, only 4 out of 7 students actually graduated in four years. Approximately how many of your classmates are expected to graduate in four years?

434 students

If i stands for income and e stands for expenses, what is the formula for p, profits?

D.

To estimate the number of people in Springfield, population 10,000, who have a swimming pool in their backyard, 250 people were interviewed. Of those polled, 119 had a swimming pool. How many people in the city might one expect to have a swimming pool? (Round to the nearest whole number, if necessary.)

4760 people

The scale on a map states that 1 centimeter corresponds to 20 kilometers. On the map, two cities are 0.3 cm apart. Find the actual distance.

6 km

There are 96 girls in a junior class of 176 students. Find the ratio of girls to boys.

6:5

Complete the following table by performing the following sequence of operations on the original number: Original Number Result of Sequence of Operations 4 6 8 10 Multiply the number by 4 Add 12 to the product Divide the sum by 2 Subtract 6 from the quotient

8, 12, 16, 20

At Whitewater Junior High School, there are 360 students and 39 teachers. What is the ratio of students to each teacher rounded to the nearest tenth?

9.2:1

A basketball player made 36 free throws in 16 games. Find the ratio of free throws to games.

9:4

A paratrooper jumps from a plane at an altitude of 4500 ft and descends at the rate of 20 ft/sec. What is the formula for the paratrooper's height, h, above the ground after t seconds?

B.

The formula for the circumference of a circle is . Determine the circumference when the radius r is 10 cm.

B.

Translate the sentence into an equation using n as the unknown number. Then solve the equation for n. Round to the nearest hundredth if necessary. The quotient of a number divided by 6 is 3.5.

B.

48/8 = 42/x Please select the best answer from the choices provided

B. x=7

n/32 = 1/16

C. n = 2

n/39 = 8/13

C. n = 24

Solve the proportion.

D. -17/3

The distance between New York City, New York and Los Angeles, California is approximately 4485 kilometers. What is the distance between these two major cities in miles? Use the conversion equivalency of 1 mile = 1.609 kilometers and round to the nearest mile.

WRONG - 7216 miles

An automobile factory is assembling cars and they need to have all of the parts in stock at the assembly line. Each car needs four tires and a spare tire for the trunk. If they produce c cars per day, what formula shows how to calculate the number of tires, t, needed?

WRONG - A.

Translate the sentence into an equation using n as the unknown number. Then solve the equation for n. Two times a number increased by 5 is 15.

WRONG - D.

If n stands for number sold and c stands for cost per item, in which column would you use the formula:

WRONG - column E

Determine the correct equation for the following verbal sentence: The total distance traveled, d, at a constant speed of 45 miles per hour is the product of the speed and the number of hours traveled, h.

d = 45h

What is the verbal phrase for the following expression? 5n

five times a number

Select the common unit rate you would use to solve a problem involving the speed of a vehicle.

kilometers per hour

An algebraic equation is an equation that includes:

one or more variables

Determine the correct equation for the following verbal sentence: The ticket price, t, for a concert attended by 220 people equals the total revenue, r, divided by the number of people who attended.

t = r/220

84/12 = 28/x

x = 4