INVENTORY A nursery has $40,000 of inventory in dogwood

The process of translating phrases or sentences into algebraic expressions or equations is called ________ ________.

A good approach to mathematical modeling is a two-stage approach, using a verbal description to form a ________ ________, and then, after assigning labels to the quantities, forming an ________ ________.

Area of a circle: ________

Perimeter of a rectangle: ________

Volume of a cube: ________

Volume of a circular cylinder: ________

Balance if dollars is invested at % compounded monthly for years: ________

Simple interest if dollars is invested at % for years: ________

x

u 5

2 3

4 5

z 10 7

3 b 21

12x x 5

4 p 1 p

q 4 3 q 2q

The sum of two consecutive natural numbers

The product of two consecutive natural numbers

The product of two consecutive odd integers, the first of which is

The sum of the squares of two consecutive even integers, the first of which is

The distance traveled in hours by a car traveling at 55 miles per hour

The travel time for a plane traveling at a rate of kilometers per hour for 900 kilometers

The amount of acid in liters of a 20% acid solution

The sale price of an item that is discounted 33% of its list price

The perimeter of a rectangle with a width and a length that is twice the width

The area of a triangle with base 16 inches and height inches

The total cost of producing units for which the fixed costs are $2500 and the cost per unit is $40

The total revenue obtained by selling units at $12.99 per unit

Thirty percent of the list price

The amount of water in quarts of a liquid that is 28% water

The percent of 672 that is represented by the number

The percent change in sales from one month to the next if the monthly sales are and respectively

In Exercises 35 and 36, write an expression for the area of the region in the figure.

In Exercises 35 and 36, write an expression for the area of the region in the figure.

The sum of two consecutive natural numbers is 525. Find the numbers.

The sum of three consecutive natural numbers is 804. Find the numbers.

One positive number is 5 times another number. The difference between the two numbers is 148. Find the numbers.

One positive number is of another number. The difference between the two numbers is 76. Find the numbers.

Find two consecutive integers whose product is 5 less than the square of the smaller number

Find two consecutive natural numbers such that the difference of their reciprocals is the reciprocal of the smaller number.

What is 30% of 45?

What is 175% of 360?

432 is what percent of 1600?

459 is what percent of 340?

12 is of what number?

70 is 40% of what number?

FINANCE A salespersons weekly paycheck is 15% less than a second salespersons paycheck. The two paychecks total $1125. Find the amount of each paycheck.

DISCOUNT The price of a swimming pool has been discounted 16.5%. The sale price is $1210.75. Find the original list price of the pool.

FINANCE A family has annual loan payments equaling 32% of their annual income. During the year, their loan payments total $15,125.50. What is their annual income?

FINANCE A family has a monthly mortgage payment of $500, which is 16% of their monthly income. What is their monthly income?

Gallon of regular unleaded $1.51 $2.80 gasoline

Monthly cable rate $30.37 $42.72

Pound of 100% ground beef $1.63 $2.23

Monthly bill for cellular $45.27 $49.79 phone service

DIMENSIONS OF A ROOM A room is 1.5 times as long as it is wide, and its perimeter is 25 meters. (a) Draw a diagram that represents the problem. Identify the length as and the width as (b) Write in terms of and write an equation for the perimeter in terms of (c) Find the dimensions of the room.

DIMENSIONS OF A PICTURE FRAME A picture frame has a total perimeter of 3 meters. The height of the frame is times its width. (a) Draw a diagram that represents the problem. Identify the width as and the height as (b) Write in terms of and write an equation for the perimeter in terms of (c) Find the dimensions of the picture frame.

COURSE GRADE To get an A in a course, you must have an average of at least 90 on four tests of 100 points each. The scores on your first three tests were 87, 92, and 84. What must you score on the fourth test to get an A for the course?

COURSE GRADE You are taking a course that has four tests. The first three tests are 100 points each and the fourth test is 200 points. To get an A in the course, you must have an average of at least 90% on the four tests. Your scores on the first three tests were 87, 92, and 84. What must you score on the fourth test to get an A for the course?

TRAVEL TIME You are driving on a Canadian freeway to a town that is 500 kilometers from your home. After 30 minutes you pass a freeway exit that you know is 50 kilometers from your home. Assuming that you continue at the same constant speed, how long will it take for the entire trip?

TRAVEL TIME Students are traveling in two cars to a football game 135 miles away. The first car leaves on time and travels at an average speed of 45 miles per hour. The second car starts hour later and travels at an average speed of 55 miles per hour. How long will it take the second car to catch up to the first car? Will the second car catch up to the first car before the first car arrives at the game?

AVERAGE SPEED A truck driver traveled at an average speed of 55 miles per hour on a 200-mile trip to pick up a load of freight. On the return trip (with the truck fully loaded), the average speed was 40 miles per hour. What was the average speed for the round trip?

WIND SPEED An executive flew in the corporate jet to a meeting in a city 1500 kilometers away. After traveling the same amount of time on the return flight, the pilot mentioned that they still had 300 kilometers to go. The air speed of the plane was 600 kilometers per hour. How fast was the wind blowing? (Assume that the wind direction was parallel to the flight path and constant all day.)

PHYSICS Light travels at the speed of approximately meters per second. Find the time in minutes required for light to travel from the sun to Earth (an approximate distance of meters).

RADIO WAVES Radio waves travel at the same speed as light, approximately meters per second. Find the time required for a radio wave to travel from Mission Control in Houston to NASA astronauts on the surface of the moon meters away.

HEIGHT OF A BUILDING To obtain the height of the Chrysler Building in New York, you measure the buildings shadow and find that it is 87 feet long. You also measure the shadow of a four-foot stake and find that it is 4 inches long. How tall is the Chrysler Building?

HEIGHT OF A TREE To obtain the height of a tree (see figure), you measure the trees shadow and find that it is 8 meters long. You also measure the shadow of a two-meter lamppost and find that it is 75 centimeters long. How tall is the tree?

FLAGPOLE HEIGHT A person who is 6 feet tall walks away from a flagpole toward the tip of the shadow of the flagpole. When the person is 30 feet from the flagpole, the tips of the persons shadow and the shadow cast by the flagpole coincide at a point 5 feet in front of the person. (a) Draw a diagram that gives a visual representation of the problem. Let represent the height of the flagpole. (b) Find the height of the flagpole.

SHADOW LENGTH A person who is 6 feet tall walks away from a 50-foot tower toward the tip of the towers shadow. At a distance of 32 feet from the tower, the persons shadow begins to emerge beyond the towers shadow. How much farther must the person walk to be completely out of the towers shadow?

INVESTMENT You plan to invest $12,000 in two funds paying and 5% simple interest. (There is more risk in the 5% fund.) Your goal is to obtain a total annual interest income of $580 from the investments. What is the smallest amount you can invest in the 5% fund and still meet your objective?

INVESTMENT You plan to invest $25,000 in two funds paying 3% and simple interest. (There is more risk in the fund.) Your goal is to obtain a total annual interest income of $1000 from the investments. What is the smallest amount you can invest in the fund and still meet your objective?

INVENTORY A nursery has $40,000 of inventory in dogwood trees and red maple trees. The profit on a dogwood tree is 25% and the profit on a red maple tree is 17%. The profit for the entire stock is 20%. How much was invested in each type of tree?

INVENTORY An automobile dealer has $600,000 of inventory in minivans and alternative-fueled vehicles. The profit on a minivan is 24% and the profit on an alternative-fueled vehicle is 28%. The profit for the entire stock is 25%. How much was invested in each type of vehicle?

MIXTURE PROBLEM Using the values in the table, determine the amounts of solutions 1 and 2 needed to obtain the specified amount and concentration of the final mixture.

MIXTURE PROBLEM A 100% concentrate is to be mixed with a mixture having a concentration of 40% to obtain 55 gallons of a mixture with a concentration of 75%. How much of the 100% concentrate will be needed?

MIXTURE PROBLEM A forester mixes gasoline and oil to make 2 gallons of mixture for his two-cycle chainsaw engine. This mixture is 32 parts gasoline and 1 part two-cycle oil. How much gasoline must be added to bring the mixture to 40 parts gasoline and 1 part oil?

MIXTURE PROBLEM A grocer mixes peanuts that cost $1.49 per pound and walnuts that cost $2.69 per pound to make 100 pounds of a mixture that costs $2.21 per pound. How much of each kind of nut is put into the mixture?

COMPANY COSTS An outdoor furniture manufacturer has fixed costs of $14,000 per month and average variable costs of $12.75 per unit manufactured. The company has $110,000 available to cover the monthly costs. How many units can the company manufacture? (Fixed costs are those that occur regardless of the level of production. Variable costs depend on the level of production.)

COMPANY COSTS A plumbing supply company has fixed costs of $10,000 per month and average variable costs of $9.30 per unit manufactured. The company has $85,000 available to cover the monthly costs. How many units can the company manufacture? (Fixed costs are those that occur regardless of the level of production. Variable costs depend on the level of production.)

AREA OF A TRIANGLE

AREA OF A TRAPEZOID

MARKUP

INVESTMENT AT SIMPLE INTEREST

VOLUME OF AN OBLATE SPHEROID

VOLUME OF A SPHERICAL SEGMENT

FREE-FALLING BODY

LENSMAKERS EQUATION

CAPACITANCE IN SERIES CIRCUITS Solve for

ARITHMETIC PROGRESSION

ARITHMETIC PROGRESSION

GEOMETRIC PROGRESSION

Two children weighing 50 pounds and 75 pounds are playing on a seesaw that is 10 feet long.

A person weighing 200 pounds is attempting to move a 550-pound rock with a bar that is 5 feet long.

VOLUME OF A BILLIARD BALL A billiard ball has a volume of 5.96 cubic inches. Find the radius of a billiard ball.

LENGTH OF A TANK The diameter of a cylindrical propane gas tank is 4 feet. The total volume of the tank is 603.2 cubic feet. Find the length of the tank

TEMPERATURE The average daily temperature in San Diego, California is 64.4F. What is San Diegos average daily temperature in degrees Celsius?

TEMPERATURE The average daily temperature in Duluth, Minnesota is 39.1F. What is Duluths average daily temperature in degrees Celsius? (

TEMPERATURE The highest temperature ever recorded in Phoenix, Arizona was 50C. What is this temperature in degrees Fahrenheit?

TEMPERATURE The lowest temperature ever recorded in Louisville, Kentucky was What is this temperature in degrees Fahrenheit?

8 less than cubed divided by the difference of squared and 9 can be written as

The volume of a cube with a side of length 9.5 inches is greater than the volume of a sphere with a radius of 5.9 inches.

Consider the linear equation (a) What is the sign of the solution if (b) What is the sign of the solution if In each case, explain your reasoning.

CAPSTONE

Write a linear equation that has the solution (There are many correct answers.)