Interpreting Graphs. Interpreting a Bar Graph

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24 60. FOOTBALL The season attendance at your school s football games is 1000 people one year. For each of the next 3 years, the attendance is double the previous year s attendance. Write an expression with a power that shows the season attendance at the football games after 3 years. 61. INLINE SKATING An inline skater is at the top of a hill. The hill is 30 feet long and is angled such that the speed of a skater going down the hill doubles every 6 feet. A skater is going 3 miles per hour after the first 6 feet. What is the speed of the skater when the skater reaches the bottom of the hill? 62. MULTIPLE REPRESENTATIONS At an archeological dig, the lead scientist decides that the dig should be organized by repeatedly dividing the square area into four smaller squares as shown. Stage 1 Stage 2 Stage 3 a. Make a Table Make a table that shows the number of squares at each stage from the 1st stage through the 6th stage. b. Write an Expression Write an expression as a power for the number of squares in the dig at the 7th stage. c. Write a Description How many squares are along each side of the dig at the 7th stage? If the whole dig is 64 feet on a side, what is the side length of each individual square at the 7th stage? 63. EXTENDED RESPONSE On an ostrich farm a single breeding pair hatches 30 eggs per season. These hatchlings will form breeding pairs the following season. Each new breeding pair will hatch about 30 eggs per season. How many breeding pairs would be on the farm after 1 breeding season, assuming all survive? after 2 seasons? after n seasons? Explain your answer. 64. EVALUATING POWERS Some powers of 11 read the same forward and backward. For example , What is the smallest n such that 11 n does not read the same forward and backward? 65. REASONING Evaluate 7 4,7 3,7 2, and 7 1. Based on this pattern, what is the value of 7 0? Predict the value of x 0, where x is a whole number greater than 0. Explain your reasoning. 66. CHALLENGE The personal computers of the early 1980s had 64 kilobytes of memory. Today they have more than one gigabyte of memory. Use the table. Write, as a power, the number of bytes of memory that personal computers of the early 1980s had. Name Bytes Kilobyte 2 10 Megabyte 2 20 Gigabyte Powers and Exponents 23

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26 STATE TEST PRACTICE classzone.com Lessons MULTI-STEP PROBLEM Muntz metal is an alloy of copper and zinc. A sample of Muntz metal has a volume of 15 cubic centimeters. The volume of the copper in the sample is x cubic centimeters. The mass of this copper is 80.1 grams. a. Write an expression in terms of x for the volume of zinc in the sample. b. Use the fact that 1 cubic centimeter of zinc has a mass of 7.1 grams to write an expression in terms of x for the total mass of the sample. c. What is the sample s total mass if the volume of its copper is 9 cubic centimeters? Show your calculations. 4. EXTENDED RESPONSE You are participating in a 20 mile fundraising walk. People can contribute a certain amount per mile that you walk or just make a fixed contribution. The fixed individual contributions that you collected total \$150. The per mile contributions total \$15 per mile. a. Write an expression for the amount of money you raise if you walk the entire 20 miles. b. How much will you raise if you complete the walk? c. How far will you have to walk to raise \$300? 2. EXTENDED RESPONSE The frequency table shows the heights of 30 students. Height (inches) Frequency a. Make a histogram of the data shown in the frequency table. b. Which height interval has the most students? c. Can you use the histogram to determine the number of students who are between 60 and 65 inches tall? Explain. 3. GRIDDED ANSWER The expression 16t 2 is used to find the distance in feet that an object has fallen t seconds after being dropped. When dropping a rock off of a 512 foot cliff, how many more feet does it fall in 4 seconds than in 3 seconds? 5. SHORT RESPONSE Your car s fuel gauge is broken. The car can go 22 miles on one gallon of gasoline. You start a trip with 13 gallons of gasoline, and you want to always have at least two gallons in the tank. What is the farthest you should drive before stopping for more gasoline? Explain. 6. OPEN-ENDED Consider the expression Find at least six values for the expressions that result from inserting one pair of parentheses. For one of these expressions, write a real-world problem that can be modeled by the expression. Show your calculations. Mixed Review of Problem Solving 25

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31 SEE EXAMPLE 3 on p. 27 for Exs WRITING Explain how you can tell if 5 is a solution of 4x MULTIPLE CHOICE You are writing invitations to a party. It takes you four minutes to complete each invitation. What is the equation for finding x, the number of invitations you can complete in one hour? A 4 } x 5 60 B x } C 4x 5 60 D x SEE EXAMPLE 4 on p. 28 for Ex SHORT RESPONSE Your town s fireworks show lasted 20 minutes. The total cost was \$25,000. Use a verbal model to write and solve an equation to find the cost per minute. What is the cost of a show at the same rate per minute that lasts twice as long? Explain your answer. 51. OPEN-ENDED MATH Describee a situation that can x be modeled by } Then solve the equation MARATHON To qualify for the Boston Marathon, Maria needs to run a qualifying time of 3 hours 40 minutes or less. Her best time so far is 4 hours 5 minutes. Write and solve an equation to find the fewest minutes by which Maria must improve her time to qualify. 53. VOLUNTEERING You want to volunteer 200 total hours ata zoo. After 5 weeks, you have worked 80 hours. Write and solve an equation to find how many hours you will work per week over the remaining 8 weeks. 54. CONSECUTIVE NUMBERS Consecutive numbers are numbers that follow one after another, such as 1, 2, and 3. The sum of two consecutive numbers divided by 3 is 71. What are the two numbers? 55. CHALLENGE Joe had a box of gumballs. He gave half of them to Antowain, one sixth to Shaniqua, and one fourth to Naresh. He has 4 left. How many gumballs did Joe have before he gave some away? 56. CHALLENGE Jen has } 4 as much money as Bob. Tim has \$50 more than 5 Jen. Rita has \$150, which is \$35 more than Bob. How much money does Tim have? MIXED REVIEW Prepare for Lesson 1.6 in Exs Evaluate the expression when y 5 8. (p. 13) 57. 7y ( ) p y 59. y p p y y Estimate thesum or difference. (p. 766) MULTIPLE CHOICE What is the value of ( ) 6? (p. 19) A 6 B 14 C 30 2 } 3 D EXTRA PRACTICE for Lesson 1.5, p. 801 ONLINE QUIZ at classzone.com

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33 1.6 Variables in Familiar Formulas Before You evaluated variable expressions. Now You ll use formulas to find unknown values. Why? So you can calculate distances, as in Ex. 31. KEY VOCABULARY formula, p. 32 perimeter, p. 32 area, p. 32 A formula is an equation that relates two or more quantities such as perimeter, length, and width. The perimeterr of a figure is the sum of the lengths of its sides. The amount of surface the figure covers is called its area. a Perimeter is measured in linear units such as feet. Area is measured in square units such as square feet, written as ft 2. You may have found the formula for area in the Investigation on p. 31. area perimeter length width KEY CONCEPT For Your Notebook Perimeter and Area Formulas Rectangle Diagram Perimeter Area w P 5 l 1w 1 l 1w P 5 or A 5 lw l P 5 2l 1 2w Square s P 5 4s A 5 s 2 s E XAMPLE 1 Finding Perimeter and Area Find the perimeter and area of the rectangle. 5 ft READING The mark tells you that an angle is a right angle, which measures 908. SOLUTION 8 ft Find the perimeter. Find the area. P 5 2l 1 2w Write formula. A 5 lw Write formula. 5 2(8) 1 2(5) Substitute. 5 (8)(5) Substitute Multiply, then add Multiply. c Answer The perimeter is 26 feet, and the area is 40 square feet. 32 Chapter 1 Variables and Equations

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49 1.6 Variables in Familiar Formulas pp E XAMPLE Find the length and perimeter of the rectangle. Its area is 54 square feet. 6 ft For area use the formula A 5 lw. For perimeter use the formula P 5 2l 1 2w. A5 lw Write formula. P 5 2l 1 2w Write formula l(6) Substitute. 5 2(9) 1 2(6) Substitute. 9 5 l Use mental math Multiply, then add. c Answer The length is 9 feet and the perimeter is 30 feet. EXERCISES Find the unknown value for the rectangle or square. SEE EXAMPLES 1 AND 3 on pp for Exs rectangle: P 5 56 cm, l 5 12 cm, w 5? 38. square: A ft 2, s 5? 39. Cars A car travels at an average rate of 50 miles per hour for 3 hours. How far does it travel? 1.7 A Problem Solving Plan pp E XAMPLE You need 3 pitcherfuls to fill a 5-gallon aquarium with a pitcher. How many trips will you need to fill a 55-gallon aquarium with the same pitcher? Read and Understand and Make a Plan Find how many times as great the capacity of the larger tank is than the smaller tank. Compare using division. Then multiply that number by 3, because it takes 3 pitcherfuls to make 5 gallons. 55 gal Solve the Problem } p 3 trips 5 11 p 3 trips 5 gal 5 33 trips c Answer You need 33 pitcherfuls to fill the larger aquarium. EXERCISES SEE EXAMPLE 3 on p. 39 for Ex Sugar You like 2 teaspoons of sugar in an 8-ounce glass of iced tea. How much sugar should you add to a 36-ounce thermos of iced tea? 48 Chapter 1 Variables and Equations

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