Chapter 5
5-9. Find the missing values on the diagram below. Assume that each line is evenly divided. Homework Help ✎
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5-10.A fish tank that holds 80 gallons of water is 55% full. Homework Help ✎
1. Create a drawing like Louis’s in problem 5-4 to represent this situation.
2. How many gallons are in the tank now? How many more gallons are needed to fill the tank?
5-11. Fill in the missing numbers in each number sentence. Homework Help ✎
3. 2. 3. 4.
5. What strategies did you use to find the numbers in the Giant One in parts (b), (c), and (d)?
5-12. Complete a Proportions Web for the following situation. Homework Help ✎
Clifford works 40 hours per week while working as a laboratory technician. He earns $453.60 for each week of work.
5-13. Simplify the following expressions. Homework Help ✎
a.
b.
c.
5-18. A shade of orange paint is made with 5 parts red paint and 15 parts yellow paint. Homework Help ✎
1. What percent of the paint is red?
2. What is the simplified ratio of yellow to red paint?
5-19. Janelle earned 90% on a test and got 63 points. How many total points were possible on the test? Draw a diagram to organize your information before solving the problem. Homework Help ✎
5-20. The diagram at right is the floor plan of Randy’s apartment. All measurements are in feet. Use the diagram to answer the following questions. Homework Help ✎
1. What are the dimensions (length and width) of Randy’s living room?
2. Randy’s friends are coming to visit him soon. He plans to keep them out of his bedroom. Findthe area of each of the other three rooms he will have to clean.
3. What is the total area of the rooms he will have to clean?
· 5-21. Simplify each expression. Homework Help ✎
1.
2.
5-22. The trapezoids at right are similar shapes. Homework Help ✎
1. What is the scale factor between shape A and shape B?
2. Find the lengths of the missing sides.
5-29.Find the probability of each event. Write your answer as a fraction and as a percent. Homework Help ✎
1. Drawing a diamond from a standard deck of cards.
2. Rolling a number less than five on a standard number cube.
3. Drawing a blue marble from a bag of 18 marbles, three of which are blue.
5-30.Imagine a standard deck of cards with all of the aces and twos removed. Find each probability below.Explore cards with theProbability eTool. Homework Help ✎
1. P(heart)
2. P(black)
3. P(face card)
4. How is the P(face card) different with this deck from the probability if the deck was not missing any cards? Which probability is greater? Why?
5. P(not heart)
5-31. The Kennedy High School cross-country running team ran the following distances in recent practices. 5-31 HW eTool (CPM).
3.5 miles, 2.5 miles, 4 miles, 3.25 miles, 3 miles, 4 miles, and 6 miles.
· Find the mean and median of the team’s distances. Homework Help ✎
· 5-32. Find the area of each figure below. Homework Help ✎
1. 2.
· 5-33. Simplify the following expressions using the order of operations. Homework Help ✎
1. 3(8 − 4) + 42 − (2 + 3)
2. 7 · 4 − 3 · 8 + 22 − 6
3. 7 − (−3) + (−4 + 3)
4. −6 −4(3 · 2) + 52
· 5-38. A BETTER CHANCE OF WINNING
Each of the problems below describes two different games you can play with a random number generator. In each case, you will win if the random number generator gives you the indicated kind of number. Find the theoretical probability that you win each game below. Decide and justify whether Game I or Game II in each part, (a) through (c), gives you a better chance of winning. Explore using the random generator found in the Probability (CPM) eTool. Homework Help ✎
Game I / Game IIa. / Picking a prime number from the integers between 1 and 20 / Picking a prime number from the integers between 21 and 40
b. / Picking a multiple of 5 from the integers between 1 and 20 / Picking a multiple of 5 from the integers between 1 and 40
c. / Picking a multiple of 7 from the integers between 1 and 40 / Picking a multiple of 6 from the integers between 1 and 25
· 5-39.If you used a random number generator for the numbers from 1 through 20 to play a game, what is the theoretical probability of getting each of these outcomes? Homework Help ✎
1. A multiple of 3 or a multiple of 7, P(multiple of 3 or multiple of 7)
2. P(even or odd)
3. P(prime or 1)
4. How did you find the probabilities of these events? Be ready to share your ideas with the class.
5-40. The average annual rainfall in Tucson, Arizona is 12 inches. Between January and April, 2.4 inches of rain fell. What percentage of the annual rainfall fell after April (May through December)? You may want to draw a diagram to organize information. Homework Help ✎
5-41. Evaluate the expression 2x2 + x + 6 for the given values of x below. Homework Help ✎
1. x = 3 2. x = −2 3. x = 0 4. x = 5
5-42. Use graph paper to solve the following problem. 5-42 HW eTool (Desmos). Homework Help ✎
1. Draw a four-quadrant graph and label each axis. Plot the following ordered pairs: (−3, 2), (−8, 2), (−10, 8), (−5, 8). Connect the points in the order given as you plot them, then connect the fourth point to the first one.
2. Describe the shape on your graph. What is its area?
5-49. For each of the following probabilities, write “dependent” if the outcome of the second event depends on the outcome of the first event and “independent” if it doesnot. Homework Help ✎
1. P(spinning a 3 on a spinner after having just spun a 2)
2. P(drawing a red 6 from a deck of cards after the 3 of spades was just drawn and not returned to the deck)
3. P(drawing a face card from a deck of cards after a jack was just drawn and replaced and the deck shuffled again)
4. P(selecting a lemon-lime soda if the person before you reaches into a cooler full of lemon-lime sodas, removes one, and drinks it)
5-50.Skye’s Ice Cream Shoppe is Mario’s favorite place to get ice cream. Unfortunately, because he was late arriving there, his friends had already ordered. He did not know what they ordered for him. They told him that it was either a waffle cone or a sundae and that the ice cream flavor was apricot, chocolate, or blackberry. Homework Help ✎
1. Make a list of all of the possible ice cream orders.
2. What is the probability that Mario will get something with apricot ice cream?
3. What is the probability that he will get a sundae?
4. What is the probability that he will get either something with chocolate or a waffle cone with blackberry?
5. What is the probability that he will get orange sherbet?
· 5-51.On your paper, sketch the algebra tile shape shown at right. Write expressions for the area and perimeter of the shape. Then calculate the area and perimeter of the shape for each xvalue. Homework Help ✎
1. x = 9 cm
2. x = 0.5 cm
3. x = 15 cm
5-52.Elin has made twenty-nine note cards for her friends. She plans to send out a total of fortycards. What percentage of the cards has she finished? Represent your work clearly on your paper. Homework Help ✎
5-53. Copy and simplify the following expressions by combining like terms. Using algebra tiles may be helpful. Homework Help ✎
1. 3 + 4x + 2 + 2x + 2x
2. 8x + 4 − 3 − x
3. 7x2 + 3x + 4 + 7x2 + 3x + 4
4. 5x + 4 + x + x2 + 1
5-60. Maggie was at the state fair and decided to buy a sundae from an ice cream stand. The ice cream stand had four flavors of ice cream (chocolate, vanilla, mint chip, and coconut) and two toppings (hot fudge and caramel). How many different sundaes could Maggie create using one scoop of ice cream and one topping? Make a probability table to support your answer. Homework Help ✎
5-61. The Aloha Stadium in Honolulu, Hawaii, has seats for 50,000 people. At an upcoming football game, a company is planning to give away free hats to people based on where they are sitting. Homework Help ✎
1. The seats are divided into 40 different sections. If hats are given in only 5sections, what is the probability of a guest’s sitting in a section that gets a hat?
2. The company is going to choose three rows in each section to win the hats. There are 46 rows in a section. If you are sitting in a winning section, what is the probability that you are not sitting in a winning row?
3. The company plans to give away 750 hats. If you buy a ticket to the game, what is the probability that you will receive a hat?
5-62. A lemonade recipe calls for using a ratio of 2 cups of lemon juice for every 4cups of water. 5-62 HW eTool (Desmos) Homework Help ✎
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1. Draw and label a diagram like the one above to show the percent of lemonade that is water and the percent that is lemon juice.
2. What is the ratio of lemon juice to total liquid?
3. Angel made 10 cups of lemonade. She used 3 cups of lemon juice in her mixture. Did she follow the same recipe? In other words, did she use the same ratio of lemon juice to total liquid?
5-63. Robert found an old game in a closet and wanted to play it. However, a portion of the spinner shown at right could not be read. Find the missing portion of the spinner for Robert. Homework Help ✎
· 5-64. Copy and complete each of the Diamond Problems below. The pattern used in the Diamond Problems is shown at right. Homework Help ✎
· 5-71. WALKING THE DOG
Marcus and his brother always argue about who will walk the dog. Their father wants to find a random way of deciding who will do the job. Heinvented a game to help them decide. Eachboy will have a bag with three colored blocks in it: one yellow, one green, and one white. Each night before dinner, each boy drawsablock out of his bag. If the colors match, Marcus walks the dog. If the two colors do not match, his brother walks the dog. Marcus’s father wants to be sure that the game is fair. Help him decide. 5-71 bag 1 HW eTool (CPM) and5-71 bag 2 HW eTool(CPM). Homework Help ✎
1. Make a probability tree of all of the possible combinations of draws that Marcus and his brother could make. How many possibilities are there?
2. What is the probability that the boys will draw matching blocks? Is the game fair? Justify your answer.
5-72. For Shelley’s birthday on Saturday, she received:
· Two new shirts (one plaid and one striped);
· Three pairs of shorts (tan, yellow, and green); and,
· Two pairs of shoes (sandals and tennis shoes).
· On Monday she wants to wear a completely new outfit. How many possible outfit choices does she have from these new clothes? Draw a diagram to explain your reasoning. Homework Help ✎
· 5-73. In 2009, the federal government budget was $3.1 trillion ($3,100,000,000,000). The government was looking to cut costs. Homework Help ✎
1. If it decided to cut 1%, how much money did it cut?
2. If the government reduced the budget by 7%, how much money did it cut?
3. If the government eliminated $93 billion ($93,000,000,000) from the budget, what percentage did it cut?
· 5-74.Evaluate each expression. Homework Help ✎
1. · 7 + (–3)
2. (10)(–5)
3. –5 + 6
4. (–2) ÷ (–2)
· 5-75.Write expressions for the perimeter andthe area of this algebra tile shape. Then simplify each expression by combininglike terms. Homework Help ✎
· 5-83. Darnell designed the spinner at right for a game. It still has one incomplete section. 5-83 HW eTool (CPM). Homework Help ✎
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1. Help him figure out the probability of selecting a card on any turn. Show how you got your answer.
2. What is the probability that on any turn you will not get to spin again?
3. Which is more likely: to lose a turn or to select a card? Show how you know.
· 5-84. Manuel used pattern blocks to build the shapes below. The block marked A is a square, B is a trapezoid, C is a rhombus (a parallelogram with equal sides), and D is a triangle. Find the area of each of Manuel’s shapes. Homework Help ✎
1. 2.
· 5-85. Rachel is collecting donations for the local animal shelter. So far she has collected $245, which is 70% of what she hopes to collect. How much money does Rachel plan to collect for the shelter? Show your work. Homework Help ✎