Instructor: Diana Stinson Course: Harvard

Transcription

1 Student: Date: Instructor: Diana Stinson Course: Harvard Assignment: Summer Assignment Due 9/1 Havard 1. 1 A recipe calls for cup of ingredient A for ever 1 1 cups of ingredient B. You use 4 cups of ingredient A. How man cups 5 of ingredient B do ou need? You need cups of ingredient B. (Simplif our answer. Tpe an integer, proper fraction, or mied number.). Reasoning A carpenter uses 9 1 ft of cedar for ever 5 ft of redwood for a construction project. If the carpenter uses ft of cedar, how much redwood does he need? Use pencil and paper. Is there more than one wa to find the amount of redwood? Eplain. The carpenter needs ft of redwood. (Simplif our answer. Tpe an integer, proper fraction, or mied number.) 3. 3 Think About the Process For ever mile Shandra runs, she walks 1 miles. Suppose Shandra plans to run 1 3 miles To find how far Shandra should walk, she first writes the ratio. What is the net step? How far should Shandra walk? 9 4 What is the net step? 11 A. Find an equivalent ratio with denominator B. Find an equivalent ratio with numerator. 8 3 C. Find an equivalent ratio with numerator. 4 Shandra should walk miles. (Simplif our answer. Tpe an integer, proper fraction, or mied number.) 4. A recipe calls for 1 teaspoons of mustard seeds, 4 cups of tomato sauce, and 6 3 cups of beans. You use cups of 4 3 tomato sauce. How man teaspoons of mustard seeds do ou need? How man cups of beans do ou need? You need teaspoon(s) of mustard seeds. (Simplif our answer. Tpe an integer, proper fraction, or mied number.) You need cup(s) of beans. (Simplif our answer. Tpe an integer, proper fraction, or mied number.) 1/3

2 5. Challenge The table lists recommended amounts of food to order for 3 part guests. Nathan and Amanda are hosting a graduation part for 4 guests. The know there will also be guests stopping b who ma have come from other parties. For ordering purposes, the will count each of these "drop-in" guests as half a guest. How much of each food item should Nathan and Amanda order for a graduation part with 35 drop-in guests? Part Food Item Amount Fried Chicken 8 pieces Deli Meats 3 pounds 3 Lasagna 11 3 pounds 4 6. Nathan and Amanda should order pieces of chicken. (Simplif our answer. Tpe an integer, proper fraction, or mied number.) Nathan and Amanda should order pounds of deli meats. (Simplif our answer. Tpe an integer, proper fraction, or mied number.) Nathan and Amanda should order pounds of lasagna. (Simplif our answer. Tpe an integer, proper fraction, or mied number.) A glass bead has the shape of a rectangular prism with a smaller rectangular prism removed. What is the volume of the glass that forms the bead? 4 cm The volume of the glass that forms the bead is cm 3. 4 cm 6 cm 7 cm 6 cm (The figure is not to scale.) 7. A steel tube has the shape of a regular heagonal prism with a smaller regular heagonal prism removed. What is the volume of the steel that forms the tube?.6 cm 16 cm (The figure is not to scale.) 3.5 cm 4 cm 3 cm The volume of the steel that forms the tube is cm The bottom part of this block is a rectangular prism. The top part is a square pramid. You want to cover the block entirel with paper. How much paper do ou need? Use pencil and paper to eplain our reasoning. 4 cm 5 cm 6 cm 6 cm (The figure is not to scale.) You need cm of paper. /3

3 9. A landscaper uses tiles to make a walkwa through a garden. Each tile is a regular heagonal prism. The material used for the tiles weighs 3 g per cubic centimeter. How much does each tile weigh? 15.6 cm 18 cm 5 cm (The figure is not to scale.) Each tile weighs g. 1. in. 14 in. 5 in. (The figures are not to scale.) Ben uses cla to make the rectangular prism to the left. Naomi uses cardboard to make the triangular prism to the right. Compare the volumes of the prisms. Use pencil and paper. Describe two different methods b which ou can compare the volumes. 4 in. 5 in. 17 in. Which statement best compares the volumes of the two prisms? A. Ben's prism has the greater volume. B. Naomi's prism has the greater volume. C. The prisms have the same volume. 11. A water tank has the shape of a regular heagonal prism topped with a pramid. Your friend incorrectl claims that the volume of the tank is 7,837.5 ft 3. What is the correct volume? What is our friend's error? 3 ft Base of Water Tank (The figures are not to scale.) 5 ft 11 ft 9.5 ft 11 ft 3 The correct volume is ft. What is our friend's error? A. Your friend onl found the volume of the prism. B. Your friend subtracted the volume of the pramid from the volume of the prism. C. Your friend onl found the volume of the pramid. D. Your friend subtracted the volume of the prism from the volume of the pramid. 1. The lid of this bo is made from two lateral faces of a triangular prism. The third lateral face fits on top of a rectangular prism. Theo wants to paint the outside of the bo, ecept for the bottom. Round the given lengths to the nearest inch. Then use these rounded values to estimate the area that Theo will paint. 1.8 in. 8. in. 4.5 in. 1.8 in. 8. in. (The figure is not to scale.) Theo will need to paint about in.. 3/3

4 13. An artist needs to make 4 identical square pramids for a sculpture. To do this, she makes this mold b removing a square pramid from a rectangular prism. The material she uses for the mold weighs 4 g per cubic centimeter. How much does the mold weigh? 3 cm 3 cm 7 cm (The figure is not to scale.) The mold weighs g. 14. Think About the Process A baker just finished making a cake of two laers that are rectangular prisms. Each laer is in. high. Give an epression that represents the volume of the cake. Then find the volume of the cake. 9 in. in. 8 in. in. 8 in. 16 in. (The figure is not to scale.) Which of these epressions represents the volume of the cake? A. ()( 16)( 8)( ) B. ( 16)( 8)( )( 9)( 8) C. ( 16)( 8)( ) ( 9)( 8)( ) D. ( 16)( 8)( ) + ( 9)( 8)( ) E. ()( 9)( 8)( ) 3 The volume of the cake is in.. 4/3

5 15. Think About the Process A gift comes in a bo that is a regular heagonal 4.3 in. prism. A sheet of wrapping paper covers 1 in.. How can ou find the number of sheets ou need to wrap the bo? If ou have 5 sheets of wrapping paper, do ou have enough to wrap the bo? You ma assume that no paper goes to waste. 5 in. 6 in. What could ou do to find how man sheets of wrapping paper ou need to wrap the bo? A. Find the lateral area of the prism. Then divide it b 1 and round up to the nearest whole number. B. Find the surface area of the prism. Then divide it b 1 and round down to the nearest whole number. C. Find the surface area of the prism. Then divide it b 1 and round up to the nearest whole number. D. Find the lateral area of the prism. Then divide it b 1 and round down to the nearest whole number. You (1) enough wrapping paper. (1) do not have have 16. A cake has two laers. Each laer is a regular heagonal prism. You cut and remove a slice that takes awa one face of each prism as shown. What is the volume of the slice? What is the volume of the remaining cake? Use pencil and paper. Describe two was to find the volume of the slice. 5 in. 4.3 in. 4 in. in. 7 in. 6.1 in. (The figure is not to scale.) 3 The volume of the slice is in.. (Round to the nearest whole number as needed.) 3 The volume of the remaining cake is in.. (Round to the nearest whole number as needed.) 5/3

6 17. Challenge You want to paint the outside walls and shingle the roof of this doghouse. It costs $ 1.6 to paint each square foot. Shingles cost $.91 per square foot. How much will this project cost? You ma assume that no paint or shingles go to waste. The project will cost $. 1.8 ft 4 ft 3 ft 1 ft 3 ft 1 ft 5 ft (The figure is not to scale.) 18. Challenge You are making a cake with two laers. Each laer is a regular heagonal prism. You want to frost the visible parts of the cake. How much of the cake do ou need to frost? If each can of frosting covers 64 in., how man cans of frosting should ou bu? 5 in. 4.3 in. 3 in. 6 in. 8.7 in. 1 in. (The figure is not to scale.) You need to frost in.. (Round to the nearest whole number as needed.) You should bu at least (Round up to the nearest whole number.) can(s) of frosting. 6/3

7 19. Draw a bar diagram and write an equation to model the following problem. Then solve the equation. In a cit, Building P is 48 feet taller than two times the height of Building Q. The height of Building P is 836 feet. What is the height of Building Q? Which diagram and equation represent the problem? A. B. C q 836 q 48 q q q q + 48 = 836 The height of Building Q is q + 48 = 836 feet. q = 48. Find W if A = LW, A = 18 m, and L = 9 m. W = m 1. Which situation could the equation + 18 = 49 model? Solve the equation for and interpret our answer in the contet of the problem. Susan has 49 dollars, 18 times as man as David. David has 18 dollars, 49 dollars less than Rich. Michelle has 49 dollars, 18 more dollars than Susan. Which situation could the equation + 18 = 49 model? A. Susan has 49 dollars, 18 times as man as David. B. Michelle has 49 dollars, 18 more dollars than Susan. C. David has 18 dollars, 49 dollars less than Rich. Solve for and interpret our answer in the contet of the correct situation. Select the correct choice below and fill in the answer bo to complete our choice. A. Susan has dollars. B. David has dollars. C. Rich has dollars. 7/3

8 . Reasoning Write an addition equation to model the following problem. Then solve the equation. Use pencil and paper. Wh would ou use addition, instead of another operation, to model this situation? A traffic helicopter ascends 156 meters more than two times its original height. This is 1,38 meters above the ground. What was the original height h of the helicopter? Write an addition equation that models the problem. Choose the correct answer below. A. h + 1,38 = 156 B h = 1,38 C. (h + 1,38) = 156 D. (h + 156) = 1,38 What was the original height of the helicopter? h = meters 3. Leon sas that ou can use the equation 5 c = 49 to find the number of Calories burned jogging one mile if ou burn 49 Calories jogging 5 miles. Santana sas that ou can use the given equation to find the total Calories c burned if ou jog 49 meters per minute for 5 minutes. Which friend is correct? Solve the equation for c. Use pencil and paper. Interpret our solution in the contet of the problem. Then write several situations to which ou could appl the equation. Which friend is correct? A. Santana is correct. B. Leon is correct. C. Both Leon and Santana are correct. D. Neither Leon nor Santana are correct. What is the value of c? c = 4. How long will it take Claire to drive 1 miles if she averages 4 miles per hour on the trip? Use the distance formula d = rt where d represents distance, r represents rate, and t represents time to find our answer. It would take hours for Claire to drive 1 miles. (Tpe an integer or a decimal.) 5. 7 The formula A = LW represents the area of a rectangle. Solve the equation W = 7 for W to find the width of the rectangle 3 9 in inches. Use pencil and paper. Describe a situation when ou could use this equation. What does the value of W represent in our problem? W = inch(es) (Tpe an integer or a simplified fraction.) 8/3

9 6. Which question can ou answer with the equation 5 1 d? Solve for d and interpret our solution. = 64 How man miles will an object travel in 5 1 hours if its speed is 64 miles per hour? How man miles will an object travel in 5 1 hours if it has alread gone 64 miles? How long will it take an object to travel 5 1 miles if its speed is 64 miles per hour? Which question can ou answer with the equation 5 1 d? = 64 A. How man miles will an object travel in 5 1 hours if it has alread gone 64 miles? B. How long will it take an object to travel 5 1 miles if its speed is 64 miles per hour? C. How man miles will an object travel in 5 1 hours if its speed is 64 miles per hour? Solve for d and interpret our solution. Select the correct choice below and fill in the answer bo to complete our choice. A. It will take hours to travel 5 1 miles. B. The object will travel miles in 5 1 hours if its speed is 64 miles per hour. C. The object will travel miles in 5 1 hours if it has alread gone 64 miles. 7. Write an equation to model the following problem. Then solve the equation. A group of 5 friends each have action figures in their collections. Each friend bus 14 more action figures. Now the 5 friends have a total of 19 action figures. How man action figures did each friend start with? Which equation models the problem? A. 5 ( + 14 ) = 19 B = 19 C. 14 ( + 5 ) = 19 D. + 7 = 19 How man action figures did each friend start with? action figures 9/3

10 8. Think About the Process Auditions for the net school pla took place on Wednesda, Thursda, and Frida. Onl 1 students can be in the pla. Each da, t students tried out. The number of students who tried out but did not get a role is 54. Draw a bar diagram and write an equation to model this situation. Then solve the equation to find the number of students who tried out on Thursda. Which diagram and equation represent the problem? A. B. C. t t t t t t t + 1 = 54 t 54 3(1) + t = t 1 = 54 The total number of students who tried out for the pla on Thursda is Think About the Process The volume of the prism shown is 67 cm. Write an equation for the volume V of the prism. Then solve for. What is the height of the prism? +3 cm 7 cm 8 cm Write an equation for the volume V of the prism. Choose the correct answer below. = A. V = ( 7)( 8)( 3) B. V = C. V = ( 7)( 7 )( + 3) D. V = ( 7)( 8 )( + 3) The height of the prism is cm Substitute the given values into the formula A = h(b + c) and solve for h. A = 56 mm, b = 5 mm, c = mm h = mm 1/3

11 31. Challenge Write an addition equation to model the following problem. Then solve the equation. In 3 months, a shopkeeper spends $8,5 for rent, electricit, and water. Each month, she spends $,5 for rent and $ 17 for electricit. How much does she spend for water each month? Let w be the amount in dollars the shopkeeper spends on water each month. What is an addition equation that models the problem? A. 3(,67 + w) = 8,5 B. 3(,5 + w) = 8,5 C. 8,5 + 3 w =,67 D. 3( 17 + w) =,5 The shopkeeper spends $ for water each month. 3. Challenge Which situation can ou model with the equation = 34? Solve the equation for. Use pencil and paper. What does the value of represent in the problem? Does our solution make sense in the contet of the problem? Eplain. Three friends combine their mone to purchase two items. Five friends decide if the have enough mone to bu train tickets. Two friends combine their mone to purchase two items with some mone left over. Three friends compare their scores on a test. Which situation can ou model with the given equation? A. Three friends combine their mone to purchase two items. B. Two friends combine their mone to purchase two items with some mone left over. C. Three friends compare their scores on a test. D. Five friends decide if the have enough mone to bu train tickets. Solve the equation for. = 33. The initial cost to rent a bike is $ 4. Each hour the bike is rented costs $ Connor is going to rent a bike and can spend at most $ Write and solve an inequalit to find how long he can rent the bike. Connor can rent a bike for at most hours. 34. A 15-pound person burns 6.3 calories per minute when walking at a speed of 4 miles per hour. While walking, this person eats a snack that has 8 calories. This snack subtracts from the calories burned while walking. How long must the person walk at this speed to burn at least calories? Use pencil and paper. Describe what values the person could change so that the amount of time spent walking would be less. The person must walk for at least minutes in order to burn at least calories. (Round up to the nearest minute.) 35. The cost of a car rental is $ 3 per da plus 18 per mile. You are on a dail budget of $ 75. Write and solve an inequalit to find the greatest distance ou can drive each da while staing within our budget. Use pencil and paper. Find other two-step inequalities with the same solutions. You can drive at most miles per da. 11/3

12 36. Think About the Process Maria sells computer sstems. Her annual base salar is $ 33,. She also earns a commission of 1.4% on the sale price of all computer sstems that she sells. Maria wants her annual salar to be at least $ 1,6. Write an inequalit to model this situation. Solve the inequalit. Let s = the total sales. Which inequalit models this situation? A. 33, +.14 s > 1,6 B. 33, +.14s 1,6 C. 33, s +.14 > 1,6 D. 33, s ,6 Maria's annual salar will be at least $ 1,6 if she sells at least $ worth of computer sstems. 37. An appliance store decreases the price of a 19-in. television set 17 % to a sale price of $ What was the original price? The original price of the television was $ (Round to the nearest cent.) 38. A rectangular athletic field is twice as long as it is wide. If the perimeter of the athletic field is 4 ards, what are its dimensions? What is the width? ards What is the length? ards 39. Danielle and James are sightseeing for the da. Between the two of them the take 98 pictures. If Danielle takes 14 more than three times as man pictures as James, how man pictures does each friend take? How man pictures does James take? pictures How man pictures does Danielle take? pictures 4. Think About the Process A famil of 3 joins a gm. Each person pas $ 75 to join plus $ 1 per month. The famil decides to stop going after the have paid $ 555 all together. How could the equation be written? How man months did the famil go to the gm? Let represent the total number of months. How could the equation be written? A ( 75 ) = 555 B = 555 C. 3( 1 ) + 75 = 555 D. 3( ) = 555 The famil went to the gm for months. 1/3

13 41. Challenge A compan has 96 total emploees. The compan has three departments. There is a marketing department, an accounting department, and a human resources department. The number of emploees in the accounting department is more than three times the number of emploees in the human resources department. The number of emploees in the marketing department is twice the number of emploees in the accounting department. How man emploees are in each department? How man emploees are in the human resources department? emploees How man emploees are in the accounting department? emploees How man emploees are in the marketing department? emploees 4. Decide whether the function is linear or nonlinear using both a table and a graph. = Complete the table of values for the function. 1 1 Graph the function. Choose the correct graph below. A. B. C Is the function linear or nonlinear? Eplain. Choose the correct answer below. A. The function is nonlinear because the rate of change is constant and the graph of the function is a line. B. The function is nonlinear because the rate of change is not constant and the graph of the function is not a line. C. The function is linear because the rate of change is not constant and the graph of the function is not a line. D. The function is linear because the rate of change is constant and the graph of the function is a line. 13/3

14 43. A student was asked to decide whether the function below is linear or nonlinear using both a table and a graph. She said the function is nonlinear because the rate of change is constant and the graph of the function is not a line. Decide whether the function is linear or nonlinear using both a table and a graph. What mistake might the student have made? = 6 Complete the table of values for the function. 1 1 Graph the function. Choose the correct graph below. A. B. C. D Decide whether the function is linear or nonlinear. Eplain. Choose the correct answer below. A. The function is linear because the rate of change is constant and the graph of the function is a line. B. The function is nonlinear because the rate of change is not constant and the graph of the function is not a line. C. The function is linear because the rate of change is not constant and the graph of the function is not a line. D. The function is nonlinear because the rate of change is constant and the graph of the function is a line. What mistake might the student have made? A. She said the rate of change is constant, but the rate of change is not constant. B. She said the graph of the function is not a line, but it is a line. C. She said the function is nonlinear, but the function is linear. 14/3

15 44. Decide whether the function is linear or nonlinear using both a table and a graph. 4 = ( 1) Complete the table of values for the function. 1 1 Graph the function. Choose the correct graph below. A. B. C Decide whether the function is linear or nonlinear. Eplain. Choose the correct answer below. A. The function is nonlinear because the rate of change is constant and the graph of the function is a line. B. The function is linear because the rate of change is not constant and the graph of the function is not a line. C. The function is nonlinear because the rate of change is not constant and the graph of the function is not a line. D. The function is linear because the rate of change is constant and the graph of the function is a line. 15/3

16 45. Decide whether the function is linear or nonlinear using both a table and a graph. = ( + ) + Complete the table of values for the function Graph the function. Choose the correct graph below. A. B. C Decide whether the function is linear or nonlinear. Eplain. Choose the correct answer below. A. The function is linear because the rate of change is not constant and the graph of the function is not a line. B. The function is nonlinear because the rate of change is constant and the graph of the function is a line. C. The function is linear because the rate of change is constant and the graph of the function is a line. D. The function is nonlinear because the rate of change is not constant and the graph of the function is not a line. 16/3

17 46. Think About the Process What do ou need to determine from the table and the graph to decide whether the function is linear or nonlinear? Decide whether the function is linear or nonlinear. = What do ou need to determine from the table and the graph to decide whether the function is linear or nonlinear? A. Whether the function is increasing or decreasing. B. Whether the rate of change is constant or not and whether the function is a line. C. Whether the -intercept is positive or negative and whether the -intercept is positive or negative. D. Whether the -intercept is positive or negative and whether the slope is positive or negative. Complete the table of values for the function. 1 1 Graph the function. Choose the correct graph below. A. B. C Decide whether the function is linear or nonlinear. Eplain. Choose the correct answer below. A. The function is nonlinear because it is increasing. B. The function is linear because the -intercept and the slope have the same sign. C. The function is linear because the rate of change is constant and the graph of the function is a line. D. The function is nonlinear because the - and -intercepts have different signs. 17/3

18 47. Challenge Decide whether the function is linear or nonlinear using both a table and a graph. Use pencil and paper. Find a linear function. Make a table and a graph for the function to eplain wh it is linear. = ( 1) 4 Complete the table of values for the function Graph the function. Choose the correct graph below. A. B. C Decide whether the function is linear or nonlinear. Eplain. Choose the correct answer below. A. The function is linear because the rate of change is constant and the graph of the function is a line. B. The function is nonlinear because the rate of change is not constant and the graph of the function is not a line. C. The function is linear because the rate of change is not constant and the graph of the function is not a line. D. The function is nonlinear because the rate of change is constant and the graph of the function is a line. 48. A fitness walker walking at a constant speed finishes her first.5 mile lap around a lake in 45 minutes. Write a linear function that models the time t in minutes it takes to walk an distance d. Use the function to predict how long it will take to walk her goal of 7 miles. Which linear function models the number of minutes t it takes to walk an distance d? A. t = 45d B. t =.5d C. t = d D. t = 7d How long will it take to walk her goal of 7 miles? It will take minutes. 18/3

19 49. The after-school Activities Club charges $ to join for the ear. It charges a materials fee of $6 for each activit ou choose. Write a linear function to model the cost, c, of joining the club and choosing t activities. Find the value of the function for t = 3. Eplain the meaning of this function value in terms of the situation. Which linear function models the cost, c, of joining the club and choosing t activities? A. c = 6 t + B. c = 3 t + C. c = t + 6 D. c = 6t 3 Find the value of the function for t = 3. The value of the function for t = 3 is. Which statement best eplains the meaning of this value of the function in terms of the situation? A. You ma onl choose fewer than activities. B. You cannot choose a negative number of activities, so this function makes sense for onl nonnegative values of t. C. If ou choose 3 activities, ou get a $ discount. D. If ou signed up 3 das ago, ou would have saved $. 5. You go on a 4-da vacation and bring $ 1 for spending mone. You spend $ 5 each of the first 3 das. Write a linear function that describes the amount of mone, a, that ou have after d das. On the last da, ou want to bu a sweatshirt that costs $ 45. Do ou have enough mone to bu the sweatshirt? Which function describes how much mone ou have after d das? A. a = 1 + 5d B. a = d C. a = d D. a = d E. a = 1 5d F. a = 45d G. a = 1 45d H. a = 5d On the last da, do ou have enough mone to bu the sweatshirt? Yes No 19/3

20 51. Your friend is delivering flers to homes in the area. She earns $7 per da plus $. for ever fler delivered. The first da, she delivers 1 flers and earns $7. Your friend thinks that if she delivers twice as man flers () the net da, she will earn twice as much mone. Write a linear function to show the dail pa p (in dollars) for delivering f flers. How much should our friend get paid for delivering flers in a da? Is our friend's reasoning correct? Which linear function models the dail pa p (in dollars) for delivering f flers? A. p = 7 + 1f B. p = 7 + f C. p = 7 +.f D. p = + 7f How much should our friend get paid for delivering flers in a da? A. She should get paid $ 4. B. She should get paid $54. C. She should get paid $ 47. Is our friend's reasoning correct? No Yes 5. Bianca and Shamira were selling subscriptions to raise funds for their class trip. Together the had a goal to raise $,. Bianca sold 5 subscriptions, earning $5. Shamira sold 1 subscriptions, earning $1,. Bianca states that since $1, is half the goal, the need to sell 1 more subscriptions. Write a linear function of the form = m where is the amount of mone made in dollars, and is the number of subscriptions sold. How man subscriptions must the sell in all to raise $,? How man more must the sell to reach the goal? What likel was Bianca's mistake? Which equation models this situation? A. = 5 B. = 1 C. =, D. = 1 E. = 5 F. = 1, G. = H. = 5 How man total subscriptions must the sell to raise $,? The must sell subscriptions. How man more subscriptions must the sell to reach the goal? The must sell more subscriptions. What likel was Bianca's mistake? A. Bianca forgot to add the number of subscriptions she has sold to the number of subscriptions Shamira has sold. B. Bianca did not correctl calculate the amount earned for each of the subscriptions sold. C. Bianca did not correctl calculate half of $,. /3

21 53. You open a savings account with $ 1 and plan to save regularl each week. After 3 weeks ou have $136. Write a linear function to model the amount S saved in w weeks. Find the value of the function for w =. Eplain the meaning of this value of the function in terms of the situation. Which linear function models the amount S saved in w weeks? A. S = w B. S = w C. S = 1 + 1w D. S = 1 + 3w Find the value of the function for w =. The value of the function is $. Which statement best eplains the meaning of this value of the function in terms of the situation? A. Since w is negative, ou spent 76 dollars in the weeks before opening the account. B. The value has no meaning, since w represents time. The account did not eist at w =, so w can never be negative. C. You had saved 76 dollars weeks before opening the account. The value of S can be less than Write a linear function for the graph in the form = m, where is the total change and is the number of ears since. What would the total change be b 13? Use pencil and paper. Describe a situation that can be modeled b the function. Total Change Change Over Time Years Since What is the linear function for the graph? The function is =. What would the total change be b 13? The total change would be. 1/3

22 55. A famil has a suppl of 43 logs to use in the fireplace during a vacation. If the famil uses eactl 5 logs each night, how man nights will the suppl of logs last? Write a linear function to model this situation where G is the number of logs remaining after N nights. Which linear function models this situation? A. G = 3 + 5N B. G = N C. G = 43 5N D. G = 5 43N If the famil uses eactl 5 logs each night, how man nights will the suppl of logs last? Their suppl will last nights, with log(s) left over. 56. Your friend bought a plant that was 13 cm tall. She followed the care and watering instructions, and each week the plant grew at a constant rate. She recorded the plant's height each week in the table shown. Write a linear function of the form = m + b to model the height of the plant after weeks. Find the value of the function for = 4. Could this value of the function be possible? Plant Growth Number of Weeks Height (cm) Which linear function models the height of the plant after weeks? A. = B. = C. = D. =.9 4 Find the value of the function for = 4. The value is cm. Can this value of be used to represent the height of a plant? No Yes /3

23 57. Think About the Process Most U.S. paper mone weighs one gram per bill. To the nearest whole number, there are 454 grams in one pound. Write a linear function to model the value V of 3 pounds of U.S. bills of an one denomination d. How would ou find the value of 3 pounds of $ bills? What is the value? Which linear function models the value V of 3 pounds of U.S. bills of an given denomination d? A. V = 1,36d B. V = 4,54d C. V = 454d D. V = 454d + 3 How would ou find the value of 3 pounds of $ bills? A. Use the linear function to find the value of V when d = 3. B. Use the linear function to find the value of V when d =. C. Use the linear function to find the value of d when V = 1,36. D. Use the linear function to find the value of d when V =. What is the value of 3 pounds of $ bills? The value of 3 pounds of $ bills is $. 58. Think About the Process At the beginning of the month, the price of 1 share of a certain stock was $ 18.. Each da for a certain number of das, the price of the stock decreased b $1.75. Write a linear function to model the price, p, of 1 share of this stock after d das. How can ou tell that the model does not make sense for some values of d? Use pencil and paper. Describe the values of d for which the model makes sense and those for which it does not. Which linear function models this situation? A. p = d B. p = 1.75 d C. p = 1.75 d D. p = 1.75 d How can ou tell that the model does not make sense for some values of d? A. The price of a share of stock cannot be a decimal, so this model does not make sense for values of d that give non-integer values of p. B. The model does not make sense if d is a negative number. C. The price of a share of stock cannot be negative, so this model does not make sense for the values of d that give negative values of p. D. The price of a share of stock can be positive or negative, so this model does make sense for all values of d. 3/3

24 59. You go shopping at a store where ever item costs eactl $ 4. You have a $ 5 gift card to use in the store. When ou pa, ou will first use the gift card. Then ou will pa for the remainder of our purchase with cash. Write a linear function that models the amount C of our own cash that ou will have to spend when ou purchase n items. How much cash will ou have to spend if ou purchase 7 items? Find the value of C when n = 1. Eplain the meaning of this value of the function in terms of the situation. Which linear function models the situation? A. C = 4 n + 5 B. C = 4n 5 C. C = 7n 5 D. C = 5 n + 4 E. C = 7 n + 4 F. C = 5n 4 How much cash will ou have to spend if ou purchase 7 items? $ Find the value of C when n = 1. When n = 1, the value of C is. Which statement best eplains the meaning of this value of the function in terms of the situation? A. You do not have to spend an cash. You have a balance of $ 1 on the gift card. B. You must pa $ 1 in cash to cover our purchase. C. You ma still purchase 1 items using the gift card. D. The value has no meaning, since C is in dollars. 6. Challenge A professional sports league decides the minimum salar increase for each of its plaers. The graph models what the minimum increase will cost a team. Use the graph to write a linear function for the total cost C for a team with plaers. How much, at least, can one plaer epect to get for a raise? What will be the total salar increase, at least, for 8 plaers? Use pencil and graph paper. Draw that part of the graph for a team that normall would have 15 to plaers. Increase (thousands of $) Total Salar Increases (Minimum Raises Onl) 1 3 Number of Plaers What is the linear function for the total cost C, in thousands of dollars, for the minimum salar increase for plaers? C = How much, at least, can one plaer epect to get for a raise? One plaer can epect to get at least $ this ear. What will be the total salar increase, at least, for 8 plaers? The total salar increase for a team with 8 plaers will be at least $ thousand. 4/3

25 61. Challenge The cook at a summer camp orders 5 cases of frozen meatballs before the start of camp. Each case has 16 bags that contain 3 pounds each. The cook uses 8 pounds of meatballs each week. Write a linear function where represents the number of pounds of meatballs remaining after weeks. Will there be enough meatballs to last the entire 6 weeks of camp? If not, for how man full weeks must the cook order more meatballs? What is the linear function where is the number of pounds of meatballs remaining after weeks? = Will there be enough meatballs to last the entire 6 weeks of camp? If not, for how man full weeks must the cook order more meatballs? A. Yes, there will be more than enough meatballs. B. Yes, there will be eactl enough meatballs. C. No. The chef must order more meatballs for 3 full weeks. D. No. The chef must order more meatballs for 5 full weeks. E. No. The chef must order more meatballs for full weeks. 6. Use a net to find the surface area of the open clinder with onl one base. Use 3.14 for. 8 cm 63. The surface area of the clinder is about cm. (Round to the nearest tenth as needed.) Reasoning Use a net to find the surface area of the open clinder with onl one base. Use 3.14 for. Use pencil and paper. Without doing an calculations, would ou epect the lateral area or the area of a base of the clinder to increase b a greater amount if the diameter were doubled? Eplain our reasoning. 9 cm (The figure is not to scale.) 9.6 in..1 in. The surface area of the clinder is about in.. (Round to the nearest tenth as needed.) (The figure is not to scale.) An open clinder has onl one base. Its diameter is 1 in., and its height is 18 in. Use a net to find the surface area of 8 8 the clinder. Use 3.14 for. The surface area of the clinder is about in.. (Round to the nearest tenth as needed.) 5/3

26 65. What does the indicated point on the scatter plot represent? Cost of CDs The indicated point represents a CD that has songs and costs $. Price (dollars) Number of Songs 66. Writing What does the indicated point on the scatter plot represent? Use pencil and paper. Eplain wh it is possible for two storms to have the same duration but produce different amounts of rain. 4 1 Rainfall The indicated point represents a minute storm that produced millimeters of rain. Amount of Rain (millimeters) Duration (minutes) 6/3

27 67. What do the indicated points on the scatter plot represent? Point A represents a horsepower car that Average Gas Mileage (miles per gallon) A Fuel Econom B usuall gets Point B represents a usuall gets miles per gallon. horsepower car that miles per gallon Horsepower 68. The table shows the average price of a pair of jeans and the number of pairs of jeans sold. Complete the scatter plot to represent the data. Jeans Sales Average Price ($) Number Sold Number Sold Jeans Sales Average Price ($) Which scatter plot represents the data? A. B. C. D. Jeans Sales Jeans Sales Jeans Sales Jeans Sales Number Sold Average Price ($) Number Sold Average Price ($) Number Sold Average Price ($) Number Sold Average Price ($) 7/3

28 69. Writing The table shows the number of reported rainstorms in two different regions of a countr. Complete the scatter plot to represent the data. Use pencil and paper. Eplain how a scatter plot shows the relationship between the data points. Rainstorms Region A Region B Region B Number of Rainstorms 3 Region A Which scatter plot represents the data? A. B. C. D. Number of Rainstorms Number of Rainstorms Number of Rainstorms Number of Rainstorms Region B 8 Region A Region B 8 Region A Region B 8 Region A Region B 8 Region A 7. Think About the Process The table shows the calories and fat content for a chicken sandwich at certain restaurants. How should ou plot each point to complete the scatter plot? Complete the scatter plot. Chicken Sandwiches Restaurant A B C D E F Number of Calories Number of Fat Grams , Number of Fat Grams 6 Sandwiches Number of Calories How should ou plot each point to complete the scatter plot? Move (1) the number of units to plot the number of calories. Move () the number of units to plot the amount of fat. Which scatter plot represents the data? Number of Fat Grams A. 6 1, Number of Calories Number of Fat Grams B. Sandwiches Sandwiches Sandwiches Sandwiches 6 1, Number of Calories Number of Fat Grams C. 6 1, Number of Calories Number of Fat Grams D. 6 1, Number of Calories (1) up down right left () down left up right 8/3

29 71. You ask 6 of our classmates how the get to school. There are 1 girls who walk to school and 5 who do not. There are 5 bos who walk to school and who do not. Construct a two-wa frequenc table to show the results of the surve. Construct the two-wa frequenc table. Yes No Gender Girls Bos Total Total 7. Writing You ask 11 of our classmates if the like sports. There are 35 girls who like sports and 1 bos who like sports. There are 5 bos and 4 girls who do not like sports. Complete the two-wa frequenc table to show the results of the surve. What are the categories of the row variable? What are the categories of the column variable? Use pencil and paper. How does the table change if the row and column variables are switched? Construct the two-wa frequenc table. Yes No Total Gender Girls Bos Total Choose the correct answer below. A. For this table the column categories are Girls and Bos. The row categories are Yes and No. C. For this table the column categories are Girls and Bos. The row categor is Total. B. For this table the column categories are Yes and No. The row categories are Girls and Bos. D. For this table the column categor is Gender. The row categories is Yes and No. 73. At one point last ear, the local animal shelter had onl cats and dogs. There were 7 animals in all. Of the cats, 3 were male and 17 were female. Of the dogs, 8 were male and 4 were female. Construct a two-wa frequenc table of the data. Use pencil and paper. Construct a two-wa frequenc table if the tpe of animal were the row variable instead of the column variable. Construct the two-wa frequenc table. Male Female Total Tpe of Animal Cat Dog Total 9/3

30 74. The two-wa frequenc table shows the number of tos sold in one da in three countries for different tpes of stores. How man tos were sold through catalogs? How man tos were sold in Countr C? To Sales Tpe of Store To Chain Store Department Store Catalog Online Total Countr A 6, , ,651 Countr B 5,118, ,863 Countr C 4,85,34 6 6,745 Total 15,96 5,33, ,59 The number of tos sold through catalogs was. The number of tos sold in Countr C was. 75. Writing The table shows the number of licensed drivers in a state b age and b gender. How man drivers are between and 9 ears old? How man drivers are women? Use pencil and paper. Give an eample for which the information in the table might be of interest. Eplain. Licensed Drivers Age Under or Older Total Men 4,78 8,696 8,81 9,83 8,53 6,167 45,937 Women 4,715 8,657 8,8 9,6 8,84 6,19 45,96 Total 9,443 17,353 17,63 18,543 16,537 1,357 91,863 There are drivers between and 9 ears old. There are drivers who are women. 76. Students at a local school were asked, "About how man hours do ou spend on homework each week?" The two-wa frequenc table shows the results of the surve. How man students spend between 5 and 6 hours on homework each week? How man students were surveed? Homework Number of Hours Less More than 1 than 6 Total Sith Seventh Eighth Total The number of students who spend between 5 and 6 hours on homework each week is. The number of students surveed was. 3/3

31 77. A school surves 1 students about how the get to school. You want to know if more girls than bos walk to school. Which table will be more helpful in finding that information? Eplain our choice. Frequenc Table Gender Row Relative Frequenc Table Gender Girls Bos Total Girls Bos Total Yes 3 5 Yes 4 % 6 % 1% No No 3 % 7 % 1% Total Total 35 % 65 % 1% Choose the correct answer below. A. The row relative frequenc table is more helpful because ou are interested in percents, not frequencies. C. The frequenc table is more helpful because ou are interested in percents, not frequencies. B. The row relative frequenc table is more helpful because ou are interested in frequencies, not percents. D. The frequenc table is more helpful because ou are interested in frequencies, not percents. 78. Writing Each of 55 college students was asked if he or she studied more than a week for final eams and if his or her grade improved. You want to know if students who studied less than a week tended to see less grade improvement. Which table will be more helpful in finding that information? Eplain our choice. Use pencil and paper. Give a question where a total relative frequenc table would be more helpful in interpreting the data. 1 Click the icon to view the frequenc and row relative frequenc tables. Choose the correct answer below. A. The frequenc table is more helpful because ou are interested in frequencies, not percents. B. The row relative frequenc table is more helpful because ou are interested in percents, not frequencies. C. The frequenc table is more helpful because ou are interested in percents, not frequencies. D. The row relative frequenc table is more helpful because ou are interested in frequencies, not percents. 1: Frequenc and Row Relative Frequenc Table Frequenc Table Grade improved? Yes No Total Studied less than a week Studied more than a week Total Row Relative Frequenc Table Grade improved? Yes No Total Studied less than a week 56 % 44 % 1% Studied more than a week 4 % 6 % 1% Total 47.3 % 5.7 % 1% 31/3

32 79. Business To boost compan morale, a manager is thinking about changing the office's summer schedule to four 1-hour workdas with three das off. The current schedule is five 8-hour workdas with two das off. He surves a sample of emploees in each of the three different departments. He will make his decision based on how man people choose the new schedule. Which table will be more helpful to the manager? Eplain. Frequenc Table Department Accounting Sales HR Total New Current Total Column Relative Frequenc Table Department Accounting Sales HR Total New 57.7% 5.9% 38.5% 5.1% Current 4.3% 47.1% 61.5% 47.9% Total 1% 1% 1% 1% Choose the correct answer below. A. The column relative frequenc table is more helpful because the manager is interested in frequencies, not percents. C. The frequenc table is more helpful because the manager is interested in frequencies, not percents. B. The column relative frequenc table is more helpful because the manager is interested in percents, not frequencies. D. The frequenc table is more helpful because the manager is interested in percents, not frequencies. 8. You surve 1 students, asking each if he or she plas sports. You want to know if bos are more likel than girls to pla sports. Which table will be more helpful in finding that information? Eplain our choice. Use pencil and paper. Which table would be more helpful if ou wanted to know if it is more likel than not that students pla sports? Frequenc Table Gender Column Relative Frequenc Table Gender Girls Bos Total Girls Bos Total Yes Yes 8 % 7 % 76% No No % 8 % 4% Total Total 1% 1% 1% Choose the correct answer below. A. The frequenc table is more helpful because ou are interested in percents, not frequencies. C. The column relative frequenc table is more helpful because ou are interested in frequencies, not percents. B. The column relative frequenc table is more helpful because ou are interested in percents, not frequencies. D. The frequenc table is more helpful because ou are interested in frequencies, not percents. 3/3