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## Question 31 a

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**Question 31 a**Miguel is three years younger than Aminata. Miguel is m years old. If Aminata is 23 years-old, the equation below can be used to determine Miguel’s age. m + 3 = 23 Solve the equation to find out how old Miguel is. Show your work. Answer _______**Question 31 b**Leonardo is three years older than someone who is twice the age of Yamil. Leonardo is twenty-three years-old. If Yamil is y years old, the equation below can be used to determine Yamil’s age. 2y + 3 = 23 Solve the equation to find out Yamil age. Show your work. Answer ________________________ years old**Question 31c.**Darnell shops at two stores for a new jacket. The jacket at a fancy store costs three times the cost, c, of the jacket at a discount store. The jacket at the fancy store costs $75. The equation below can be used to determine the cost of the jacket at the discount store. 3c = 75 Solve the equation to find the cost of the jacket at the discount store. Show your work. Answer $_________________________**Question 31 dTest item**Erin shops at two stores for a new sweater. The sweater at the first store costs $15 less than three times the cost, c, of the sweater at the second store. The sweater at the first store costs $90. The equation below can be used to determine the cost of the sweater at the second store. 3c – 15 = 90 Solve the equation to find the cost of the sweater at the second store. Show your work. Answer $_________________________**Question 32a**Joanne and Jimmy need to find the greatest common factor of 12 and 20. Joanne starts by finding the prime factorization of 12. Part A What is the prime factorization of 12? Show your work. Answer_____________________________________ Part B Write the result of the prime factorization of 12 in exponential form. Answer____________________________**Question 32b**Joanne and Jimmy need to find the greatest common factor of 12 and 20. Jimmy starts by finding the prime factorization of 20. Part A What is the prime factorization of 20? Show your work. Answer___________________ Part B Write the result of the prime factorization of 20 in exponential form. Answer____________________________**Question 32 c**Ms. Zephyr assigns homework to her mathematics class. The assignment requires students to find the prime factorization of 81. Part A What is the prime factorization of 81? Show your work. Answer___________________________________________ Part B Write the result of the prime factorization of 81 in exponential form. Answer___________________________________________**Question 32 d Test Item**Mr. Hardy assigns homework to his mathematics class. The assignment requires students to find the prime factorization of 648. Part A What is the prime factorization of 648? Show your work. Answer________________________________________ Part B Write the result of the prime factorization of 648 in exponential form. Answer____________________________**Question 33 a**This year, James has been collecting state quarters and wheat pennies. He has collected 49 quarters and 112 pennies. Use estimation to calculate the amount of money he has collected. NOTE: Do not calculate everything exactly and then round your final answer – estimate first, then calculate. Show your work. Answer $______________________**Question 33 b**Marianne has been collecting coins from her change. She has 9 quarters, 21 dimes, 42 nickels and 11 pennies. Use estimation to calculate the amount of money she has collected in change. Show your work. Answer $______________________**Question 33c**Nathali wants to paint the entire outside of her rectangular storage box shown in the diagram below. Use estimation to calculate the total surface area, in square inches, of the storage box. Show your work. Answer ______________________ square inches**Question 33 d Test item**Keisha wants to paint the entire outside of her rectangular storage box shown in the diagram below. Use estimation to calculate the total surface area, in square inches, of the storage box. Show your work**Question 34 a**The Bronx Leadership Academy has monthly fundraisers for their after-school sports program. The table below shows the amount of money they raised and their fundraising expenses each month for four months. Based on the data in the table, create a bar graph on the graph paper provided to only show the amount of money the band raises for each month. Be sure to title the graph label the axes graph all the data provide an appropriate key for the graph**Question 34 b**MS 95 has a weekly math competition. Students submit their answers to a math problem of the week and the winner is selected from the right answers submitted. The table below shows the number of submissions and the number of correct submissions for the first two weeks of January. Based on the data in the table, create a double-bar graph on grid paper to show the number of submissions and the number of correct answers for each week. Be sure to title the graph label the axes graph all the data provide an appropriate key for the graph**Question 34 c.**The graduating eighth graders at MS 4 has monthly fundraisers. The table below shows the amount of money the students raised and their fundraising expenses each month for four months. Based on the data in the table, create a double-bar graph on grid paper to show the amount of money the band raises and the fundraising expenses as bars next to each other for each month. You are not representing their profit – simply how much they raised and how much their expenses are each month. Use the horizontal axis to represent the months. Be sure to title the graph label the axes graph all the data provide anappropriate key for the graph Question 35 d Test item Gilda’s family goes on vacation. They travel 125 miles in the first 2.5 hours. If Gilda’s family continues to travel at this rate, how many miles will they travel in 6 hours? Distance = rate x time Show your work. Answer_____________________ miles**Question 34 d. Test item**The Roosevelt Middle School band has monthly fundraisers. The table below shows the amount of money the band raises and their fundraising expenses each month for four months. Based on the data in the table, create a double-bar graph on grid paper to show the amount of money the band raises and the fundraising expenses for each month. Be sure to title the graph label the axes graph all the data provide an appropriate key for the graph**Question 35 a**Andrea can buy 8 apples for $2. How much would it cost for Andrea to buy 12 apples? Show your work. Answer ______________________ apples**Question 35 b**Edwin’s car can travel 20 miles on a gallon of gas. Assuming this rate remains the same, how much gas would Edwin need in order to travel 150 miles to Albany? Show your work. Answer ________________________ gallons**Question 35 c**Kevin is riding the bus across the city. He travels 8 miles in the first 2 hours. If Kevin continues to travel at the rate, how far will he travel in 3 hours? Distance = rate x time In the space below, set up a proportion that will help you to solve this problem. In the space below, use your proportion to determine how far Kevin will travel in 3 hours. Show your work. Answer___________________________________ miles**A= П r2**Question 36 a Francisca wants to cover the bottom of a can so that she does not have to use a coaster with it. The can is shown below. Calculate the area of the bottom of the can. Round your answer to the nearest whole square centimeter. Show your work. Answer _______ square centimeters**C= П d**Question 36b Francisca now wants to cover up the logo that is on the side of the can. She needs to know the area of a piece of material that would just cover the side of the can. The can is the same can as in Q36a. Calculate the area of the curved surface of the can. Round your answer to the nearest whole square centimeter. Hint: You need to find the circumference first. Show your work Answer _____________ cm2**Question 36c**Alexander wants to cover the bottom and outside of a small crate with material to make a CD rack. He needs to know the surface area of the outside of the crate shown below. Part A Calculate the surface area, in square centimeters, of the outside of Alexander’s CD rack using the formula wl + 2lh + 2 wh. Round your answer to the nearest tenth. Show your work. Answer _______________________ square centimeters Part B On the lined paper, explain why the formula wl + 2lh + 2 wh is used to find the surface area of Mary’s pencil holder instead of 2wl + 2lh + 2 wh.**Question 36d Test item**Mary wants to cover the bottom and outside of a can with material to make a pencil holder. She needs to know the surface area of the outside of the can shown below Part A Calculate the surface area, in square centimeters, of the outside of Mary’s pencil holder using the formula πr2 + 2πrh. Round your answer to the nearest tenth. Show your work. Answer ________________________ square centimeters Part B On the lined paper, explain why the formula πr2 + 2πrh is used to find the surface area of Mary’s pencil holder instead of 2πr2 + 2πrh.**Question 37a**Robert has a collection of unlabelled bootleg CDs. The chart below shows the number of CDs of each type of music in the collection Robert randomly picks a CD from his collection. What is the probability that he will listen to rap when he starts to play the CD? Show your work. Answer __________________________**Question 37 b**Tykima has a bag containing 10 chips, 3 white and 7 red. As part of a probability experiment for her math class, Tykima randomly picks a chip from the bag and then replaces it. She repeats this 100 times. She reports that picked a white chip 50 times and a red chip 50 times. Could she be correct in her report? Why or why not?**Question 37 c**Shakera has a bag containing 10 marbles. The table below shows the number of marbles of each color in the bag. As part of a probability experiment for her science class, Shakera randomly picks a marble from the bag and then replaces it. She repeats this 100 times Part A Shakera randomly picks a marble from the bag. What is the probability the marble will be blue? Show your work. Answer ___________________________ Part B Predict the number of times out of 150 Shakera will pick a blue marble. Show your work. Prediction ____________________ times**37 d Test item**Dylan has a bag containing 15 marbles. The table below shows the number of marbles of each color in the bag. As part of a probability experiment for his science class, Dylan randomly picks a marble from the bag and then replaces it. He repeats this 300 times Part A Dylan randomly picks a marble from the bag. What is the probability the marble will be red? Show your work. Answer ___________________________ Part B Predict the number of times out of 300 Dylan will pick a red marble. Show your work. Prediction ____________________ times**Question 38 a**A square room is 12 feet on each side. Part A What is the area of the room, in square feet? Show your work. Answer _______________________ square feet Part B What is the area of the room in square yards? Show your work. Answer __________________________ square yards Part C How many square feet are in one square yard? Answer __________________________ square feet**Question 38b**Gabe is preparing to serve a snack to the younger kids in his program. Each kid will get 1 cup of juice. There are about 250 kids in the program. Estimate the number of gallons of juice that Gabe will use. Show your work. Answer __________________ gallons**Question 38c**The Santiagos are buying tile for the kitchen in their apartment. They need about 45 square feet of tile. The tile they want to buy is sold by the square yard. Part A Calculate the number of square yards of tile the Santiagos need for their kitchen. Show your work. Answer ______________________ square yards Part B Describe the strategy the Santiagos should use to determine how many square yards of tile they should buy.**Question 38 d test Item**The Gatlins are buying new carpet for their house. They need about 1,175 square feet of carpet. The carpet they buy is sold by the square yard. Part A Estimate the number of square yards of carpet the Gatlins need for their house. Show your work. Answer _______________________ square yards Part B On the lined paper, describe a strategy the Gatlins should use to correctly estimate the number of square yards of carpet they need for their house.