Study Island Copyright 2014 Edmentum - All rights reserved. Generation Date: 03/05/2014 Generated By: Brian Leslie Unit Rates 1. Tanya is training a turtle for a turtle race. For every of an hour that the turtle is crawling, he can travel of a mile. At what unit rate is the turtle crawling? A. B. C. D. Ratios and Proportions 2. A college has a student to teacher ratio of 25 to 2. If there are 186 teachers at the college, how many students attend the college? A. 1,860 B. 930 C. 3,255 D. 2,325 Triangles 3. How many triangles exist with the given side lengths? 7 in, 7 in, 7 in
More than one triangle exists with the given side lengths. A. Exactly one unique triangle exists with the given side lengths. B. No triangle exists with the given side lengths. C. Ratios and Proportions 4. Solve for n. A. n = 7 B. n = 168 C. n = 4 D. n = 28 Percents 5. Nathan took his car in for service and repairs. He had a coupon for 15% off. Original Prices Labor $203.25 Parts $302.65 Other $59.67 Which amount is closest to Nathan's total costs after the 15% discount and including 7% sales tax? [Assume tax is applied after the discount is applied.] A. $514 B. $481 C. $441 D. $447 Scale Drawings 6.
Above are two different models of the same television. If the screen in the model on the left has a 10-inch diagonal, what is the diagonal of the screen in the model on the right? A. 20 in B. 40 in C. 60 in D. 30 in Proportional Relationships 7. A line passing through which of the following pairs of coordinates represents a proportional relationship? A. (1, 2) and (2, 3) B. (1, 3) and (3, 6) C. (1, 1) and (1, 3) D. (1, 3) and (2, 6) Scale Drawings 8.
Above are two different models of the same triangular-shaped garden. If the height of the model on the left is 15 cm, what is the height of the model on the right? A. 30 cm B. 17 cm C. 20 cm D. 22.5 cm Percents 9. Bert is planning to open a savings account that earns 1.6% simple interest yearly. He wants to earn exactly $224 in interest after 2 years. How much money should he deposit? A. $700 B. $70 C. $3,584 D. $7,000 Unit Rates 10. Richard can read of a book in of an hour. At this rate, how much can Richard read in one hour? A. of a book
B. of a book C. books D. of a book Unit Rates 11. On a trip to Italy, Chandra traded her U.S. dollars for Euros, based on the graph below. Based on the graph, what is the unit rate of Euros per dollar? A. 1.30 Euros per U.S. dollar B. 1.10 Euros per U.S. dollar C. 1.20 Euros per U.S. dollar D. 1.40 Euros per U.S. dollar Ratios and Proportions 12. Chase plays the piano and the cello. For every 2 hours he practices the piano, he practices the cello for 3 hours. If he practiced the piano for 7 hours last week, how many hours did he spend practicing the cello?
A. 21 B. 6 C. 42 D. 10.5 Scale Drawings 13. Trisha drew a blueprint of her bedroom, shown below. Denoted by a 1 on the blueprint, her bed's blueprint dimensions are inches by inches. If the scale of the blueprint is 1 inch = 2 feet, what are the actual dimensions of Trisha's bed? A. B. C. D. Percents 14. A CD usually sells for $12.00. If the CD is 30% off, and sales tax is 7%, what is the total price of the CD, including tax?
A. $9.24 B. $9.63 C. $9.07 D. $8.99 Proportional Relationships 15. The total amount of money, M, that Bob earns each week at his job is proportional to the wages, w, that he earns per hour for working h hours. Which equation represents the relationship between the total amount Bob earns and hours worked? A. B. C. D. Triangles 16. A triangle has one angle that measures 12 degrees, one angle that measures 48 degrees, and one angle that measures 120 degrees. What kind of triangle is it? A. isosceles triangle B. equilateral triangle C. right triangle D. scalene triangle Triangles 17. Which of the following are acute scalene triangles?
W. X. Y. Z. A. X and Y only B. W, X, and Y only C. X, Y, and Z only D. W and X only Proportional Relationships 18. Does the table below represent a proportional relationship? x 1 2 3 4 y -4-8 -12-16 A. Yes, because all the ratios of y to x are equal to -2. B. No, because the table has negative numbers. C. No, because the ratios of y to x are not equal. D. Yes, because all the ratios of y to x are equal to -4. Answers 1. D 2. D 3. B 4. A 5. A 6. D 7. D 8. A 9. D 10. D 11. A 12. D 13. D 14. D
15. A 16. D 17. A 18. D Explanations 1. To determine at what unit rate the turtle is crawling, divide mile by hour. Therefore, the unit rate is of a mile per hour. 2. The student to teacher ratio is 25 to 2. Set up a proportion in terms of students to teachers and solve. Therefore, 2,325 students attend the college. 3. According to the triangle inequality theorem, the sum of any two sides must be greater than the third side. Since the sum of 7 in and 7 in is greater than 7 in, the side lengths do form a triangle. A triangle with three equal sides is an equilateral triangle. Only one equilateral triangle with side lengths of 7 in exists. Therefore, exactly one unique triangle exists with the given side lengths. 4. To solve a proportion for an unknown variable, cross-multiply and divide. 5. First, find the total cost for service and repairs. $203.25 + $302.65 + $59.67 = $565.57 Next, determine the total after the 15% discount. $565.57-0.15($565.57) = $565.57 - $84.84
= $480.73 Finally, apply the 7% sales tax. $480.73 + 0.07($480.73) = $480.73 + $33.65 = $514.39 The closest amount to Nathan's total costs is $514. 6. The scale for the television on the left is 1 cm = 6 in. The scale for the television on the right is 1 cm = 2 in. So, the television on the right is 3 times larger than the television on the left. Multiply the diagonal of the screen in the television on the left by 3 to find the diagonal of the screen in the television on the right. 10 in 3 = 30 in 7. A straight line passing through the points (1, 3) and (2, 6) also passes through the origin, as shown on the graph below. Therefore, a line passing through coordinates (1, 3) and (2, 6) represents a proportional relationship. 8. Since the scale for the model on the left is 1 cm = 15 ft, and the scale for the model on the right is 1 cm = 7.5 ft, the model on the right is 2 times larger than the model on the left. Multiply the height of the model on the left by 2 to find the height of the model on the right. 15 cm 2 = 30 cm 9. The formula for computing simple interest is shown below, where p is the principal (starting amount), r is the interest rate (in decimal form), and t is the time (in years). The desired interest is $224, the time is 2 years, and the interest rate is 1.6%, or 0.016. Substitute these amounts into the given formula, and simplify.
Therefore, Bert needs to deposit $7,000. 10. To find how much Richard can read in one hour, which is the unit rate, divide the amount he read by the fraction of an hour. Therefore, Richard can read of a book in one hour. 11. A unit rate compares a quantity to one. In a proportional relationship, graphically speaking, the unit rate is equivalent to the slope. Furthermore, in a proportional relationship, the slope is equivalent to the ratio of y to x. Find a point (x, y) on the graph to determine the unit rate. Using the point (1, 1.30), the ratio of y to x is 1.30 Euros per U.S. dollar. 12. Set up a proportion in terms of piano hours to cello hours and solve. Therefore, Chase practiced the cello for 10.5 hours. 13. Let x represent the actual length of the bed. Set up a proportion and solve for x using cross multiplication. Let y represent the actual width of the bed. Set up a proportion and solve for y using cross multiplication. Therefore, the actual dimensions of Trisha's bed are feet by feet. 14. To figure out the cost with the 30% discount before sales tax, subtract 30% from the original price. Convert 30% to 0.3. discounted price = $12.00 - ($12.00 0.3)
= $8.40 Now, add the 7% sales tax. $8.40 + ($8.40 0.07) = $8.99 15. The total amount of money that Bob earns, M, can be found by multiplying the number of hours, h, that he works by the wages, w, that he earns each hour. Therefore, the equation is M = wh. 16. A scalene triangle is a triangle with NO congruent sides and NO congruent angles. 17. Triangle W is an obtuse scalene triangle. Triangle X is an acute scalene triangle. Triangle Y is an acute scalene triangle. Triangle Z is a right scalene triangle. Therefore, X and Y only are acute scalene triangles. 18. In order for the table to represent a proportional relationship, all the ratios of y to x in the table must be equivalent. -4 1 = -4-8 2 = -4-12 3 = -4-16 4 = -4 So, the table represents a proportional relationship because all the ratios are equal to -4.