4. Based on the table below, what is the joint relative frequency of the people surveyed who do not have a job and have a savings account?

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1 Name: Period: Date: Algebra 1 Common Semester 1 Final Review 1. How many surveyed do not like PS4 and do not like X-Box? 2. What percent of people surveyed like the X-Box, but not the PS4? 3. What is the conditional relative frequency of people surveyed who like PS4, given that they like X-Box? Like PS4 Like X-Box Yes No Total Yes No 8 32 Total Based on the table below, what is the joint relative frequency of the people surveyed who do not have a job and have a savings account? Have a job Have a savings account Yes No Yes No The table below shows the results of a survey of students favorite subjects. What is the relative frequency that a student s favorite subject is not English? Subject Science English Math Total The fuel economy in miles per gallon of several vehicles is given below. Use this data to make a box plot. In exercises 7 12, use the box and whisker plot to find the given measure. Data Set A miles per gallon Least value 8. Median 9. Greatest value 10. Third quartile 11. Range 12. First quartile

2 Make a box and whisker plot for each set of data. 13. Hours of exercise per week: 0, 7, 2, 5, 12, 2, 0, Number of cars in a parking lot: 12, 35, 20, 17, 24, 30, 28, The environmental club is selling water bottles for $8 and tote bags for $12 to raise $240 to donate to charity. Complete the table and write the linear equation for the fundraising goal. Water Bottles 0 15 Tote Bags A repair bill for your car is $553. The parts cost $265. The labor cost is $48 per hour. Write and solve an equation to find the number of hours of labor spent repairing the car. Solve each equation (6x 4) 5(2x 8) ( d 12) (2d 6) (2c + 7) -3c = 7(c + 5) 18. 3b+12 +b = b 20. 3(-5y+2) = k 9 7

3 Solve the inequality. Graph the solution < m k (3-3k) > z > 6 + 3z y > 8 or 2y 6 > n + 3 < 6n + 8 2n < c + 2 < 3 Write an equation for the n th term of the arithmetic sequence. Then fine a , -1, 1, , -3, -8, , 14, 25, , 11, 7, 3 Determine if the sequence is arithmetic. If so: a. find the common difference b. write the next three terms c. write the explicit rule d. graph 33. 1, 5, 9, , -7, , -2, 3, What is the common difference of the sequence represented in the table? 37. Write an explicit rule for the sequence. 38. Find the elevation of the diver after 15 minutes. Time in minutes, m Elevation of a scuba diver in feet, f(n)

4 Find the rate of change for of each line For each line below, determine whether the slope is: positive, negative, zero, or undefined (circle one). 45. positive, negative, 46. positive, negative, 47. positive, negative, zero, or undefined zero, or undefined? zero, or undefined? Write a rule for each table using algebraic notation X Y X Y

5 50. The graph below shows the relationship between the number of tortilla chips and total number of calories of the chips. Find and interpret the slope. Write an equation of the line in slope-intercept form. 51. Find the x- and y-intercepts of each equation. 52. y = 3x y = 5x x = 4y x 6y = 24 Graph the linear function y x y x y x 4 2 2

6 57. y 2x y x 3 Find the linear function graphed on the coordinate grid, state the value of m and the value of b. 68. f(x): m =, b = 69. g(x): m =, b = 70. h(x): m =, b = 71. A school sell T-shirts to promote school spirit. The school s profit is given by the function P9x) = 8x 150, where x is the number of T-shirts sold. During the play-offs, the school increases the price of the T-shirts. The school s profit during the play-offs is given by the function Q(x) = 16x 200, where x is the number of T-shirts sold. Describe the transformation from the graph of P to the graph of Q. Write an equation in point-slope form of the line with the given information. 72. slope = 3/7; y-intercept = Slope = -1/2 passes through ( -6, 10) 73. passes through (4, 7) (-1, 17) 76. (3, 4); 1 m (2, -6); m 77. (-2, 3); m = 4 4

7 Write the point-slope form of the equation with the given characteristics. 78. slope = 3; y-intercept = Slope = -3; passes through (-4, 7) Write an equation of the line that passes through the given point and is parallel to the given line. 80. (1, 2); y = 5x (18, 2); 3y x = y = 7 x 5 ; passes through (0, 7) 83. y = -5x 3; passes through (7, -11) 9 Write an equation of the line that passes through the given point and is perpendicular to the given line. 84. ( 3, 3); 2y = 8x (8, 1); 2y + 4x = y = -3x 7; passes through (6, 7) 87. y = ½x 4; passes through (3, -4) 88. You are planning a school carnival. The equipment costs $180 to rent. You plan to charge $4.00 per ticket. You would to have profit of at least $500. Write and solve an inequality that represents the number of tickets t that you need to sell. 89. You want to purchase a calculator for at most $115. You have saved $30 so far. You earn $7.50 per hours at your job. Write and solve an inequality that represents the number of hours h that you need to work.

8 A bowling alley charges $4.00 per game and will rent a pair of shoes for $2.50 for any number of games. The bowling alley has an earnings goal of $500 for the day. 90. Write a linear equation that describes the problem. 91. Graph the linear equation. 92. If the bowling alley rents 40 pairs of shoes, approximately how many games will need to be played to reach its goal? 93. An account charges an initial fee of $100 plus a rate of $40 per hour. The function shows the total fees charged is f(x) = 40x How would you graph the function change if the accountant raised his rate to $45 per hour? A baker sells bread for $3 a loaf and rolls for $1 each. The baker needs to sell $24 worth of baked goods by the end of the day. 94. Write a linear equation that describes the problem. 95. Graph the linear equation. Make sure to label both axes with appropriate titles. 96. Use the graph to approximate how many loaves of bread the baker must sell if 12 rolls are sold. The function y = 3.5x represents the cost y (in dollars) of a taxi ride of x miles. 97. Identify the independent and dependent variables. 98. You have enough money to travel at most 20 miles in the taxi. Find the domain and range of the function.

9 Opal walked from school to home, which was a distance of 12 miles. She walked at a rate of 4 miles per hour. The graph represents the remaining distance Opal had to walk. 99. Find the slope of the line Find the x-intercept, and explain what it represents in the context Find and interpret the y-intercept Write an equation for the line in slope-intercept form The table below represents the amount of money (in dollars) a Booster Club made washing cars for a fundraiser. Use this information to find the rate of change in dollars per car. Draw a graph to represent each situation. Classify each as either discrete or continuous Two children are selling lemonade. They are charging $2 for a cup. They only sell 12 cups You decide to hike up a mountain. You climb steadily for 4 hours, then take a 30 minute break for lunch. Then you continue to climb, slower than before. When you make it to the summit, you enjoy the view for an hour. Finally, you decide to climb down the mountain Alma earns $15 an hour. How much does she earn in 4 hours? Independent Variable: Solution: Dependent Variable: Function:

10 The data in the table shows the amount of taxes to be paid by married couples filing a joint tax return for the given taxable income amounts. (Source 2006 IRS Tax Table, y = ax + b a = b = Taxable Income (thousand dollars) x Tax Paid (dollars) y Looking at the regression equation what is the practical meaning of the slope? 108. Use the regression equation and explain the meaning of the y-intercept Use the linear regression model to predict the amount of tax paid by a married couple with an income of $52,000. (Explain your answers and show all work) Use the table to answer the following questions f(4) = 111. g(5) = 112. f(1) = 113. Write the rules for f(x) and g(x) If f(x) = 10, find x. Hours f(x) g(x) If g(x) = -4, find x For the function {(-1, 2), (3, 3), (1, 5), (0, 2)} write the domain and range of the function. Domain: Range:

11 117. Create a mapping diagram for the ordered pairs 2, 4, 0, 1, 2, 5. Is the relation above a function? Determine whether each of the following is a function (1, 2), (2, 1), (3, 6), (4, 13), (5, 22) (7, 4), (5, 1), (3, 8), (1, 5), (3, 6) For each problem, circle the relation that represents a function

12 Write the domain and range of each relation below. Determine if the relation is a function Domain: < x < Domain: < x < Domain: < x < Range: < y < Range: < y < Range: < y < Function: Yes/No Function: Yes/No Function: Yes/No Find the value of x so that the function has the given value h(x) = 7x; h(x) = m(x) = 4x + 15; m(x) = t(x) = 3x; t(x) = k(x) = 6x 12; k(x) = 18 Let c(t) be the number of customers in a restaurant t hours after 8 A.M. Explain the meaning of each statement c(0) = c(3) = c(8) 140. c(n) = c(13) < c(12)

13 Write a linear function f with the given values f(0) = 7, f(3) = f(0) = 4 and f(1) = f(4) = -3, f(0) = -2 Evaluate the function when x = -1 and x = g(x) = 3x b(x) = -2x h ( x) x The graph represents Joe s distance from home over time on his walk. What is happening at the part of the graph labeled A? A. Joe is stopped. B. Joe is walking away from home. C. Joe is walking towards home. D. Joe is slowing down

14 Match each graph below with the description that best matches it A. Mr. Wilson asked his class to sketch a graph that would represent the following activity: Start 3 meters away from me and slowly walk away for 8 seconds. Then stand still for 3 seconds and then walk quickly toward me for 4 seconds. B. Mr. Wilson asked his class to sketch a graph that would represent the following activity: Start 4 meters away from me and slowly walk toward me for 8 seconds. Then stand still for 3 seconds and then walk quickly away from me for 4 seconds. C. Mr. Wilson asked his class to sketch a graph that would represent the following activity: Start 3 meters away from me and quickly walk away for 3 seconds. Then stand still for 8 seconds and then walk quickly toward me for 3 seconds. D. Ashley walked up a hill at a steady speed and then increased her speed as she walked down the hill E. John was driving in heavy traffic. As he took off from a stoplight, he was able to increase his speed until he came to another stoplight where he had to brake and decrease his speed quickly. He came to a stop and when the light turned green, he increased his speed again. F. John took off from a stop light and increased his speed until he reached the speed limit. He kept his speed right at the speed limit until he passed a sign saying the speed limit had increased so he sped up again.