MATH 30 C1 - Fall 2017 EXAM 1 Student Name: ____ Student ID#: _______________ This is a take-home, open-book open-notes exam. You are required to work aloneno assistance from any other person. You may not get help from the math tutors. Each question counts one point. There will be no partial credit. CHOOSE THE ONE BEST ANSWER. DUE DATE: The exam is due at 11:55 PM, Pacific Time, on Saturday, September 30, 2017. A GRADE PENALTY OF 10% WILL BE ASSESSED FOR EVERY DAY OR PORTION OF A DAY THAT THE EXAM IS LATE. RETURN EXAM TO ME THROUGH DROPBOX. Since it is multiple-choice, only the answers need to be submitted. Use the answer sheet below to answer your question and send only page 1 (make sure all fifteen answers are there) through the Dropbox. Answer sheet Question # 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. Total Points MATH 30 C1 - Fall 2017 INSTRUCTOR: Piradee Nganrungruang MIDTERM EXAM #1 Answer E D C A B E A B D A C E D B A 1 Questions 1. x2/3 + 3x1/3 and y = 10What are the values of X? (A) -2, 5 (B) -5, 2 (C) -125, 8 (D) -8, 125 (E) None of the above 2. When a number is decreased by 20% of itself, the result is 144. What is the number? (A) 11 (B) 36 (C) 72 (D) 180 (E) 900 3. A car rental agency charges $175 per week plus $0.20 per mile to rent a car. How many miles can you travel in one week for $295? (A) 234 miles (B) 575 miles (C) 600 miles (D) 1295 miles (E) 1755 miles 4. The length of a rectangular room is 6 feet longer than twice the width. If the room's perimeter is 156 feet, what are the room's dimensions? (A) Width = 24 ft; length = 54 ft MATH 30 C1 - Fall 2017 INSTRUCTOR: Piradee Nganrungruang MIDTERM EXAM #1 2 (B) Width = 29 ft; length = 64 ft (C) Width = 36 ft; length = 42 ft (D) Width = 48 ft; length = 108 ft (E) Width = 52 ft; length = 48 ft 5. Find the result of ( 6 25)( 6+ 25) (A) -19 (B) 6-25i (C) 6 + 5i (D) 31 (E) None of the above 6. Fine the answer for | 2(x+1) + 4 | =10 (A) {-6, 0} (B) {-6, 4} (C) {-6, 8} (D) {-8, 0} (E) {-8, 2} 7. A landscaping company sells 40-pound bags of top soil. The actual weight x of a bag, however, may differ from the advertised weight by as much as 0.75 pound. Write an inequality involving absolute value that expresses the relationship between the actual weight x of a bag and 40 pounds. Solve the inequality, and express the answer in interval form. (A) |40 - x| 0.75; [39.25, 40.75] (B) |40 + x| 0.75; [39.25, 40.75] MATH 30 C1 - Fall 2017 INSTRUCTOR: Piradee Nganrungruang MIDTERM EXAM #1 3 (C) |x + 0.75| 40; [39.25, ) (D) |x|- 40 0.75 ; (-, 40.75] (E) None of the above 8. Write an equation that passes through (1, -6) with x-intercept = -1. (A) y + 6 = - 3(x - 1) or y = - 3(x - 1) (B) y + 6 = - 3(x - 1) or y = - 3(x + 1) (C) y - 6 = - 3(x + 1) or y = - 3(x + 1) (D) y - 6 = - 3(x - 1) or y = - 3(x - 1) (E) y - 1 = - 3x or y - 6 = - 3(x + 1) 9. Suppose a life insurance policy costs $20 for the first unit of coverage and then $5 for each additional unit of coverage. Let C(x) be the cost of insurance of x units of coverage. What will 10 units of coverage cost? (A) $ 30 (B) $45 (C) $55 (D) $65 (E) $75 10. An investment is worth $2282 in 2006. By 2010 it has grown to $2986. Let y be the value of the investment in year x, where x =0 represents 2006. Write a linear equation that models the value of the investment in the year x. (A) y=176 x +2282 (B) y=176 x+ 2282 (C) y=176 x +2986 MATH 30 C1 - Fall 2017 INSTRUCTOR: Piradee Nganrungruang MIDTERM EXAM #1 4 (D) y=176 x+ 2986 (E) y=176 x +3690 11. What is the equation for the line that passes through (4, 3) and perpendicular to the line whose equation is y = 8x + 7. (A) y4= 1 (x - 3) 8 (B) y4= 1 (x + 3) 8 (C) y3= (D) y 3= (E) 1 (x - 4) 8 1 (x + 4) 8 y3=8(x4) 12. The linear function f(x) = -9.8x + 24 models the percentage of people, f(x), who eats at fast food restaurants each week x years after 2009. What is the slope and what does it mean? (A) m = 9.8; the percentage of people eating at fast food restaurants each week has decreased at a rate of 9.8% per year after 2009. (B) m = -9.8; the percentage of people eating at fast food restaurants each week has increased at a rate of -9.8% per year after 2009. (C) m = 24; the percentage of people eating at fast food restaurants each week has increased at a rate of 24% per year after 2009. (D) m = 24; the percentage of people eating at fast food restaurants each week has decreased at a rate of 24% per year after 2009. (E) m = -9.8; the percentage of people eating at fast food restaurants each week has decreased at a rate of -9.8% per year after 2009. 13. The function f(t) = 0.12t 2+ 0.53 t+30.8 models the U.S population in millions, ages 65 and older, where t represents year after 1990. The function g(t) = 0.55 t 2 +11.89 t +105.3 models the total yearly cost of Medicare in billions of dollars, MATH 30 C1 - Fall 2017 INSTRUCTOR: Piradee Nganrungruang MIDTERM EXAM #1 5 where t represents years after 1990. What does the function g f represents. Find g (15) f (A) Cost per person in thousands of dollars. $0.16 thousand (B) Cost per person in thousands of dollars. $0.03 thousand (C) Cost per person in thousands of dollars. $8.64 thousand (D) Cost per person in thousands of dollars. $34.67 thousand (E) Cost per person in thousands of dollars. $30.8 thousand 14. Find the inverse function of f(x) = 1 ( x )=3 x5 (A) f (B) f (C) f 1 ( x )= x+5 (D) f 1 ( x )=3 x+125 (E) f 1 1 x5 ( x )=3 x+5 ( x )=3 x125 15. Find the center and the radius of the circle y+ 3 ( x4)2+ (A) (4, -3), r = 8 (B) (-3, 4), r = 8 (C) (-4, 3), r = 64 (D) (-3, -4), r = 64 (E) (-4, -3), r = 64 MATH 30 C1 - Fall 2017 INSTRUCTOR: Piradee Nganrungruang MIDTERM EXAM #1 6 MATH 30 C1 - Fall 2017 INSTRUCTOR: Piradee Nganrungruang MIDTERM EXAM #1 7