Reference no: EM133104507

MATH-302 Math Methods - Expressions, Equations, & Functions Retake

Question 1: Solve this equation for x:

6x (2/3x - 0.4) + 5 = x² - 2x(1.2 - 1.5x) - 13

Which statement regarding this equation is true?

a. x = 5
b. x = -13
c. This equation is always true for any value of x
d. This equation is never true for any value of x

Question 2: Consider this expression:

2C[3a + 2b - 4(a + bc)]

Which of the following is NOT equivalent to this expression?

a. -2ac + 4bc - 8bc²
b. 2ac + 4bc + 8bc²
c. -2c[a - 2b(1 - 2c)]
d. 2c(-a + 2b) - 8bc²

Question 3: Alicia wrote the following problem on a recent quiz:

Sven wants to treat his entire family to a movie. Parking at the theater costs $6, and tickets for one show cost x. Including Sven, there are 8 people in his family, which requires the use of two cars.

a. Suppose Sven wants to treat his family to a double feature. Write an expression that reflects the total amount Sven will spend taking his family to the movies if they want to see two movies.

b. Suppose tickets cost $11.50. Sven has $275 to spend. At most, how much can each member of Sven's family, including Sven, spend on popcorn and sodas?

Which of the following student responses is correct?

a.

a. 16x + 12
b. Let y = amount available for popcorn and soda

16(11.50) + 12 + y ≤ 275

b.

a. 2(8x +6)
b. Let y = amount available for soda and popcorn
196 + 8y ≤ 275

c.

a. 16x + 6
b. Let y = amount available for soda and popcorn

190 + 8y ≤ 275

d.

a. 8(2x + 6)
b. Let y = amount available for soda and popcorn

8(29) + y ≤ 275

Question 4: Solve the following equation for x:

2.5x - 4(3 - 1.2x) = 1/2 (3x - 7) -8.5

Question 5: There are approximately 3.2 × 10⁸ cubic miles of water in the Earth's oceans. One cubic mile is equivalent to 1.1 × 10¹² gallons of water.

The Atlantic Ocean contains 8.1 × 10¹⁹ gallons of water.

Approximately what percent of the Earth's total ocean water is in the Atlantic Ocean?

a. 2.3%
b. 4.3%
c. 23.0%
d. 39.5%

Question 6: In fulfillment of your New Year's resolution, you decide to join a local fitness club. Club A charges a $75 one-time membership fee in addition to a monthly charge of $25. Club B charges a $15 one- time membership fee in addition to a monthly charge of $35. Not wanting to pay the steep membership fee, you decide to join Club B.

After how many months of paying for Club B does your membership start becoming less cost- effective than if you had joined Club A?

a. 5
b. 6
c. 7
d. 10

Question 7: Fast Cab Company charges customers $2.25 for every mile traveled, plus a $2 pickup fee. The table below shows costs based on number of miles traveled for Reliable Cab Company. Reliable Cab Company also charges a constant rate per mile traveled and a standard drop fee:

Based on this information, which of the following statements is true?

a. Reliable Cab Company charges a lower pickup fee than Fast Cab Company
b. Fast Cab Company charges less per mile traveled than Reliable Cab Company
c. If you need to travel 10 miles, you will spend more money using Reliable Cab Company
d. If you need to travel 5 miles, you will spend less money using Fast Cab Company

Question 8: Darius is a popular independent hair stylist. He leases a space in a local salon. In order to use the salon's space, he has to pay the salon $300 per month, plus 15% of all of his total earnings in the salon that month. During his first month at the salon, his total earnings in the salon were x. This month, he wants his earnings to be $150 more than twice what he earned last month.

Assuming Darius meets his goal, which of the following describes the amount that Darius will have to pay the salon this month as a function of his total earnings during his first month?

a. s(x) = 300 + 0.15x
b. s(x) = 300 + (2x + 150)
c. s(x) = 322.5 + 0.3x
d. s(x) = 322.5 + 0.15(2x + 150)

Question 9: Which of the following does NOT represent y as a linear function of x?

a. y - 5x = 3(x-2)/1.25

b. The area of a square, y ,in terms of the length of one of its sides, x
c. The perimeter of a square, y, in terms of the length of one of its sides, x
d.

Question 10: Consider the graph below:

Which of the following scenarios could be represented by this graph?

a. If miles per hour is represented on the vertical axis and time is represented on the horizontal axis, then this graph represents a race car that accelerates and decelerates as it goes around a track
b. If distance traveled is represented on the vertical axis and time is represented on the horizontal axis, then this graph represents a race car that accelerates and decelerates as it goes around a track
c. If distance traveled is represented on the vertical axis, and time is represented on the horizontal axis, then this graph represents a race car traveling at a constant speed around a circular track
d. If miles per hour is represented on the vertical axis, and time is represented on the horizontal axis, then this graph represents a race car traveling at a constant speed around a circular track