Math

The graph represents the total charge, in dollars, by an electrician for x hours of work. The electrician charges a onetime fee plus an hourly rate. What is the best interpretation of the slope of the graph?

A. The electrician’s hourly rate

B. The electrician’s onetime fee

C. The maximum amount that the electrician charges

D. The total amount that the electrician charges

From a population of 50,000 people, 1,000 were chosen at random and surveyed about a proposed piece of legislation. Based on the survey, it is estimated that 35% of people in the population support the legislation, with an associated margin of error of 3%. Based on these results, which of the following is a plausible value for the total number of people in the population who support the proposed legislation?

A. 350

B. 650

C. 16,750

D. 31,750

The circle shown has center O, circumference 144π, and diameters PR¯ and QS¯. The length of arc PS is twice the length of arc PQ. What is the length of arc QR?

A. 24π

B. 48π

C. 72π

D. 96π

A rectangle has a length of x units and a width of x-15 units. If the rectangle has an area of 76 square units, what is the value of x?

A. 4

B. 19

C. 23

D. 76

A cylinder has a diameter of 8 inches and a height of 12 inches. What is the volume, in cubic inches, of the cylinder?

A. 16π

B. 96π

C. 192π

D. 768π

In triangle JKL, cos(K) = 2451 and angle J is a right angle. What is the value of cos(L)?

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In the xy-plane, a line with equation 2y = c for some constant c intersects a parabola at exactly one point. If the parabola has equation y = -2x² + 9x, what is the value of c?

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If 5x + 4 = 4x + 4 + 29, what is the value of x + 4?

A. -4

B. 25

C. 29

D. 33

A neighborhood consists of a 2-hectare park and a 35-hectare residential area. The total number of trees in the neighborhood is 3,934. The equation 2x + 35y = 3,934 represents this situation. Which of the following is the best interpretation of x in this context?

A. The average number of trees per hectare in the park

B. The average number of trees per hectare in the residential area

C. The total number of trees in the park

D. The total number of trees in the residential area

For a certain rectangular region, the ratio of its length to its width is 35 to 10. If the width of the rectangular region increases by 7 units, how must the length change to maintain this ratio?

A. It must decrease by 24.5 units.

B. It must increase by 24.5 units.

C. It must decrease by 7 units.

D. It must increase by 7 units.

For the function f, for each increase in the value of x by c, where c is a positive constant, the value of f(x) increases by a factor of 27. Which of the following equivalent forms of the function f displays 1/c as a coefficient of x?

A. f(x) = 48(3)^(1/2)x

B. f(x) = 48(3³)^(1/6)x

C. f(x) = 48(9)^(1/4)x

D. f(x) = 48(27^(1/3)x)^1/2

Circle A in the xy-plane has the equation (x+5)² + (y-5)² = 4. Circle B has the same center as circle A. The radius of circle B is two times the radius of circle A. The equation defining circle B in the xy-plane is (x+5)² + (y-5)² = k, where k is a constant. What is the value of k?

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A business owner plans to purchase the same model of chair for each of the 81 employees. The total budget to spend on these chairs is $14,000, which includes a 7% sales tax. Which of the following is closest to the maximum possible price per chair, before sales tax, the business owner could pay based on this budget?

A. $148.15

B. $161.53

C. $172.84

D. $184.94

8x + y = -11

2x² = y + 341

The graphs of the equations in the given system of equations intersect at the point (x, y) in the xy-plane. What is a possible value of x?

A. -15

B. -11

C. 2

D. 8

The graph of y = f(x) + 14 is shown. Which equation defines function f?

A. f(x) = -14x - 12

B. f(x) = -14x + 16

C. f(x) = -14x + 2

D. f(x) = -14x - 14

4x - 6y = 10y + 2

ty = ½ + 2x

In the given system of equations, t is a constant. If the system has no solution, what is the value of t?

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For the linear function f, the table shows three values of x and their corresponding values of f(x). Function f is defined by f(x) = ax + b, where a and b are constants. What is the value of a - b?

A. -64

B. 62

C. 128

D. 192