Math

The scatterplot shows the relationship between two variables, x and y. An equation for the exponential model shown can be written as y = a(b)^x, where a and b are positive constants. Which of the following is closest to the value of b?

A. 0.83

B. 1.83

C. 18.36

D. 126.35

The number of zebras in a population in 2018 was 1.27 times the number of zebras in this population in 2014. If the number of zebras in this population in 2014 is p% of the number of zebras in this population in 2018, what is the value of p, to the nearest whole number?

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f(x) = x² - 48x + 2304

What is the minimum value of the given function?

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The function g is defined by g(x) = x(x - 2)(x + 6)². The value of g(7 - w) is 0, where w is a constant. What is the sum of all possible values of w?

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A grove has 6 rows of birch trees and 5 rows of maple trees. Each row of birch trees has 8 trees 20 feet or taller and 6 trees shorter than 20 feet. Each row of maple trees has 9 trees 20 feet or taller and 7 trees shorter than 20 feet. A tree from one of these rows will be selected at random. What is the probability of selecting a maple tree, given that the tree is 20 feet or taller?

A. 9164

B. 310

C. 1531

D. 917

A rectangle is inscribed in a circle, such that each vertex of the rectangle lies on the circumference of the circle. The diagonal of the rectangle is twice the length of the shortest side of the rectangle. The area of the rectangle is 1,089√3 square units. What is the length, in units, of the diameter of the circle?

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The positive number a is 2,241% of the sum of the positive numbers b and c, and b is 83% of c. What percent of b is a?

A. 23.24%

B. 49.41%

C. 2,324%

D. 4,941%

7/8 y - 5/8 x = 4/7 - 7/8 y

5/4 + 7/4 = py + 15/4

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

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A circle has center G, and points M and N lie on the circle. Line segments MH and NH are tangent to the circle at points M and N, respectively. If the radius of the circle is 168 millimeters and the perimeter of quadrilateral GMHN is 3,856 millimeters, what is the distance, in millimeters, between points G and H?

A. 168

B. 1,752

C. 1,760

D. 1,768

The function f is defined by f(x) = ax² + bx + c, where a, b, and c are constants. The graph of y = f(x) in the xy-plane passes through the points (7, 0) and (-3, 0). If a is an integer greater than 1, which of the following could be the value of a + b?

A. -6

B. -3

C. 4

D. 5