If \(a = 3c − 4\) and \(b = 2(3 − c)\) what is \(3b\) expressed in terms of \(a\)?

A polynomial function \(f\) has real coefficients and degree 4. Three of its zeros are \(−4, 4\), and \(2i\), where \(i\) is the imaginary unit. Which graph could represent \(y = f(x)?\)

Given that \(2 \le a \le 5, 3 \le b \le 6\), and \(4 \le c \le 8\), what is the greatest possible value of \(\left(\dfrac{a}{b}\right)\left(\dfrac{c}{2}\right)\)?

The table gives values of \(f(x), g(x)\), and \(h(x)\) for all positive integers \(x \le 6\).

If \(h(g(f(a))) = 2\), where \(a\) is a positive integer no greater than \(6\), what is the value of \(a\)?

For nonzero complex numbers \(z\) and \(w\), the quotient \(\dfrac{z}{w}\) is an irrational real number. Which of the following statements cannot be true?

The probability distribution for the discrete random variable \(Y\) is given in the table below. What is the expected value of \(Y\)?

A cyclist’s speed increased over an 8-second interval. Her initial speed was 5 meters per second, and her speed 8 seconds later was 17 meters per second. Which of the following was the average rate of change of the cyclist’s speed over this 8-second interval?

A meteorologist is predicting the weekend weather. Let Event \(A\) be that it rains on Saturday, and let Event \(B\) be that it rains on Sunday. The meteorologist determines that the probability of Event \(A\) is \(P(A) = 0.7\), and the probability of Event \(B\) is \(P(B) = 0.6\). Which of the following represents the range of all possible values for the probability that it rains on both days, \(P(A \ \text{and} \ B)?\)

A right circular cone is formed by taking a circular paper sector with a radius of 12 inches and a central angle of 270 degrees, and joining its two straight edges together without any overlap. What is the height, in inches, of the resulting cone?

A circle in the standard \((x,y)\) coordinate plane has its center at the point \((3, −2)\) and passes through the point \((6, 2)\). What is the y-intercept of the line that is tangent to the circle at the point \((6, 2)\)?