For the function f, if f(3x) = x - 6 for all values of x, what is the value of f(6) ?

The given diagram represents Edward T. Hall's concept of space surrounding a person defined by 4 nonoverlapping regions. Intimate space is the region inside a circle of radius 1 foot. Personal space is the region within a circle of redius 4 feet but outside Intimate space. Social space is the region within a circle of radius 12 feet but outside personal space. Public space is the region within a circle of radius 25 feet but outside social space. What is the area, in square feet, of the shaded region representing a person's social space?

A manufacturer determined that right cylindrical containers with a height that is 4 inches longer than the radius offer the optimal number of containers to be displayed on a shelf. Which of the following expresses the volume, V, in cubic inches, of such containers, where r is the radius, in inches?

The manager of an online news service received the report above on the number of subscriptions sold by the service. The manager estimated that the percent increase from 2012 to 2013 would be double the percent increase from 2013 to 2014. How many subscriptions did the manager expect would be sold in 2014?

In the xy plane, line l has a slope of 2. If line k is perpendicular to line l, which of the following could be an equation of line k?

A psychologist designed and conducted a study to determine whether playing a certain educational game increases middle school students' accuracy in adding fractions. For the study, the psychologist chose a random sample of 35 students from all of the students at one of the middle schools in a large city. The psychologist found that students who played the game showed significant improvement in accuracy when adding fractions. What is the largest group to which the results of the study can be generalized?

A circle in the xy‑plane has equation (x + 3)²  +  (y – 1)² =  25. Which of the following
points does NOT lie in the interior of the circle?

g(t) = -0.34 (t - 5.51)² + 8.26
The function g above models the growth rate of a certain plant, in millimeters per day (mm/day), in terms of the watering time t, in minutes per day (min/day). What is the meaning of (5.51,g(5.51)) in this context?

In the given equation, k is a constant. If the equation has exactly one solution, which of the following could NOT be the value of k ?

In the xy‑plane above, a point (not shown) with coordinates (s, t) lies on the graph of the linear function f. If s and t are positive integers, what is the ratio of t to s ?

From 2005 through 2014 , the number music CDs sold in the United States declined each year by approximately 15% of the number sold the preceding year. In 2005 , approximately 600 million CDs were sold in the United States. Of the following, which best models C, the number of millions of CDs sold in the United States, t years after 2005 ?

The graph of the equation ax + ky = 6 is a line in the xy-plane, where a and k are constants. If the line contains the points (-2 , -6) and (0 , -3), what is the value of k ?

The world’s population has grown at an average rate of 1.9 percent per year since 1945. There were approximately 4 billion people in the world in 1975. Which of the following functions represents the world’s population P, in billions of people, t years since 1975 ? (1 billion = 1,000,000,000)

We know the world's population one year after 1975 can be written as food into 1.01, nine to twelve years after 1975 can be written as '4' into 1.0 192, and so on. Similarly, suppose we continue to calculate three years after 1975. In that case, the world population will be 4.1.0 1923, and finally, we can conclude that the world population two years after 1975, as determined by the function P of t, will be equal to 4 into 1.0 19 t, and we can see that option one is the correct answer.

f(x) = -500x² + 25,000x
The revenue f(x), in dollars, that a company receives from sales of a product is given by the function f above, where x is the unit price, in dollars, of the product. The graph of y = f(x) in the xy-plane intersects the x-axis at 0 and a. What does a represent?

Refer to the following information.
If the 180 food calories in a granola bar come entirely from p grams of protein, f grams of fat, and c grams of carbohydrate, which of the following expresses f in terms of p and c ?
Energy per Gram of Typical Macronutrients

The table above gives the typical amounts of energy per gram, expressed in both food calories and kilojoules, of the three macronutrients in food

The graph of a line in the xy-plane has a positive slope and intersects the y-axis at a point that has a negative y-coordinate. Which of the following could be an equation of the line?