The best way to approach this question is through POE. Choice (A) states that the majority of students polled logged in more times than they posted. The values along the x-axis of the graph are, for most of the data points, higher than the values along the y-axis of the graph, and thus (A) is true according to the data provided. This same data contradicts (B) and (C). You can eliminate (D) because the data does, in fact, allow you to draw a conclusion about the relationship between the variables.

Don’t get too thrown off by the graph. All you need to know to solve this question is that perpendicular lines have slopes that are the negative reciprocals of each other. Since the standard equation for a line is y = mx + b, the slope of the f(x) line is 3. The slope of the h(x) line must therefore be ​\( -\frac{1}{3} \)​. The only answer choice that matches is (B).

The best way to deal with this question is to Plug in the Answers (PITA), starting with (A). If x = 6, then y = ​\( 3^6 \)​ = 729. This is less than 4,000, so eliminate (A) and move to the next answer choice. If x = 7, then y = ​\( 3^7 \)​ = 2,187. This is still less than 4,000, so eliminate (B). If x = 8, then y = ​\( 3^8 \)​ = 6,561. This is greater than 4,000, so (C) must be the correct answer.

The first step here is to simplify the equation and solve for a. Start by multiplying both sides by 16 to get 16a = 4a². Divide both sides by 4 to get 4a = a². Divide both sides by a to get 4 = a. This is now your target answer. Plug a = 4 into the values of a in the answer choices to determine which one matches 4. Choice (D) is the answer, since ​\( 2\sqrt[]{a} \)​ = ​\( 2\sqrt[]{4} \)​ = 2(2) = 4.

Since work = rate × time, the 280 in the equation must represent the total number of meals (i.e. the “work”). All three chefs are working together, so they work for the same amount of time, and x must represent that time. The coefficients 8, 4, and 2 must therefore represent the chefs’ respective rates, or how many meals each prepares in a set amount of time. Since 8 is the greatest of these three coefficients, 8x must be the meal output of the fastest chef, either (B) or (C). Now you need to solve the equation: 8x + 4x + 2x = 280. Combining like terms gives you 14x = 280. Divide both sides by 14 to determine that x = 20. This number represents the amount of time that the chefs worked, so the actual number of meals prepared by the fastest chef would be 8 × 20 = 160 meals, which is (B).