Unit Test — Cumulative exam Answers

Consider the graphs of j(x) = and k(x) = .Which feature of the graph of k(x) is different from the graph of j(x)?

What is rewritten using the power property?

Suppose f(x) = 2(x + 1)2 and f(g(x)) = 2(2x + 4)2. What is g(x)?

What is one possible solution for the triangle below?

A consumer agency wants to determine which of two laundry detergents, A or B, cleans clothes better. Fifty pieces of fabric are subjected to the same kinds of stains (grass, mud, coffee). Then 25 pieces are randomly assigned to be cleaned with detergent A and the remaining 25 pieces are cleaned with detergent B. After being laundered, the pieces of fabric are rated on a scale from 1–10, with 1 being the least clean to 10 being the most clean. The difference in mean ratings (A – B) was determined to be 1.5. Assuming there is no difference in the two detergents, 200 simulated differences in sample mean ratings are displayed in the dotplot.Using the dotplot and the difference in mean ratings from the samples, is there convincing evidence that the one detergent is better than the other?

Review the diagram of the unit circle.

An initial investment of $200 is now valued at $350. The annual interest rate is 8% compounded continuously. The equation represents the situation, where t is the number of years the money has been invested. About how long has the money been invested? Use a calculator and round your answer to the nearest whole number.

A farmer sows 100 seeds of a new type of corn and wants to quickly determine the yield, or total number of ears of corn, for the crop when it has matured. He decides to take a simple random sample of the crop by using a random digit table. What is the fewest number of digits that should be used, given that there are 100 plants in total?

Jamal draws triangle XYZ. If what is the approximate length of XY?

Many movie theaters show advertisements before feature films to increase concession sales. However, many customers complain about the length the advertisements add to their time at the theater. To understand the effect of advertising, a movie theater manager chooses random days during the month when the concession advertisements are not shown. On the remaining days, the concession advertisements are shown as usual. The manager then records the concession sales for each day.

What is the range of the function graphed below?

The vertices of a triangle are given in the columns of the matrix . If is found to perform a transformation, what are the coordinates of the transformed triangle?

Two different cars each depreciate to 60% of their respective original values. The first car depreciates at an annual rate of 10%. The second car depreciates at an annual rate of 15%. What is the approximate difference in the ages of the two cars?

A manager needs to order company shirts for each employee. She was quoted the following rates. If she orders 75 shirts and passes the cost along to the employees, what would each employee owe for the shirt if each pays the same amount? Round to the nearest cent. Price Quote for Company Work ShirtsNumber of shirts orderedCost per shirtFirst 19 shirts$10Next 30 shirts$8Each shirt over 49$5

Let u = ⟨1, 5⟩, v = ⟨–3, 3⟩, and w = ⟨2, 3⟩. What is the direction angle of 4w – (2u + v)?

Jake and Maddie each take the closest path from their homes to the store. Based on the picture below, what is the approximate difference in the distance each person traveled to the store?

An urban planner examines police-report data for many cities and towns and discovers that cities with professional football teams tend to have higher numbers of reported small crimes, such as burglary.

An observational study of suburban towns reveals that towns with more dedicated park land tend to have higher median home prices. A real estate agent suggests that a town’s crime rate is a more accurate predictor of median home price.

Suppose . Which value(s) of a would make the composite functions commutative?

For two complex numbers z and w, which diagram shows the geometric representation of zw?