Cumulative Exam — Cumulative exam Answers

An experiment is proposed to measure the effectiveness of a brand of sunscreen. Adult volunteers are randomly assigned to one of two brands of sunscreen and asked to enjoy a normal day at the beach. Each volunteer is asked to report back to the administrators after two hours, at which time both arms are assessed for sun exposure.

Functions f(x) and g(x) are composed to form . If , what is the value of a?

Given the vector and the transformation matrix , which vector is the image after applying the transformation to ?

If the function y = sin(x) is transformed to y = sin(2x), how does the graph change?

A botanist wants to determine if a fertilizer is effective in the growth of plants. He randomly selects 100 of the same type of seedling and randomly assigns them to two groups: one that uses the fertilizer, and one that does not. He makes sure the plants all have the same amount of water, soil, and light for two months. At the end of two months, he measures the heights of the plants and finds that the ones receiving the fertilizer are significantly taller.

What is the solution to

Manufacturers of tires report that car tires should be able to last an average of 50,000 miles. A new tire company produces a different type of tread and tests 100 randomly selected tires. This sample of 100 tires lasted an average of 51,500 miles. Assuming the new type of tread does not improve the mileage of the tire, 200 sample means were simulated and displayed on the dotplot.Using the dotplot and the sample mean mileage, is there convincing evidence that the new type of tread improves the mileage of the tire?

The graph of a logarithmic function is shown below.What is the domain of the function?

Let r = ⟨5, –1⟩, s = ⟨6, 0⟩, and t = ⟨–1, –3⟩. Aaron incorrectly determined 2r + 4s – 7t as ⟨41, –23⟩. Review his calculations.2r + 4s – 7t2⟨5, –1⟩ + 4⟨6, 0⟩ – 7⟨–1, –3⟩⟨10, –2⟩ + ⟨24, 0⟩ + ⟨7, –21⟩⟨41, –23⟩

Which of the following is true regarding the solution to the logarithmic equation below?

Which expression is equivalent to ?

Review the graph.

Which sequence explains a geometric method of determining ?

What is the solution of ?

A statistics teacher has 4 periods of introductory statistics. She wants to get students’ opinions on a new homework policy. To get a sample, the teacher groups the students by their class performance (A students, B students, etc.). Then she randomly selects 3 students from each class performance group to survey. Which sampling method was used?

A surveyor is studying a map of the community and is using vectors to determine the distance between two schools. On the map, the surveyor determined that school A is at (7, 12), and school B is at (–21, –13). The scale of the map is 1 unit = 100 meters.Which vector represents the path from school A to school B, and what is the actual distance between them?

A company that manufactures golf balls produces a new type of ball that is supposed to travel significantly farther than the company’s previous golf ball. To determine this, 40 new-style golf balls and 40 original-style golf balls are randomly selected from the company’s production line on a specific day. The balls are then placed in a bag and shaken. A golf pro then selects a ball and hits it using a driver. The distance the ball travels is then measured. The bag is shaken again, and the golf pro selects another ball and hits it with the same driver. He continues this procedure until all 80 of the golf balls are hit.

Which graph represents the following piecewise defined function?

Let |a| = 12 at an angle of 25° and |b| = 7 at an angle of 105°. What is the magnitude of a + b? Round to the nearest decimal.

What are the potential solutions of