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Math Help – Quantititive Reasoning

QUESTION 1:

Farm equipment has a class life of 10 years. The graph below illustrates the book value (or depreciated value) of one farmer’s equipment for the first two years and last two years of ownership. The equipment is being depreciated using the straight-line depreciation method. A line is provided to help you
estimate each of the values below.

Part A: Estimate the cost of the equipment.

Cost = $

Part B: Estimate the salvage value of the equipment.

Salvage Value = $

Part C: Estimate the book value of the equipment in Year 4.

Book value in Year 4 = $

Part D: The equation for the book value of the farm equipment is

Value = 130,000 – 12,000(Years)

Use the equation to determine the book value when the equipment is six years old.

Book value at the end of Year 6 = $

Part E: Is your answer for Part D an example of interpolation or extrapolation? Part F: Which of the following is the correct interpretation of the “12,000” in this equation?

· $12,000 is the total depreciation of the equipment.

· $12,000 is the salvage value of the equipment.

· $12,000 is the annual depreciation of the equipment.

· $12,000 is the basis of the equipment.

Part G: The book value of the equipment will be $70,000 at the end of Year

QUESTION 2

Part A: Estimate the basis (cost) of the rental property.

Basis = $

Part B: Estimate the book value of the property in Year 15.

Book value at Year 15 = $

Part C: Estimate the book value of the property in Year 25.

Book value at Year 25 = $

Part D: Is your answer from Part C an example of interpolation or extrapolation?

· Interpolation

· Extrapolation

Part E: Rental property does not have a salvage value; it depreciates to a value of zero. Estimate the class life used for this property.

Class life = years

Question3

QUESTION 3:Paleontologists study prehistoric life, such as dinosaurs. They study fossils in a variety of ways. The following graph shows data taken from the Dinosaur Project, displaying humerus length and femur length for Ceratopsian (horned) dinosaurs and Thyreophoran (the group including Stegosaurs and Ankylosaurs) dinosaurs. Examine the graph to consider the extent to which the length of the two bones for these dinosaurs are related.

Part A: The relationship between Femur Length and Humerus Length is:

a. Negatively correlated

b. Positively correlated

Part B: The relationship is stronger for which class of dinosaurs?

a. Ceratopsians

b. Thyreophorans

QUESTION 4: The Global Assessment of Functioning (GAF) is a 100-point tool that rates a person’s overall ability to function psychologically, socially, and occupationally. The higher the score, the better the person is at functioning. A shorter test that is designed to measure similar attributes is called the Functioning Assessment Short Test (FAST).

The two tests were given to several subjects, and their scores plotted as pairs of data are shown below:

Part A: Is the correlation positive or negative?

Negative

Positive

Part B: There are five pairs of data that are marked with solid dots. These five dots are called “outliers.” That is, they seem to be outside most of the other observed values. One of the outliers shows a score of about 38 on the FAST. It is paired with a GAF score of approximately:

a. 40

b. 50

c. 60

d. 70

e. 80

QUESTION 5:

Two friends drove from Las Vegas to Los Angeles, a trip that took about four hours. The first three hours of that trip traversed through the desert, across valleys, and over mountains. In some segments, there were few fuel and restroom stops. If it weren’t for traffic, a driver could set the cruise control, relax, and enjoy the scenery. Since the rental car had a display that showed the amount of fuel left in the tank and an indicator that showed the miles traveled on this trip, the two friends tracked the two variables over time. They decided the best way to collect the data was to record the time into the trip and the distance traveled when the fuel gauge showed whole gallons. The table below shows a portion of the data they collected.

Time (minutes)	Distance Traveled (miles)	Fuel in the Tank (gallons)
0	0	18
18	21.1	17
35	41.7	16
53	63.1	15
70	84	14
88	105.3	13
103	125.1	12
117	144.1	11
125.5	154	10.55

Part A: Consider the two variables Time and Distance Traveled. Which is dependent?

a. Distance Traveled

b. Time

Part B: Describe the relationship between Time and Distance Traveled.

a. Positive

b. Negative

Part C: Consider the two variables Time and Fuel in the Tank. Which one is dependent?

a. Fuel in the Tank

b. Time

Part D: Describe the relationship between Time and Fuel in the Tank.

a. Negative

b. Positive

Part E: Create a scatterplot of Time and Distance Traveled and a scatterplot of Time and Fuel in the Tank. You may use a spreadsheet or create sketches by hand. Take a screenshot or a picture and upload.

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