Math Help - Quantititive Reasoning

QUESTION 1:

The annual income of 20 engineers is shown in the table and in  QR_9C_Spreadsheet [+]. This list is an example of  univariate (one variable) data because we know one thing about each engineer.

Part A: The data are arranged from smallest to largest, and the sum of the 20 numbers is shown at the bottom. Find the average annual income of the 20 engineers. Hint

 Average annual income = $  Part B: Numerical data, after being arranged in ascending order (or descending, ranked), can be grouped by relative size. The median divides the data into two sets: half of the data set is in a set of smaller values and the other half of the data set is in a set of larger values. Find the median income of the 20 engineers. Median income = $  Part C: Quartile values divide the ranked data into four equal groups: the first quartile is the median of the smaller half of the data, below the median. Find the first quartile income.

First quartile income = $  Part D: The third quartile is the median of the greater half of the data, above the median. Find the third quartile income. Third quartile income = $ 

QUESTION 2:

 Question 2

Let’s look at information from a customer’s bill for the use of propane. The following graphic shows the total monthly energy cost plotted against the average monthly temperature over a two-year span. Two graphs are displayed on the same grid using the same horizontal axis and scale of the months from February 2012 through January 2014. The histogram presents the cost of the propane per month. The curve presents the temperature over the months.

Part A: Choose the best description of the behavior of the variable Temperature.

· The temperature rose and fell.

· The temperature rose and fell repeatedly.

· The temperature rose continuously.

· The temperature declined continuously.

Part B: Choose the best description of the behavior of the variable Cost.

· The cost rose and fell repeatedly.

· The cost rose continuously.

· The cost declined continuously.

· The cost rose and fell.

Part C: Because the graph gives two pieces of information about each month, it is an example of  bivariate (two variable) data. Choose the best description of the relationship of the behaviors of the two variables.

· The two graphs behave basically the same.

· The two graphs have the same type of behavior but at different times.

· The two graphs have different behavior.

QUESTION 3: The American Society of Civil Engineers and the American Society of Mechanical Engineers conducted a joint engineering salary survey and published their findings. This report includes a great deal of information about the salaries of engineers. Some excerpts from the report are given below.

· "As of March 31, 2012, the average total annual income of respondents in the survey was $103,497 (including salaries, fees, cash bonuses, commissions, and profits received from the respondents’ primary jobs during the preceding 12-month period—but specifically excluding overtime pay).” (Page 7)

· “Full-time salaried respondents holding doctoral degrees in engineering have a median income of $116,000. Those with an M.S. in engineering earn a median of $95,576. Finally, those with a B.S. in engineering earn a median income of $85,900.” (Page 10)

· “Median income shows a consistent increase with increased engineering experience.” (Page 9)

· “Exhibit 12 reports income by professional responsibility/engineering grade. The graph follows the shape expected, rising from a full-time salaried median income of $55,000 for Engineer I to $150,000 for Engineer VIII.” (Page 14)

Part A: What was the average total annual income of the people who participated in the survey?

$ 

Part B: Does the second bullet point give information about mean or median income?

· Mean

· Median

Part C: The third and fourth bulleted points refer to which two variables?

· Salary and benefits

· Experience and benefits

· Salary and experience

· Experience and working conditions

Question 4 9A:

The graph below shows the book value (in dollars) of a storage building when the building is 4,5,11, and 12 years old.

Assume the book value of the storage building decreases each year by a constant amount. This means that the points must be collinear (on the same line). We can draw a line that passes through the four points and extends left to the vertical axis and right to the edge of the graph.

Part A: Use the graph to estimate the book value of the storage building at Year 10.

Estimated value in Year 10 = $

Part B: Is your answer to Part A an exact answer or an estimate?

· Estimate

· Exact answer

Part D: Use your equation from Part C to determine the book value of the storage building at Year 10.

· $ 

Part E: Is your answer to Part D an exact answer or an estimate? Explain.

· Estimate

· Exact answer

·

Part C: The building was actually valued at $30,050 when it was new (Year 0), and the book value at Year 10 was $15,050. Using V for Value and Y for Year, determine an equation that will model the value of the building based on the years since the building was purchased. 

QUESTION 5 10p:

People often use the term  exponential when they mean "increasing rapidly." Let's compare the graphs of two equations to investigate the meaning of this term. Part A: Complete the table of values for y=3x. In your notebook, create a graph by hand or print out a graph created in a spreadsheet and upload.

x	y
1
2
3
4
5
6

Part B: Complete the table of values for y=3x

In your notebook, create a graph by hand or print out a graph created in a spreadsheet and upload.

x	y
1
2
3
4
5
6

Part C: Compare the values of the dependent variable y in Parts A and B. Choose the best description of the values of y=3x compared with y=3x.

· The growth of y=3x is much more rapid than the growth of y=3x

· The growth of y=3x is similar to the growth of y=3x

· The growth of y=3x is much more rapid than the growth of y=3x

QUESTION 6 11A PRE:

Select the answers that describe the data provided.

Input	Output
1	50
2	50
3	50
4	50
5	50

Part A: In the table, as the input values increase, the output values are _________.

· remaining constant

· increasing

· decreasing

Part B: As the input values increase, the output values ________.

· change by smaller and smaller amounts each time

· are not changing at all

· change by larger and larger amounts each time

· change by the same amount each time

QUESTION 7: Select the answers that describe the data provided.

Input	Output
1	50
2	55
3	60.5
4	66.55
5	73.205

Part A: In the table, as the input values increase, the output values are _________. Hint

· remaining constant

· increasing

· decreasing

Part B: As the input values increase, the output values ________

a. are not changing at all

b. change by smaller and smaller amounts each time

c. change by the same amount each time

d. change by larger and larger amounts each time

QUESTION 8: Select the answers that describe the data provided.

Input	Output
1	50
2	47
3	44
4	41
5	38

Part A: In the table, as the input values increase, the output values are _________.

· remaining constant

· decreasing

· increasing

Part B: As the input values increase, the output values ________.

· are not changing at all

· change by larger and larger amounts each time

· change by smaller and smaller amounts each time

· change by the same amount each time

QUESTION 9

Select the answers that describe the data provided.

Input	Output
1	50
2	135.9155
3	369.4602
4	1004.307
5	2730.017

Part A: In the table, as the input values increase, the output values are _________.

· increasing

· decreasing

· remaining constant

Part B: As the input values increase, the output values ________.

· change by the same amount each time

· change by smaller and smaller amounts each time

· change by larger and larger amounts each time

· are not changing at all

QUESTION 10

Select the answers that describe the data provided.

Input	Output
1	50
2	46
3	42
4	38
5	34

Part A: In the table, as the input values increase, the output values are _________.

· decreasing

· remaining constant

· increasing

Part B: As the input values increase, the output values ________.

· change by the same amount each time

· change by smaller and smaller amounts each time

· change by larger and larger amounts each time

· are not changing at all

QUESTION 11

Consider the curve shown below. Notice that the number of horses is increasing over time.

Part A: Estimate the years when the number of wild horses is increasing by larger and larger amounts. (Increases at an increasing rate)

The number of horses is increasing by ever larger amounts from Year  to approximately Year .

Part B: Estimate the years when the number of wild horses is increasing but by smaller and smaller amounts. (Increases at a decreasing rate)

The number of horses is increasing but by ever smaller amounts from Year  to approximately Year.