Lesson 7 Step It Up, Sum It Up Practice Understanding

Ready

The chart shows the ages at death of the U.S. presidents.

Washington 67	Polk 53	Arthur 56	Roosevelt, F. 63
Adams, John 90	Taylor 65	Cleveland 71	Truman 88
Jefferson 83	Fillmore 74	Harrison, B. 67	Eisenhower 78
Madison 85	Pierce 64	McKinley 58	Kennedy 46
Monroe 73	Buchanan 77	Roosevelt, T 60	Johnson, L. 64
Adams, J.Q. 80	Lincoln 56	Taft 72	Nixon 81
Jackson 78	Johnson, A. 66	Wilson 67	Reagan 93
Van Buren 79	Grant 63	Harding 57	Ford 93
Harrison, W. 68	Hayes 70	Coolidge 60	Bush 94
Tyler 71	Garfield 49	Hoover 90

Wikipedia contributors. "List of presidents of the United States by date of death." Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 23 Aug. 2021. Web. 6 Sep. 2021.

1.

The data has been put into a histogram with bin width of $6$ . Describe the shape of the distribution.

2.

Use the data from the chart to label the following statistics on the boxplot.

the minimum number in the data set
Q1
the median
Q3
the maximum number in the data set

3.

The standard deviation, $σ (s i g m a)$ , for the data is $12.6449$ . What does this tell you?

4.

Is the mode greater or smaller than the median and the mean? What does this tell you?

Set

Calculate the value of each of the following annuity savings accounts.

5.

An annuity that earns $4 %$ interest annually, with an annual deposit of $$ 5, 000$ . The annuity matures in $35$ years.

6.

An annuity that earns $6 %$ interest annually, with an annual deposit of $$ 4, 000$ . The annuity matures in $20$ years.

7.

An annuity that earns $6 %$ interest annually, with a monthly deposit of $$ 200$ . The annuity matures in $30$ years. (Note: since the annual interest rate is $6 %$ , treat the monthly interest rate as $\frac{6 %}{12} = 0.5 %$ )

Mortgage payments are annuities for the bank that holds the account. The bank wants to earn a certain percent of interest on the money they loan the borrower, and needs to determine a monthly payment that guarantees the bank that amount of interest over the term of the loan.

8.

A bank offers a $3.6 %$ loan on a $$ 250, 000$ thirty-year mortgage. What is the future value of the loan in $30$ years? That is, what would the value of the account be in $30$ years if $$ 250, 000$ is deposited today at an annual rate of $3.6 %$ ?

9.

To determine the monthly mortgage payment, consider an annuity whose value will be equal to the amount found in problem 4 after $360$ monthly payments of $A$ dollars with a monthly interest rate of $\frac{3.6 %}{12} = 0.3 %$ . Find the value of $A$ for this annuity, which will be the monthly mortgage payment.

Go

10.

The absolute value of a sine function.
The absolute value of a quadratic function.
The sum of a quadratic function and sine function.
The sum of a linear function and a sine function.

In problems 11 and 12, let $f (x) = x^{2}$ and $g (x) = \sqrt{x}$ .

11.

The graph shows the composition of $f (g (x))$ . Explain why the only outputs are in the first quadrant.

12.

The graph shows the composition of $g (f (x))$ . Explain why the graph has outputs in both the first and second quadrants.