91Ó°ÊÓ

Suppose that the price of gasoline is \(\$ 3.09\) per gallon. a. Generate a formula that describes the cost, \(C\), of buying gas as a function of the number of gallons of gasoline, \(G,\) purchased. b. What is the independent variable? The dependent variable? c. Does your formula represent a function? Explain. d. If it is a function, what is the domain? The range? e. Generate a small table of values and a graph.

The cost of driving a car to work is estimated to be \(\$ 2.00\) in tolls plus 32 cents per mile. Write an equation for computing the total cost \(C\) of driving \(M\) miles to work. Does your equation represent a function? What is the independent variable? What is the dependent variable? Generate a table of values and then graph the equation.

Suppose that a church congregation has 100 members, each of whom donates \(10 \%\) of his or her income to the church. The church collected \(\$ 250,000\) last year from its members. a. What was the mean contribution of its members? b. What was the mean income of its members? c. Can you predict the median income of its members? Explain your answer.

a. Which (if any) of the following ordered pairs \((x, y)\) is a solution to the equation \(y=x^{2}-2 x+1 ?\) Show how yoa came to your conclusion. $$ (-2,7), \quad(1,0) $$ b. Find one additional ordered pair that is a solution to the equation above, Show how you found your solution.

Find \(f(3)\), if it exists, for each of the following functions: a. \(f(x)=(x-3)^{2}\) b. \(f(x)=\frac{1}{x}\) c. \(f(x)=\frac{x+1}{x-3}\) d. \(f(x)=\frac{2 x}{x-1}\) Determine the domain for each function.

Read Stephen Jay Gould's article "The Median Isn't the Message" and explain how an understanding of statistics brought hope to a cancer victim.

a. On the first quiz (worth 25 points) given in a section of college algebra, one person received a score of \(16,\) two people got 18 , one got \(21,\) three got \(22,\) one got \(23,\) and one got \(25 .\) What were the mean and median of the quiz scores for this group of students? b. On the second quiz (again worth 25 points), the scores for eight students were \(16,17,18,20,22,23,25,\) and 25 . i. If the mean of the scores for the nine students was 21 , then what was the missing score? ii. If the median of the scores was \(22,\) then what are possible scores for the missing ninth student?

Up to and including George W. Bush, the ages of the last 15 presidents when they first took office \(^{6}\) were 56,55,51,54 \(51,60,62,43,55,56,52,69,64,46,54 .\) a. Find the mean and median ages of the past 15 presidents when they took office. b. If the mean age of the past 16 presidents is \(54.94,\) at what age did the missing president take office? c. Beginning with age 40 and using 5 -year intervals, find the frequency count for each age interval. d. Create a frequency histogram using your results from part (c).

The accompanying table gives the ages of students in a mathematics class. Ages of Students \begin{tabular}{cc} \hline Age Interval & Frequency Count \\ \hline \(15-19\) & 2 \\ \(20-24\) & 8 \\ \(25-29\) & 4 \\ \(30-34\) & 3 \\ \(35-39\) & 2 \\ \(40-44\) & 1 \\ \(45-49\) & 1 \\ \hline Total & 21 \\ \hline \end{tabular} a. Use this information to estimate the mean age of the students in the class. Show your work. (Hint: Use the mean age of each interval.) b. What is the largest value the actual mean could have? The smallest? Why?