# Project #7196 - Algebra

10 problems to solve (see below) and attachment

1. (5 pts)  State the center and the radius of the circle represented by the equation

(x  – 4)2 + (y + 7)2  = 36

3. (7 pts) Solve the inequality 1 – (9 – 5x) ≤ 6(1 + 2x). Write the solution set in interval notation. Show work.

4. (6 pts) A car's gas tank held 20 gallons of gas. Five days later, 4 gallons of gas remained in the tank. Find the average rate of change of gas per day. Show work.

A.    – 4.0 gallons per day                                                                                                          4. _______

B.      – 3.2 gallons per day

C.         3.2 gallons per day

D.        3.8 gallons per day

5. (7 pts) Consider the following graph of y = f  (x):

 (a) State the y-intercept(s).       (b) State the value of  f  (−1).        (c) State the domain.        (d) State the range.

6. (6 pts) Find the slope-intercept equation for the line pictured below. Show work/explanation.

7. (9 pts) Let  =

(a) Calculate .

(b) State the domain of the function  =

(c) Find  and simplify as much as possible. Show work.

8. (8 pts) Consider the linear equation 5x − 2y = 8.

(a) Write the linear equation in slope-intercept form.

(b) State the value of the slope.

(c) State the y-intercept for this line.

(d) Find a point on this line other than the y-intercept. (There are infinitely many right answers! Just state one of them.)

9. (15 pts) Georgia earns a weekly paycheck consisting of base pay of \$420, plus a commission of 6.5% of her weekly sales in excess of \$5,000. (So, Georgia only earns the commission only on the amount of sales over \$5,000).

(a) Write an equation that can be used to determine Georgia's weekly paycheck P, given the amount of weekly sales, x.

(b) Determine Georgia's weekly paycheck if her weekly sales are \$15,230. Show work.

(c) Determine Georgia's weekly sales if her weekly paycheck is \$1,492.50. Show work.

10. (18 pts) Consider the points (4, –1) and (1, 8).

(a) State the midpoint of the line segment with the given endpoints.

(b) Find the distance between the points. Show some work. Give the exact answer (involving a radical), simplify the radical as much as possible, and also state an approximation to three decimal places.

(c) Find the slope-intercept equation of the line passing through the two given points. Show work.

(d) If a line is perpendicular to your line in part (c), what would the slope of that line be?

(no work/explanation required)

11. (14 pts) Life expectancy at birth is the estimated lifespan of a baby born in a particular year (given the conditions of that time period).  Based on data retrieved from http://www.indexmundi.com/facts/united-states/life-expectancy-at-birth the following chart of U.S. life expectancy has been prepared.

The regression line is y = 0.1783x  – 279.92, where x = birth year and y = U.S. life expectancy, in years. The value of r2 is 0.9748.

(a)  Use the regression line to estimate the U.S. life expectancy of a baby born in 1990, to the nearest tenth of a year. Show some work.

(b)  Use the regression line to predict the U.S. life expectancy of a baby born in 2020, to the nearest tenth of a year. Show some work.

(c)  What is the slope of the regression line and what are the units of measurement? In a sentence, interpret what the slope is telling us, in the context of this real-world application.

(d) What is the value of the correlation coefficient, r? Interpret its value – Looking at the graph and the size of r, do you judge the strength of the linear relationship to be very strong, moderately strong, somewhat weak, or very weak?

 Subject Mathematics Due By (Pacific Time) 06/02/2013 08:00 pm
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