91Ó°ÊÓ

Approximate each expression to the nearest hundredth. $$3(5.9)^{2}-2(5.9)+6$$

Approximate each expression to the nearest hundredth. $$\sqrt[3]{4.5 \times 10^{5}+3.7 \times 10^{2}}$$

Find the length of the unknown side of the right triangle. In each case, a and b represent the lengths of the legs and c represents the length of the hypotenuse. $$a=8, b=15 ; \text { find } c$$

Sketch by hand the graph of the line passing through the given point and having the given slope. Label Through \((-2,-3), m=-\frac{3}{4}\)

U.S. HIV/AIDS Infections In 2010 , there were approximately 1.2 million people in the United States living with HIV/AIDS. At that time the infection rate was \(50,000\) people per year. (a) Find values for \(m\) and \(b\) so that \(y=m x+b\) models the total number of people \(y\) in millions who were living with HIV/AIDS \(x\) years after 2010 . (b) Find \(y\) for the year 2014 . Interpret your result.

Solve each inequality analytically. Write the solution set in interval notation. Support your answer graphically. $$\frac{1}{3} x-\frac{1}{5} x \leq 2$$

Climate Change During the past 50 years, the average rate of change in temperature in Antarctica has been \(0.9^{\circ} \mathrm{F}\) per decade. (a) Write a function \(W\) that calculates the increase in temperature after \(x\) years during this time period. (b) Evaluate \(W(15)\) and interpret the result.

Suppose that P is an endpoint of a segment PQ and M is the midpoint of \(P Q .\) Find the coordinates of endpoint Q. $$P(7,-4), M(8,5)$$