91Ó°ÊÓ

Solve each equation and inequality. For the inequalities, graph the solution set and write it using interval notation. $$ \frac{11}{12}=\left|\frac{x}{3}-\frac{3 x}{4}\right| $$

The percent of the air-borne particles in a room that a Climatec furnace filter can remove is approximated by the linear function \(p(m)=\frac{6}{5} m\) where \(m\) is the time in minutes that the furnace has been operating. Use an inequality to determine the time after which at least \(60 \%\) of the air-borne particles in the room will have been removed. (Source: climatec.com)

Wikipedia. The number of articles \(a(t)\) in millions in the Englishlanguage edition of Wikipedia can be approximated by the function \(a(t)=0.54 t+0.5,\) where \(t\) is the number of years since \(2005 .\) Use an inequality to determine those years for which the number of articles surpassed 2.5 million. (Source: Wikipedia article: Size of Wikipedia)

National Parks. The number of visitors \(v(t)\) to U.S. national parks can be approximated by the function \(v(t)=-100,000 t+3,600,000,\) where \(t\) is the number of years after \(1990 .\) Use an inequality to determine those years for which the number of visitors fell below \(2,400,000 .\) (Source: National Park Service Stats)

Describe each set in words. \(\begin{array}{ll}\text { a. }(-3,3) & \text { b. }[7,12] \\ \text { c. }(-\infty, 5] \cup(6, \infty) & \end{array}\)

Solve each equation and inequality. For the inequalities, graph the solution set and write it using interval notation. $$ |0.5 x+1|<-23 $$

Solve each equation and inequality. For the inequalities, graph the solution set and write it using interval notation. $$ 15 \geq 7-|1.4 x+9| $$

Medicare. The number of workers \(w(t)\) for each Medicare beneficiary (each person receiving Medicare benefits) is approximated by the function \(w(t)=-0.05 t+4,\) where \(t\) is the number of years after \(2000 .\) Use an inequality to determine those years for which there will be less than 2 workers for each Medicare beneficiary. (Source: Kaiser Family Foundation)

What is incorrect about the double inequality \(3<-3 x+4<-3 ?\)B

In 2008 , the number of recorded earthquakes in the United States was \(3,618\). In 2009 , the total was \(4,264\). What was the percent increase in the number of earthquakes from 2008 to 2009 ? Round to the nearest percent.