91Ó°ÊÓ

Solve using matrices. Investments. Miguel receives 160 dollars per year in simple interest from three investments totaling 3200 dollars. Part is invested at 2%, part at 3%, and part at 6%. There is $1900 more invested at 6% than at 3%. Find the amount invested at each rate.

If a system has an infinite number of solutions, use set-builder notation to write the solution set. If a system has no solution, state this. Solve using the substitution method. $$ \begin{aligned} &a-2 b=3\\\ &3 a=6 b+9 \end{aligned} $$

Find the year in which the first U.S. transcontinental railroad was completed. The sum of the digits in the year is \(24 .\) The ones digit is 1 more than the hundreds digit. Both the tens and the ones digits are multiples of \(3 .\)

Automotive Maintenance. "Steady State" antifreeze is \(18 \%\) alcohol and "Even Flow" is \(10 \%\) alcohol. How many liters of each should be mixed in order to get \(20 \mathrm{L}\) of a mixture that is \(15 \%\) alcohol? (IMAGE CANNOT COPY)

Octane Ratings. The octane rating of a gasoline is a measure of the amount of isooctane in a gallon of gas. Manufacturers recommend using 93 -octane gasoline on retuned motors. How much 87 -octane gas and how much 95 -octane gas should Yousef mix in order to make 10 gal of 93 -octane gas for his retuned Ford \(\mathrm{F}-150 ?\)

A low-flow shower aerator restricts the flow and increases the force of a shower, creating a fine spray that saves water and energy without compromising shower comfort. A 1.5 -gallon-per-minute aerator can save up to \(\$ 175\) per year if a standard efficiency electric water heater is in use. A new Niagara shower head, containing a low-flow aerator, was recently bought for \(\$ 8.14 .\) Assuming savings of \(\$ 175\) per year, how long will it take to break even on the purchase?

Train Travel. A train leaves Danville Union and travels north at \(75 \mathrm{km} / \mathrm{h}\). Two hours later, an express train leaves on a parallel track and travels north at \(125 \mathrm{km} / \mathrm{h}\). How far from the station will they meet?

The perimeter of a standard tennis court used for doubles is \(228 \mathrm{ft}\). The width is 42 ft less than the length. Find the dimensions.

Metal A lloys. In order for a metal to be labeled "sterling silver," the silver alloy must contain at least \(92.5 \%\) pure silver. Nicole has 32 oz of coin silver, which is \(90 \%\) pure silver. How much pure silver must she add to the coin silver in order to have a sterling-silver alloy?

Evaluate \(-p^{2}\) for \(p=-1\) $$ [1.6] $$