In 2012 there was a total of 78 commercial and noncommercial orbital launches worldwide. In addition, the number of noncommercial orbital launches was two less than three times the number of commercial orbital launches. Determine the number of commercial and noncommercial orbital launches in 2012.

The length of fence required to enclose a rectangular field is 3000 meters.What are the dimensions of the field if it is known that the difference between its length and width is 50 meters?

Solve for x.

$$\left|\begin{array}{lll}{x} & {1} & {2} \\ {1} & {x} & {3} \\ {0} & {1} & {2}\end{array}\right|=-4 x$$

The following problem is based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Given $f(x)=x+4$ and $g(x)=x^2-3 x$, find $g(f(-3))$.

Solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent.

$$\left\{\begin{aligned} 2 x-2 y+3 z &=6 \\ 4 x-3 y+2 z &=0 \\-2 x+3 y-7 z &=1 \end{aligned}\right.$$

Find the quadratic function $y=a x^{2}+b x+c$ that passes through the three points (0,1), (1,0) and (-2,1).

Solve for x.

$$\left|\begin{array}{rrr}{x} & {2} & {3} \\ {1} & {x} & {0} \\ {6} & {1} & {-2}\end{array}\right|=7$$

In Problem given below, use the inverses found in Problems mentioned to solve each system of equations.

$$\left\{\begin{aligned} x-y+z & =2 \\ -2 y+z & =2 \\ -2 x-3 y & =\frac{1}{2}\end{aligned}\right.$$

The perimeter of a rectangular floor is 90 feet. Find the dimensions of the floor if the length is twice the width.

The following problem is based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.

Nick has a credit card balance of $\$ 4200$. If the credit card company charges $18 \%$ interest compound daily, and Nick does not make any payments on the account, how long will it take for his balance to double? Round to two decimal places.

The pH of a chemical solution is given by the formula $\mathrm{pH}=-\log _{10}\left[\mathrm{H}^{+}\right]$ where $[H^+]$ is the concentration of hydrogen ions in moles per liter. Values of pH range from 0 (acidic) to 14 (alkaline). Determine the hydrogen ion concentration of an orange (pH = 3.5).

In Problem given below, use the inverses found in Problems mentioned to solve each system of equations.

$$\left\{\begin{aligned} x+2 z & =6 \\ -x+2 y+3 z & =-5 \\ x-y & =6\end{aligned}\right.$$

What is the Lewis structure for phosphorus tribromide (PBr$_3$)?

Solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent.

$$\left\{\begin{array}{r}{2 x-3 y-z=0} \\ {3 x+2 y+2 z=2} \\ {x+5 y+3 z=2}\end{array}\right.$$