Solve any pair of the system equation $2x-y=4,\text{ } 3x+y=1, \text{ and } x-2y=5$. Show that the solution is valid for any pair chosen. What conclusions can be drawn about the graphs of the three equations.

The weight of a radioactive isotope remaining after t weeks is given by $W_{t}=8000 \times e^{-\frac{t}{20}}$ grams. Find the time for the weight to: reach 0.1% of its original value.

A solution of $\mathrm{KClO}_{3}$ is prepared using 75 grams of the solute in enough water to make 0.250 liters of solution. The gram-formula mass of $\mathrm{KClO}_{3}$ is 122 grams per mole. Assuming the solution is saturated, determine the temperature of the solution.

Determine whether the given expression is a polynomial ll it is, write it in standard form. $2 x ^ { 2 } - \sqrt { 3 } x + 4$

Write equivalent expression. $35x+30$

Use your book or dictionary to define ganglion.

Solve.

$$\begin{array} { l } { \text { a) } 3 x ^ { 2 } + 28 x + 9 = 0 } \\ { \text { b) } 4 k ^ { 2 } + 19 k + 15 = 0 } \\ { \text { c) } 8 y ^ { 2 } - 22 y + 15 = 0 } \\ { \text { d) } 16 b ^ { 2 } - 1 = 0 } \\ { \text { e) } 10 m ^ { 2 } + 30 m = 0 } \\ { \text { f) } 4 x ^ { 2 } - 12 x + 9 = 0 } \end{array}$$

If possible, compute the matrix products using paper and pencil.

$$\begin{bmatrix} 1 & 0 & -1\\0 & 1 & 1 \\ 1 & -1 & -2 \end{bmatrix} \begin{bmatrix} 1 & 2 & 3\\ 3 & 2 & 1\\ 2 & 1 & 3 \end{bmatrix}$$

Solve for x: $7^{x+1}=343$

A study of ground penetration near a toxic waste dump models the amount of pollution P at a depth x (in feet) and time t (in years) by the function

$$P(x, t)=P_{0}+P_{1} e^{-k x} \sin (A t-k x)$$

where A, k, $P_0$, and $P_{1}$ are constants. Show that P(x, t) satisfies the diffusion equation

$$\frac{\partial P}{\partial t}=c^{2} \frac{\partial^{2} P}{\partial x^{2}}$$

for a certain constant c.

Listed below are prices in dollars for one night at different hotels located on Las Vegas Boulevard (the "Strip"). If you decide to stay at one of these hotels, what statistic is most relevant, other than the measures of center? Apart from price, identify one other important factor that would affect your choice.

$$\begin{array} { c c c c c c c c } { 212 } & { 77 } & { 121 } & { 104 } & { 153 } & { 264 } & { 195 } & { 244 } \end{array}$$

Find the mean.

A denotes the area of the sector of a circle of radius r formed by the central angle $\theta.$ Find the missing quantity. Round answers to three decimal places. r = 3 meters, $\theta=120^{\circ},$ A = ?

Name the minimum components of a reflex arc.

Because different rounding results in different estimates, there is not one single, correct answer to each exercise. Determine each estimate without using a calculator. Then use a calculator to perform the computation necessary to obtain an exact answer. How reasonable is your estimate when compared to the actual answer? You lease a car at $605 per month for 3 years. Estimate the total cost of the lease.