Maximize Z=14x+21y subject to

$$\begin{aligned} 2 x+3 y & \leq 12 \\ x+5 y & \leq 8 \\ x, y & \geq 0 \end{aligned}$$

Divide. $0.8682 \div 6$

Find a fundamental matrix for the system and write the general solution as a matrix. If initial values are given, solve the initial value problem. $x_{1}^{\prime}=2 x_{1}+x_{2}-x_{3}, x_{2}^{\prime}=3 x_{1}-2 x_{2}, \ x_{3}^{\prime}=3 x_{1}+x_{2}-3 x_{3} ; x_{1}(0)=1, x_{2}(0)=7, x_{3}(0)=3$

Let R and S be nonzero rings (meaning that each of them contains at least one nonzero element). Show that $R \times S$ contains zero divisors.

Write the value of the digit 6 in each number. 6,025.9

Perform the indicated operations.

$$\left[\begin{array}{rrr} 2 & 0 & -3 \\ -1 & 4 & 0 \\ 1 & -6 & 5 \end{array}\right]+\left[\begin{array}{rrr} 2 & -3 & 4 \\ -1 & 6 & 5 \\ 9 & 11 & -2 \end{array}\right]$$

Find the approximate length of the following curve. The limacon $r=3-6 \cos \theta$

A bag contains 6 green marbles, 8 blue marbles, and 3 red marbles. Find P(B) after A has happened. A: Draw a green marble. Keep it. B: Draw a red marble.

Without using a calculator, evaluate the following expression or state that the quantity is undefined. $\sin ^{-1}\left(-\frac{1}{2}\right)$

Find the partial sum.

$$\sum_{n=1}^{500} \frac{n}{2}$$

What is an appropriate simulation tool for each situation? Explain. About $\frac{1}{2}$ of the members of a local service group are over the age of 50. You want to estimate the probability that in a group of 8 members, at least 4 are over 50.

Explain why the sum

$$\sum_{n=0}^{\infty} 5\left(\frac{4}{5}\right)^{n}$$

is finite.

Use only column interchanges to produce a triangular matrix and then give the determinant of the original matrix.

$$\left[\begin{array}{cccc} 0 & 0 & 2 & 0 \\ 0 & 0 & 1 & 3 \\ 0 & 4 & 1 & 3 \\ 2 & 1 & 5 & 6 \end{array}\right]$$

Use the menu below. $$ \begin{array}{|lcl|} \hline \text{$\mathbf{Appetizers}$} & \text{ } & \text{$\mathbf{Soups}$}\\ \text{Egg Rolls} & \text{ } & \text{Won-ton}\\ \text{Fried Won-tons} & \text{ } & \text{Sizzling Rice}\\ \text{ } & \text{$\mathbf{Main Dishes}$} & \text{ }\\ \text{ } & \text{Almond Chicken} & \text{ }\\ \text{ } & \text{Sweet & Sour Pork} & \text{ }\\ \text{ } & \text{Beef with Broccoli} & \text{ }\\ \hline \end{array} $$ At the China Panda, if you order the family dinner, you choose one appetizer, one soup, and one main dish from the menu. Draw a tree diagram to show the sample space.