Use > or < to compare the whole numbers. $74,328 \square 74,238$

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

Find the partial sum.

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

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.

Find the area of each circle. Round to the nearest tenth. radius = 4.8 centimeters

You are given the vertices and the equations of the asymptotes ofa hyperbola. Explain how you can determine the values of a and b in the standard form of the equation of the hyperbola.

Find the common difference of the arithmetic sequence with the given nth term. a$_{n}$ = 4n + 5

Evaluate the binomial coefficient $_{\text{n}}$C$_{\text{r}}$.

$$_{20} C_{14}$$

Determine whether the statement is true or false. Justify your answer.

$$\sum_{i=1}^{4}\left(i^{2}+2 i\right)=\sum_{i=1}^{4} i^{2}+\sum_{i=1}^{4} 2 i$$

Simplify. $\left(a^{4}\right)^{3}$

Simplify 7√125 −10√45