7. Karen's piggy bank has all dimes and quarters. The total value of the money in her piggy bank is \( \$ 11.40 \). If Karen has 36 quarters, write and solve a linear equation to find the number of dimes she has.

23 In a linear pattern, the \( 7^{* *} \) term is 16 and the \( 20^{\text {m }} \) term is 42 . Determine the first three (4) terms of the pattern.

For example, consider the following balanc \[ \mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2} \] From this equation, there are several possil mole ratios are the following: \[ \frac{3 \text { moles } \mathrm{H}_{2}}{1 \text { mole } \mathrm{N}_{2}} \] Which is a possible mole-mole ratio for the \[ 4 \mathrm{Fe}(\mathrm{s})+3 \mathrm{O}_{2} \]

Mai and Tyler are selling items to earn money for their elementary school. The school earns \( w \) dollars for every wreath sold and \( p \) dollars for every potted plant sold. Mai sells 14 wreaths and 3 potted plants and the school earns \( \$ 70.50 \). Tyler sells 10 wreaths and 7 potted plants and the school earns \( \$ 62.50 \). This situation is represented by this system of equations: \( \left\{\begin{array}{l}14 w+3 p=70.50 \\ 10 w+7 p=62.50\end{array}\right. \) Explain why it makes sense in this situation that the solution of this system is also a solution to \( 4 w+(-4 p)=8.00 \).

Use the elimination method to evaluate \( \operatorname{det}(A) \) : \( A=\left(\begin{array}{rrrr}0 & 1 & 2 & 3 \\ 1 & 1 & 1 & 1 \\ -2 & -2 & 3 & 3 \\ 1 & 2 & -2 & -3\end{array}\right) \)

\( \sqrt[3]{0, \hat{2}} \cdot \sqrt[3]{\frac{4}{3}}= \) b) \( \left(\frac{3}{5}\right)^{24}:\left(\frac{3}{5}\right)^{26}= \)