a. If there is a charge of \( \$ 8 \) to play the game, what is the game's expected value? \( \$-1.33 \) (Round to the nearest cent.) b. What does this expected value mean? Choose the correct statement below. A. This value represents the expected loss over the long run for each game played. B. This value represents the expected win over the long run for each game played. C. The player can expect to break even over the long run.

DIFERENCIA DEL INTESTINO DELGADO ENTRE EL EQUINO Y PORCINO

\begin{tabular}{l} He earns \( \$ 10.95 \) per hour and \\ also works 80 hours per month. \\ Alex receives a monthly \\ allowance of \( \$ 20 \) for his \\ uniforms, but has to pay labor \\ union dues of \( \$ 17.15 \) per \\ month. \\ \hline Monthly Earnings \\ \hline Yearly Earnings \\ \hline Yearly Amount for Uniforms \\ \hline Yearly Amount for Union Dues \\ \hline Annual Value of Job \\ \hline\end{tabular}

Find the critical values \( \chi_{1-\alpha / 2}^{2} \) and \( \chi_{\alpha / 2}^{2} \) for a \( 98 \% \) confidence level and a sample size of \( n=10 \). \( \chi_{1-\alpha / 2}^{2}=2.088 \) (Round to three decimal places as needed.) \( \chi_{\alpha / 2}^{2}=\square \) (Round to three decimal places as needed.)

(74. \( -2

4. Show that \( \left|\begin{array}{lll}a & b & c \\ a^{2} & b^{2} & c^{2} \\ b+c & c+a & a+b\end{array}\right|=k(a+b+c)(b-c)(c-a)(a-b) \) and tence determne the value of \( k \)