The number of incarcerated adults N (measured in thousands) in a certain country can be approximated by the equation \( \mathrm{N}=-2.8 \mathrm{x}^{2}+72.4 \mathrm{x}+1914 \), where x is the number of years since 2000. In 2012 , the number of incarcerated adults peaked. How many adults were incarcerated in that year? There were \( \square \) incarcerated adults in 2012.

Calcule todos los valores de a para los cuales la matriz \( A=\left[\begin{array}{lll}a & 0 & 4 \\ 1 & 1 & a \\ a & 1 & 2\end{array}\right] \) es no invertit

Simplify. \( [32-(15+5) \div 4]-[56 \div(8-1)]^{\prime} \) \( [32-(15+5) \div 4]-[56 \div(8-1)]=\square \)

\begin{tabular}{l|l}\( \begin{array}{l}\text { Simplify the expression so that no negative exponents } \\ \text { appear in the final result. Assume all variables represent } \\ \text { nonzero real numbers. }\end{array} \) & \( \begin{array}{l}\left(4 a^{-2}\right)^{4}\left(a^{4}\right)^{-3}=\square \\ \\ \left(4 a^{-2}\right)^{4}\left(a^{4}\right)^{-3}\end{array} \) \\ exponents only.) \end{tabular}

\( 1 \leftarrow \quad \) Determine whether \( B \) is the inverse of \( A \). \( A=\left[\begin{array}{rr}3 & -7 \\ -2 & 5\end{array}\right], \quad B=\left[\begin{array}{ll}5 & 7 \\ 2 & 3\end{array}\right] \)

Résoudre dans \( \mathbb{C}: \mathrm{z}^{7}=1 \)