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.

\( \begin{array}{l}\text { Simplify the expression. Assume that variables represent } \\ \text { non-zero real numbers. }\end{array} \) \( \begin{array}{ll}\frac{6 a^{5}\left(a^{-2}\right)^{6}}{\left(a^{-1}\right)^{-3}} & \frac{6 a^{5}\left(a^{-2}\right)^{6}}{\left(a^{-1}\right)^{-3}}=\square \\ \text { (Simplify your answer. Type in exponenti. } \\ \text { notation. Type positive exponents.) }\end{array} \)

\( 1 \leftarrow \quad \) 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 \( \mathbb{C}: \mathrm{z}^{7}=1 \)

Three-fifths of Jesse Black's inventory was destroyed by fire. He sold the remaining part, which was slightly damaged, for two-thirds of its value and received \( \$ 3400 \). (a) What was the value of the destroyed part of the inventory? (b) What was the value of the inventory before the fire? (a) The value is \( \$ \square \). (Round to the nearest cent as needed.)

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