\( \begin{array}{ll}(13+15) \cdot 35 & \text { b) } 12 \cdot(15+25) \\ (300-150) \cdot 2 & \text { d) }(75-33) \cdot 7\end{array} \)

P. Diggonalize the matrix \[ A=\left[\begin{array}{rrr}3 & -1 & 1 \\ -1 & 5 & -1 \\ 1 & -1 & 3\end{array}\right] \text { and find } \] \( A^{4} \) using model matrix \( P \) ?

\( A = \left[ \begin{array} { l l l } { 1 } & { 3 } & { 2 } \end{array} \right] , \quad B = \left[ \begin{array} { l } { 2 } \\ { 0 } \\ { 3 } \end{array} \right] \)

For the quadratic function \( \mathrm{f}(\mathrm{x})=-\mathrm{x}^{2}+6 \mathrm{x} \), answer parts (a) through (c) A. The y -intercept is 0 . (Type an integer or a decimal.) Bse the graphing tool to graph the function. (b) Determine the domain and the range of the function. The domain of \( f \) is \( (-\infty, \infty) \). (Type your answer in interval notation.) The range of \( f \) is ( \( -\infty, 9] \) (Type your answer in interval notation.) (c) Determine where the function is increasing and where it is decreasing The function is increasing on the interval \( \square \). (Type your answer in interval notation.)

19. A movie company invited a total of 500 people to complete their review survey after watching a new release movie. Of the 380 people who finished that survey so far, 55 percent are female and 45 percent are male. Assuming all 500 people will eventually complete the survey, how many of the rest of the respondents must be male in order for half of the total respondents

Emilia quiere llenar un tanque para su tortuga con 4 cubetas de agua. En cada viaje Emilia Ilena la cubeta desde una fuente y camina hacia el tanque, pero en el camino derrama \( 1 / 3 \) del contenido de la cubeta. ¿Cuántos viajes tiene que hacer para llenar el tanque?