6. E corresponde al espacio muestral de un experimento aleatorio y \( A \) un evento de dicho espacio muestral. La probabilidad de no ocurrencia \( A^{\prime} \) de dicho evento corresponde a \( P\left(A^{\prime}\right)=1 \) - \( P(A) \). Calcula las siguientes probabilidades de acuerdo con la anterior definición: a. En un salón de clase, hay 20 estudiantes hombres y 16 mujeres. ¿Cuál es la probabilidad de que al escoger una persona al azar no sea hombre?

\( \int _ { \pi / 6 } ^ { \pi / 2 } x \csc ^ { 2 } x d x \)

Suma: \( -7 x-4 y+6 z ; 10 x-20 y-8 z ;-5 x+24 y+2 z \)

Determine the location and value of the absolute extreme values of \( f \) on the given interval, if they exist. \( f(x)=-x^{2}+9 \) on \( [-3,4] \) What is/are the absolute maximum/maxima of \( f \) on the given interval? Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The absolute maximum/maxima is/are 9 at \( x=0 \). There is no absolute maximum of \( f \) on the given interval. (Use a comma to separate answers as needed.) What is/are the absolute minimum/minima of \( f \) on the given interval? Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The absolute minimum/minima is/are \( \square \) at \( x=\square \). (Use a comma to separate answers as needed.) B. There is no absolute minimum of \( f \) on the given interval.

Practice It! Select the statement(s) that accurately describe the distance-time graph shown. \( \square \) object A traveled at a constant speed of 5 meters per second. \( \square \) objects A, B and C traveled uphill. \( \square \) objects C traveled the shortest distance in 60 seconds. \( \square \) objects A, B and C are showing positive acceleration. \( \square \) Object B traveled at a constant speed of 0.4 meters per second.

a. Use the definition \( m_{\tan }=\lim _{x \rightarrow a} \frac{f(x)-f(a)}{x-a} \) to find the slope of the line tangent to the graph of \( f \) at \( P \). b. Determine an equation of the tangent line at \( P \). c. Plot the graph of \( f \) and the tangent line at \( P \). \( f(x)=x^{2}+4, P(-5,29) \)