50. Marginal Productivity The production function \( z \) for the United States was once estimated as \[ z=x^{0.7} y^{0.3}, \] where \( x \) stands for the amount of labor and \( y \) the amount of capital. Find the marginal productivity of labor and of capital. 51. Marginal Productivity A similar production function for Canada is \[ z=x^{0.4} y^{0.6} \text {, } \] with \( x, y \), and \( z \) as in Exercise 50 . Find the marginal productiv- ity of labor and of capital.

Find the inverse of the following matrix, if possible. Reduce all fractions to lowest terms. \[ A=\left[\begin{array}{ccc}-3 & 0 & -2 \\ -2 & 5 & 4 \\ 1 & -2 & 1\end{array}\right] \] Answer Selecting an option will display any text boxes needed to complete your answer. Does this matrix have an inverse? O Yes No

23. Para el Día del Medioambiente, estudiantes de \( 6^{\circ} \) básico elaboraron un afiche con medidas para el cuidado del planeta. ¿Cuál de las siguientes frases que usaron en el afiche apunta al cuidado de la atmóstera? (A) Cuida la energia, lapaga la luz! (B Reduce la basura que tiras, irecicla lo más que puedas! (C) Cierra la llave! No utilices el agua corriendo cuando te laves los dientes. (D) Moja el suelo antes de barrer la vereda, iprotege tus pulmones!

With a minimum of computations, use only a simple calculator and cofactor expansions to find the determinant of the matrix, \( M=\left[\begin{array}{cccc}2 & 0 & 0 & -9 \\ 2 & 6 & 9 & -1 \\ -2 & 0 & 0 & 0 \\ 7 & 6 & -2 & -5\end{array}\right] \)

Why is a feature-benefit chart considered a valuable selling tool? To compare competitors' products To display a company's financial performance To calculate pricing strategies To show the features of a product and the related customer benefits Question 17 (1 point)

Consider the following. \[ \mathbf{u}=\langle 7,-4\rangle, \mathbf{v}=\langle 2,1\rangle \] (a) Calculate proj \( \mathbf{v} \mathbf{u} \). \( \operatorname{proj}_{\mathbf{v}} \mathbf{u}=\square \) \( \mathbf{u}_{1}=\square \) (b) Resolve \( \mathbf{u} \) into \( \mathbf{u}_{1} \) and \( \mathbf{u}_{2} \), where \( \mathbf{u}_{1} \) is parallel to \( \mathbf{v} \) and \( \mathbf{u}_{2} \) is orthogonal to \( \mathbf{v} \). \( \mathbf{u}_{2}=\square \)