Chapter 8.3, Problem 64PE

Ina certain county, the proportion of voters in each age group registered as Republicans, Democrats, or Independents is given by the following matrix, which well call A.

$\begin{array}{l}\begin{array}{lll}\hfill & \text{Age}\hfill & \hfill \end{array}\\ 18-3031-50\text{Over50}\\ \begin{array}{l}\text{Republicans}\hfill \\ \text{Democrats}\hfill \\ \text{Independents}\hfill \end{array}\left[\begin{array}{lll}0.40\hfill & 0.30\hfill & 0.70\hfill \\ 0.30\hfill & 0.60\hfill & 0.25\hfill \\ 0.30\hfill & 0.10\hfill & 0.05\hfill \end{array}\right]\end{array}$

The distribution, by age and gender, of this county’s voting population is given by the following matrix, which we'll call B.

$\begin{array}{l}\text{Male}\text{Female}\\ \begin{array}{l}\text{18-30}\hfill \\ \text{Age}\text{31-50}\hfill \\ \text{Over 50}\hfill \end{array}\left[\begin{array}{ll}6000\hfill & 8000\hfill \\ 12,000\hfill & 14,000\hfill \\ 14,000\hfill & 16,000\hfill \end{array}\right]\end{array}$

a. Calculate the product AB.

b. How many female Democrats are there?

c. flow many male Republicans are there?