The total time, measured in units of $100$ hours, that a teenager runs her hair dryer over a period of one year is a continuous random variable $x$ that has the density

function below. Use the theorem below to evaluate the mean of the random variable $Y=64x^2+20x,$ where $Y$ is equal to the number of kilowatt hours expended

annually.

$xE[g(x,Y)+-h(x,Y)]=E[g(x,Y)]+-E[h(x,Y)]$

${}_Y=$