\[ P(x)=-x^{3}+\frac{27}{2} x^{2}-60 x+100, x \geq 5 \text { is an approximation to the total profit (in thousands of dollars) } \] from the sale of \( x \) hundred thousand tires. Find the number of hundred thousands of tires that must be sold to maximize profit. A. 4.5 hundred thousand B. 4 hundred thousand C. 5.5 hundred thousand D. 5 hundred thousand

Solve the following exponential equation. Express irrational solutions in exact form. \[ 2^{2 x}+2^{x}-56=0 \]

Solve the following exponential equation. Express irrational solutions in exact form. \[ 3 \cdot 36^{x}+5 \cdot 6^{x}+7=0 \]

Solve for y in the equation \( -3y = 12 \) using properties of equality.

Write the expression as a single logarithm. Express powers as factors. \[ \ln \left(\frac{x}{x-4}\right)+\ln \left(\frac{x+4}{x}\right)-\ln \left(x^{2}-16\right) \]

What does the author want to communicate about Bud's feelings about family through the scene with Billy?