#### Answer

60$^{\circ}$F

#### Work Step by Step

Since October is represented by $x=9$, we substitute $x=9$ in the equation to find the value of $t$:
$t=60-30\cos\frac{x\pi}{6}$
$t=60-30\cos\frac{9\pi}{6}$
$t=60-30\cos\frac{3\pi}{2}$
$t=60-30(0)$
$t=60-0$
$t=60$
Therefore, the maximum afternoon temperature for the month of October is 60$^{\circ}$F.