We have \(p(x)q(x)=(ax^2-5x+6)(bx^2+3x-2)\), so \(20=3a-5b\) and \(30=-2a+6b-15\). Solving the system of equations gives \(a=43.125\) and \(b=21.875\), so \(a+b=65\).
The final answer is \(101\) btw.
Area is \((4)(9)+2^2+(4)(5)+\frac12(3^2)\pi = 74.13\).
Note that \(0.0\overline2 = \frac2{90}\), and \(0.1=\frac1{10}\), so the decimal is \(\frac2{90} + \frac1{10} = \frac{11}{90}\).
By the way, since the flavors can be repeated there would be more than just \(\binom n3\) selections.
They probably forgot to copy the LaTeX from their homework
This would mean that \(1+\frac1n \implies \frac1n\) is an integer, so the only possible value of \(n\) would be \(1\).
