yes or just 4g
No.
$350(1-0.025) - 700(0.025) = $341.25 - $17.5 = $323.75
\(deg(p(x)) > deg(q(x)) \Rightarrow deg((p+q)(x)) = deg(p(x))\)
\(c_0 + c_1 + c_2 + \dots + c_n = f(1) =32\)
\(\text{There are 2 T's}\\ \text{So let's look at permutations by how many T's they contain}\\ 0 - \dbinom{4}{0}\dbinom{8}{4}4! = 1680\\ 1 - \dbinom{4}{1}\dbinom{8}{3}3! = 1344 \\ 2 -\dbinom{4}{2}\dbinom{8}{2}2! = 336\\ \text{These sum to }n = 3360\)
\(E[profit] = P[win] (\text{profit if win} )+ P[lose](\text{"profit" if lose})= \\ (0.2)((0.1)400000-2000)+ (1-0.2)(-2000) = \$6000 \)
\(\text{There's no way that }q(x) \text{ can cancel any terms higher than degree }7\\ \text{Thus the sum will still be of degree }11 \text{ given all }q(x)\)
\(P[!defective]=1-P[defective]\\ E[profit] = P[!defective]\cdot \$350 - P[defective]\cdot \$700\\ \text{I leave you to plug and chug}\)
\(x(x+5) = -n\\ x^2 + 5x +n =0\\ \text{no real roots if discriminant is negative}\\ D = 25-4n\\ D < 0 \Rightarrow n \geq 7\\ P[n \geq 7] = \dfrac{4}{10} = \dfrac{2}{5}\)
\(\hat{u} = B-A\\ d = \dfrac{\|AQ \times \hat{u}\|}{\|\hat{u}\|}\)
\(\hat{u} = (1,2,2)\\ \|\hat{u}\|=3\\ AQ = Q-A=(2,-8,-3)\\ \dfrac{\|AQ \times \hat{u} \|}{\|u\|}= \dfrac{\|(-10, -7, 12)\|}{3} = \dfrac{\sqrt{293}}{3}\\ d=293\)
+6248 