Answer:
694 ft²
Step-by-step explanation:
Calculate the area of all 6 walls, noting that the front and back faces are congruent as are the 2 side faces and top/bottom faces
area = 2(13 × 8.5) + 2(11 × 8.5) + 2(13 × 11)
= 221 + 187 + 286 = 694 ft²
84 because 36 x 2 =72 and then 1/3 of 36 is 12 and 12+72=84
Say she chooses topic A. She needs at least one book to arrive on time. The probability that no books arrive on time is 0.1 x 0.1 = 0.01 so the probability that at least one book arrives on time is 1 - 0.01 = 0.99.
Say she chooses topic B. She needs at least two books to arrive on time. The probability of no books arriving on time is 0.1 x 0.1 x 0.1 x 0.1 = 0.0001. The probability of exactly one book arriving on time is 4 x 0.1 x 0.1 x 0.1 x 0.9 = 0.0036 (binomial probability distribution formula - the 4 comes from 4C1). So the probability of her not getting enough books is 0.0001 + 0.0036 = 0.0037 and the probability she does get the books she needs on time is 1 - 0.0037 = 0.9963.
So she should choose topic B.
A) -3, -6 B) 3, 3 C) 2, -6
first off let's notice that hmmm the vertex is above the point (3,-3), so if we "assume" is a vertical parabola, then it'd be opening downwards.... anyhow that said, let's plug in those values.
![\bf ~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}](https://tex.z-dn.net/?f=%5Cbf%20~~~~~~%5Ctextit%7Bvertical%20parabola%20vertex%20form%7D%20%5C%5C%5C%5C%20y%3Da%28x-%20h%29%5E2%2B%20k%5Cqquad%20%5Cbegin%7Bcases%7D%20%5Cstackrel%7Bvertex%7D%7B%28h%2Ck%29%7D%5C%5C%5C%5C%20%5Cstackrel%7B%22a%22~is~negative%7D%7Bop%20ens~%5Ccap%7D%5Cqquad%20%5Cstackrel%7B%22a%22~is~positive%7D%7Bop%20ens~%5Ccup%7D%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D)
![\bf vertex~~(\stackrel{h}{2}~~,~~\stackrel{k}{1})\qquad \implies \qquad y = a(x-2)^2+1 \\\\\\ \stackrel{\textit{we also know that }}{(3~~,~~-3)} \begin{cases} x = 3\\ y = -3 \end{cases}\qquad \implies -3=a(3-2)^2+1 \\\\\\ -3=a(1)^2+1\implies -3=a+1\implies -4=a \\\\[-0.35em] ~\dotfill\\\\ ~\hfill y = -4(x-2)^2+1~\hfill](https://tex.z-dn.net/?f=%5Cbf%20vertex~~%28%5Cstackrel%7Bh%7D%7B2%7D~~%2C~~%5Cstackrel%7Bk%7D%7B1%7D%29%5Cqquad%20%5Cimplies%20%5Cqquad%20y%20%3D%20a%28x-2%29%5E2%2B1%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bwe%20also%20know%20that%20%7D%7D%7B%283~~%2C~~-3%29%7D%20%5Cbegin%7Bcases%7D%20x%20%3D%203%5C%5C%20y%20%3D%20-3%20%5Cend%7Bcases%7D%5Cqquad%20%5Cimplies%20-3%3Da%283-2%29%5E2%2B1%20%5C%5C%5C%5C%5C%5C%20-3%3Da%281%29%5E2%2B1%5Cimplies%20-3%3Da%2B1%5Cimplies%20-4%3Da%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20~%5Chfill%20y%20%3D%20-4%28x-2%29%5E2%2B1~%5Chfill)
