Thickest to thinnest....
0.33m , 0.3mm, 0.275mm, 0.25mm
![\bf \begin{array}{llllll} \textit{something}&&\textit{varies inversely to}&\textit{something else}\\ \quad \\ \textit{something}&=&\cfrac{{{\textit{some value}}}}{}&\cfrac{}{\textit{something else}}\\ \quad \\ y&=&\cfrac{{{\textit{k}}}}{}&\cfrac{}{x} \\ &&y=\cfrac{{{ k}}}{x} \end{array}\\\\ -----------------------------\\\\ \textit{p is inversely proportional to the cube of (q-2)}\implies p=\cfrac{k}{(q-2)^3} \\\\\\ now \quad \begin{cases} p=6\\ q=3 \end{cases}\implies 6=\cfrac{k}{(3-2)^3}](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Barray%7D%7Bllllll%7D%0A%5Ctextit%7Bsomething%7D%26%26%5Ctextit%7Bvaries%20inversely%20to%7D%26%5Ctextit%7Bsomething%20else%7D%5C%5C%20%5Cquad%20%5C%5C%0A%5Ctextit%7Bsomething%7D%26%3D%26%5Ccfrac%7B%7B%7B%5Ctextit%7Bsome%20value%7D%7D%7D%7D%7B%7D%26%5Ccfrac%7B%7D%7B%5Ctextit%7Bsomething%20else%7D%7D%5C%5C%20%5Cquad%20%5C%5C%0Ay%26%3D%26%5Ccfrac%7B%7B%7B%5Ctextit%7Bk%7D%7D%7D%7D%7B%7D%26%5Ccfrac%7B%7D%7Bx%7D%0A%5C%5C%0A%26%26y%3D%5Ccfrac%7B%7B%7B%20%20k%7D%7D%7D%7Bx%7D%0A%5Cend%7Barray%7D%5C%5C%5C%5C%0A-----------------------------%5C%5C%5C%5C%0A%5Ctextit%7Bp%20is%20inversely%20proportional%20to%20the%20cube%20of%20%28q-2%29%7D%5Cimplies%20p%3D%5Ccfrac%7Bk%7D%7B%28q-2%29%5E3%7D%0A%5C%5C%5C%5C%5C%5C%0Anow%20%5Cquad%20%0A%5Cbegin%7Bcases%7D%0Ap%3D6%5C%5C%0Aq%3D3%0A%5Cend%7Bcases%7D%5Cimplies%206%3D%5Ccfrac%7Bk%7D%7B%283-2%29%5E3%7D)
solve for "k", to find k or the "constant of variation"
then plug k's value back to
![\bf p=\cfrac{k}{(q-2)^3}](https://tex.z-dn.net/?f=%5Cbf%20p%3D%5Ccfrac%7Bk%7D%7B%28q-2%29%5E3%7D)
now.... what is "p" when q = 5? well, just set "q" to 5 on the right-hand-side, and simplify, to see what "p" is
Answer:
Step-by-step explanation:
This probability will be the area of the square divided by the area of the circle.
![P=\frac{(4\sqrt{2})^2}{\pi 4^2}\\ \\ P=\frac{32}{16\pi}\\ \\ P=\frac{2}{\pi }\\ \\ \text{As a percentage}\\ \\ P=\frac{200}{\pi}\\ \\ P\approx 63.7\%](https://tex.z-dn.net/?f=P%3D%5Cfrac%7B%284%5Csqrt%7B2%7D%29%5E2%7D%7B%5Cpi%204%5E2%7D%5C%5C%20%5C%5C%20P%3D%5Cfrac%7B32%7D%7B16%5Cpi%7D%5C%5C%20%5C%5C%20P%3D%5Cfrac%7B2%7D%7B%5Cpi%20%7D%5C%5C%20%5C%5C%20%5Ctext%7BAs%20a%20percentage%7D%5C%5C%20%5C%5C%20P%3D%5Cfrac%7B200%7D%7B%5Cpi%7D%5C%5C%20%5C%5C%20P%5Capprox%2063.7%5C%25%20)