which of the following rational numbers can be multiplied by two and result in a number greater than two 5/6 8/9 9/8 11/12
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See the attached picture. You'll find a tree with four branches at level 1 (each of the four sectors of the spinner). Each of these branches is divided in four sub-branches: the possible results of tossing two coins (HH, HT, TH, TT).
So, there are 16 possible outcomes (numbered below each leaf).
If you want to roll an odd number, you have to take branch 1 or 3 at first level.
Then, for each of those, you have to toss exactly one head, so you have to take HT or TH.
The good outcomes are thus 2, 3, 10 and 11, leading to a probability of 4/16=1/4=25%.
Check the picture below.
so the chord is the one in red there, making the segment, in green there, with a central angle of 45°, and the minor segment will be that green one.
![\bf \textit{area of a segment of a circle}\\\\ A=\cfrac{r^2}{2}\left[ \cfrac{\pi \theta }{180} - sin(\theta) \right]~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\ ------\\ r=3\\ \theta =45 \end{cases} \\\\\\ A=\cfrac{3^2}{2}\left[ \cfrac{\pi(45) }{180} - sin(45^o) \right]\implies A=\cfrac{9}{2}\left[ \cfrac{\pi }{4}-\cfrac{\sqrt{2}}{2} \right] \\\\\\ A=\cfrac{9}{2}\left( \cfrac{\pi -2\sqrt{2}}{4} \right)\implies A\approx 0.3523112199491](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Barea%20of%20a%20segment%20of%20a%20circle%7D%5C%5C%5C%5C%0AA%3D%5Ccfrac%7Br%5E2%7D%7B2%7D%5Cleft%5B%20%5Ccfrac%7B%5Cpi%20%5Ctheta%20%7D%7B180%7D%20-%20sin%28%5Ctheta%29%20%5Cright%5D~~%0A%5Cbegin%7Bcases%7D%0Ar%3Dradius%5C%5C%0A%5Ctheta%20%3Dangle~in%5C%5C%0A%5Cqquad%20degrees%5C%5C%0A------%5C%5C%0Ar%3D3%5C%5C%0A%5Ctheta%20%3D45%0A%5Cend%7Bcases%7D%0A%5C%5C%5C%5C%5C%5C%0AA%3D%5Ccfrac%7B3%5E2%7D%7B2%7D%5Cleft%5B%20%5Ccfrac%7B%5Cpi%2845%29%20%7D%7B180%7D%20-%20sin%2845%5Eo%29%20%5Cright%5D%5Cimplies%20A%3D%5Ccfrac%7B9%7D%7B2%7D%5Cleft%5B%20%5Ccfrac%7B%5Cpi%20%7D%7B4%7D-%5Ccfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%20%5Cright%5D%0A%5C%5C%5C%5C%5C%5C%0AA%3D%5Ccfrac%7B9%7D%7B2%7D%5Cleft%28%20%5Ccfrac%7B%5Cpi%20-2%5Csqrt%7B2%7D%7D%7B4%7D%20%5Cright%29%5Cimplies%20A%5Capprox%200.3523112199491)
so the chord is the one in red there, making the segment, in green there, with a central angle of 45°, and the minor segment will be that green one.