The table shows the ways that you can win, lose, or tie in Rock Paper Scissors. You and your opponent throw the signs for rock, paper, or scissors at random. What percent of the time do you expect to win? Lose? Tie?

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Step-by-step explanation:

d

gimmee one of those gold crowns!

~coco

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4