Students in a political science course were asked to describe their politics as "Liberal", "Moderate", or "Conservative." Here are the results: Politics Liberal Moderate Conservative Total Female 27 34 15 76 Male 39 53 19 111 Total 66 87 34 187 Given that the student is female what is the probability that she considers herself to be a "Liberal"? Round your answer to three decimal places if necessary. a. 0.351 c. 0.409 b. 0.353 d. 0.355

I think the answer is d. 0.355

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

so the possibilities of the measurement of the side of the triangle are either it is longest side or not the longest side

when it is the longest side

s < 25 + 35s < 60

if it is not the longest side

35 < 25 + s10 < sso 10 < s < 60so the perimeter70 < p < 130