Amessage center receives calls from 6 p. m. until 6 a. m. typically, 50% of the calls come in between 6 p. m. and 9 p. m.; 25% of the calls come in between 9 p. m. and midnight; 20% of the calls come in between midnight and 3 a. m.; and 5% of the calls come in between 3 a. m. and 6 a. m. what is the probability that a call will come in between 6 p. m. and midnight? question 5 options: 25% 50% 55% 75%

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