The following geometric sequences represent the populations of two bacterial cultures at the 1-hour mark, the 2-hour mark, the 3-hour mark, and so on. Culture A starts with more bacteria, but culture B has a ratio of increase that is larger. Which culture will have the greater population at the 18-hour mark? (A P E X)

answer: all of the odd numbers were opened

the first person was the one that was opening all of the lockers. since one is odd, this causes all of the odd number lockers to be opened in the end.

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step-by-step explanation:

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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