I'm getting dressed in the dark, and i have 6 pairs of white socks and 6 pairs of black socks, but they're all mixed up in my sock drawer. how many socks will i need to blindly pull out to ensure that i get five pairs of white socks?

To ensure to get five pairs of white socks, I need to pull out at least 11 pairs of socks from my sock drawer.

Step-by-step explanation:

There are 6 pairs of white socks and 6 pairs of black socks mixed up in my sock drawer. If I want to ensure to get five pairs of white socks, I need to pull out at least (6 + 5) = 11 pairs of socks since at most there can be 6 pairs of black socks in my chosen set of socks.

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

where is the diagram? shown below where? ?

step-by-step explanation: