But ... those families with one child will constitute half of all families! And the families with more males than females constitute only a quarter....
I like combinatorial proofs like this (counting the same thing in two ways), so I knew immediately what sort of thing I expected to do. But I didn't...
Before we can properly help you, we'll need to know what help you need. Asking people to solve eight whole problems for you is not the way to ask for...
Yes, that's the second key idea. Although ABC and ABD are not themselves similar, their altitudes are also the altitudes of other triangles that are...
It can be done much more simply than that. Once you have the lengths from part (a), you just need the fact that triangles on the same base have areas...
I'm having trouble finding a clear definition of the LRA system, but I think all you're asking for is the angle you marked, and that's pretty easy.
...
I was a software engineer for many years, and have been teaching at a community college since 2004. Since 1998, I was a part of Ask Doctor Math (http://mathforum.org/dr.math/ and now http://themathdoctors.org/).