Melody

Draw a sketch of what you have and then use this to finish it.

Nope, I still do not follow your explanation Ginger.  Thanks for your effort though.

Your table of what can happen with any one turn is helpful and easy to understand.

After that I am lost.

I did go off on a tangent and found that in any 2 consecutive goes:

the prob of throwing 6 heads and NOT 2 sixes is  (50+5)/(48*48) = 55/2304

And the prob of throwing 2 sixes and NOT 6 heads is  (56+7)/(48*48) = 63/2304

I do not know what to do with that ...

I am just trying to show you my train of thought.

I do not care if you give up but if you want to explain what you are saying clearly I will try and understand.

Perhaps Pangolin14 has a class solution that can be shared with us both?

Hint:

A much easier way to look at this is

How many ways can i chose a man, a woman, and one more.     

the rest automatically go into the other group.

How do you think this can be done?

You are on the right track

Certainly a part of the denominator must be  (x+2)(x-4)

And given that (2,0) is on the graph, the numerator must have (x-2) in it.

Plus it looks a bit like a parabola, with a double root at x=2  so i suspect the numerator will be squared (I am not so sure that my logic is sound here)

Anyway so far I am thinking that it might be ..

\(y=\frac{k(x-2)^2}{(x+2)(x-4)}\\\)       where k is a constant.

It looks like it might go through (0, 0.4)

when x=0

LHS= 4k / -8 = -k/2

-k/2=0.4

k=-0.8

So maybe it is

\(y=\frac{-0.8(x-2)^2}{(x+2)(x-4)}\\\)

check:

This is certainly not completely correct but the diagram you have provided is not very good.

This is probably close enough.

Maybe  -1 would have looked a little closer than -0.8 .  The the y intercept would have been  0.5

You cannot prove it because it is not true.  I assume you have written the question incorrectly.

 You want to prove that AB^2 + BQ^2 = PQ^2. 

But AB is bigger than PQ so the statement to be proven  is not true

That is a really cool technique.  Thanks Tiggsy.

You are very welcome. :)

The mean score will always be a z score of 0

Lower than the mean will have negative z scores and higher will have positive z scores.

99.7% of all the scores will have z scores of between   -3 and  +3.

Both Ann and Bill did badly because their z score is negative (less than 0)

The one that is more unusual will be the one whose score is furthest from 0. 

In this case that worst one.  Which one is that?

Please do not post multiple questions or last minute homework.  

All you need to know is that

\(Sin(x)=cos(\frac{\pi}{2}-x)\)

If you think about any right-angle triangle you will see that this is true

(at least you will see it is true for acute angles).