apple cider vinegar - is it true if you soak fresh vegetables in apple
cider vinegar for 10 minutes before cooking that 90% of pesticides can
disappear. If so, what ratio for dilution would you use.

It probably works with water as well. 

But you likely don't need to bother as most commonly used
organophosphates break down pretty quickly. As you veggies are quite a
few days from the land from whence they came, the pesticides are gone.
I would expect federal law requires certain withdrawal periods for
pesticides much as they do for drugs in food animals.

And we all know we can trust our leaders in the US, right? These same
good folks who said the air at the World Trade Center site was safe to
breathe and that Saddam was an imminent danger and pay no attention to
the man behind the curtain!

Sorry, feeling a bit cynical today. Well, more cynical than usual.

Here in Germany last week, I read an brief article that said that
washing vegitables in cold water was as effective as using warm water
to remove pesticides.
Furthermore, although the US government may not be trusted, I think we
would have heard about any real problems from pesticides  - not just
fears about theoretical potential problems.

I would be more worried about what you put in your hair then
pesticides on your vegetables. Actually you can remove 98 percent of
the pesticide just by washing and scrubbing the vegetable. Also,
another thing you can you do is buy ORGANIC.