Re: The number of
I would use "are". Effectively, you have said "The number of cars and the number of car accidents ..." so that's a total of two "numbers", therefore use the plural. It's easy to see why people would simply look at "The number" and assume it would be followed by "is" but you need to check the rest of the sentence.
Originally Posted by Snappy
The number of cars is increasing.
The number of car accidents is increasing.
The number of cars and accidents are increasing.
You might even hear "The numbers of cars and car accidents are increasing".
Remember - correct capitalisation, punctuation and spacing make posts much easier to read.