jmc

Since $28=2^2\cdot 7$, a positive integer is relatively prime with $28$ if and only if it contains neither $2$ nor $7$ in its prime factorization. In other words, we want to count the number of integers between $11$ and $29$ inclusive which are divisible by neither $2$ nor $7$.

All of the odd numbers are not divisible by 2; there are 10 such numbers. The only one of these that is divisible by 7 is 21, so there are $10-1=\boxed{9}$ numbers between 10 and 30 that are relatively prime with 28.