Out of the 400 students in the final year in senior high school, 300 are offering Biology and 190 are offering Chemistry.

How many students are offering both Biology and Chemistry, if only 70 students are offering neither Biology nor Chemistry?
How many students are offering at least one of Biology or Chemistry?

To find the number of students offering both Biology and Chemistry, we can subtract the number of students offering neither Biology nor Chemistry (70) from the total number of students (400): 400 - 70 = <<400-70=330>>330

Next, we can find the number of students offering at least one of Biology or Chemistry by adding the number of students offering Biology and the number of students offering Chemistry: 300 + 190 = <<300+190=490>>490. Answer: \boxed{330}.