Chances at UT?

Stats:
79/620
SAT:1470 (680 r/w and 790 M)
Competitive hs

Major intended:
1st option Business
2nd option Mathematics

Since you are not in the top 7% of your class, UT will be a reach. I do think you have positive things going for you - a high SAT score especially in math and your choice of majors. I think you have a shot at both majors. That being said, make sure you apply to other schools. You could consider all other public schools as safeties with possible scholarships.