Evaluate the determinant for the following matrix: -4 -4 -3 3 3 -5 -5 2 -5 a. 75 b. -203 c. -263 d. -152

The depth of a lake at a certain point, wich is a function of the distance of that point from shore, is 30 feet.

As part of an annual fundraiser to raise money for diabetes research, diane joined a bikeathon. the track she biked on was 1,920 yards long. diane biked 38.5 laps. her sponsors agreed to donate an amount of money for each mile she biked. how many miles did she bike? first fill in the blanks on the left side using the ratios shown. then write your answer. given ratios: 5280ft / 1 mi , 1 mi /5280 ft , 1,920 yards / 1 lap , 1 lap / 1,920 yards , 3 ft / 1 yard , 1 yard / 3 ft. blanks: 38.5 laps / 1 yard x (blank) x (blank) x (blank) = (blank) miles i'm really confused on how to do this, and the explanations aren't exactly . if you could walk me through how to do this, it would be greatly appreciated.

If f(x)=3x+1 and f^-1=x-1/3, then f^-1(7)=