Dilutions take perpendicular lines to perpendicular lines

Look at arnold's attempt to solve the equation for b: 3b = 12 b = 3 · 12 b = 36 describe the mistake that arnold made.

The distribution of the amount of money spent by students for textbooks in a semester is approximately normal in shape with a mean of $235 and a standard deviation of $20. according to the standard deviation rule, how much did almost all (99.7%) of the students spend on textbooks in a semester?

Parabolas y=−2x^2 and y=2x^2+k intersect at points a and b that are in the third and the fourth quadrants respectively. find k if length of the segment ab is 5.