An insurance company only pays for full replacement if a driver is in a wreck and is traveling a speed not deemed to be reckless. A speed of 80
mph or greater is considered reckless. Mallory has an accident and has
filed an insurance claim. The insurance uses a standard constant of
proportionality of .05 and she has a stopping distance of 245 feet. Will her
insurance provide a full replacement of her car? Explain why or why not
and show all work.

70 mph, Yes the insurance company Will provide a full replacement for her car.

Step-by-step explanation:

To get the equation lets use direct variation, and K for the constant, S for the speed, and D for the stopping distance. d=ks^2, find s, or the speed, which will get the equation s=√d/k. The speed s, is equal to the square root of the stopping distance divided by the constant. Next, lets plug in the numbers s=√245/.05. Then, we find the square root of each number, √245 = ~15.652, and √.05 ~.2236  s=15.652/.2236 then divide, which will equal s=70. 70<80, so the insurance company will provide a full replacement for her car.

I hope this helps!