As an odometer check, a special counter measures the miles a car travels modulo 7. explain how this counter can be used to determine whether the car has been driven 49,335; 149,335; or 249,335 miles when the odometer reads 49,335 and works modulo 100,000.

249335 miles

Step-by-step explanation:

Let x be the number of miles the car has travelled.

The odometer can only tell us that x≡49335(mod 100000).

If we also know the value of c where x≡c(mod 7)and 0≤c<7 by the Chinese remainder theorem we know the congruence satisfied by x modulo 100000•7 = 700000.

As long as the car has been driven less that 700000 this uniquely determines the number of miles driven.

In particular, we easily see that if x≡6 (mod 7)then the car was driven 49335 miles, if x≡4 (mod 7)then the car was driven 149335 miles, and if x≡2 (mod 7)then the car was driven 249335 miles

12m

step-by-step explanation:

square root means have of a number so have of 3 is 1.5 then multiply it by 8 and you get your answer!

7 ft 6 in means 7 1/2, because 6 in is 1/2 of a foot. 7 ft 8 in means 7 2/3 because 8 in is 2/3 of a foot. 23/3 = 7 2/3. 15/2 = 7 1/2.

23/3   *   15/2   = 57 1/2

step-by-step explanation: