Assume that Sunday is represented as day 0 , Monday is represented by day 1 , and so on. If today is Tuesday (day 2 ), determine what day of the week it will be 393 days after today. What is the day of the week 393 days after Tuesday? \( \square \) (Type your answer as a day of the week.)

We start by noting that the days of the week cycle every \(7\) days. Thus, to find the day of the week after \(393\) days, we determine the remainder when \(393\) is divided by \(7\): \[ 393 \div 7 = 56 \text{ remainder } 1 \] This means: \[ 393 \equiv 1 \pmod{7} \] Since today is Tuesday (day \(2\)), after \(393\) days, the day of the week will be: \[ 2 + 1 = 3 \pmod{7} \] Given the numbering: - \(0\) represents Sunday, - \(1\) Monday, - \(2\) Tuesday, - \(3\) Wednesday, the day corresponding to \(3\) is **Wednesday**.