Tahrell has nutrition classes every 5 days and respiratory therapy classes every 9 day. If he had nutrition and respiratory therapy classes on October 19, on which date w he have both classes again? Assume the year is not a leap year.

1. The nutrition classes are every \(5\) days and the respiratory therapy classes every \(9\) days. The classes will occur on the same day again after a number of days equal to the least common multiple of \(5\) and \(9\). 2. Compute the least common multiple: \[ \text{LCM}(5, 9) = 45 \] 3. Therefore, both classes will be held on the same day \(45\) days after October \(19\). 4. To find the new date, start by determining the number of days remaining in October: \[ 31 - 19 = 12 \text{ days} \] 5. Out of the \(45\) days, \(12\) days take you to October \(31\). The remaining days are: \[ 45 - 12 = 33 \text{ days} \] 6. November has \(30\) days. Subtracting these: \[ 33 - 30 = 3 \text{ days} \] 7. After November comes December, and \(3\) days into December is: \[ \text{December }3 \] Thus, Tahrell will have both classes again on **December \(3\)**.