Final answer:
Pablo teaches salsa lessons from 12 pm to 9 pm. The domain, representing the hours 't' he can teach after 3 pm, is the set {0, 1, 2, 3, 4, 5, 6}, which translates to the inequality 0 ≤ t ≤ 6.
Step-by-step explanation:
Pablo charges $20 an hour for teaching salsa lessons and works from 12 pm to 9 pm. To calculate the amount of money 'G' he makes in 't' hours, starting after 3 pm, we can express this as a function of time, given his hourly rate.
Understanding the Domain
The domain in this context is the set of all possible values of 't', the number of hours Pablo can work starting from 3 pm until 9 pm. Since he cannot start before 3 pm or end after 9 pm, and given that he charges hourly, 't' must be an integer between 0 and 6. Therefore, the domain of 't' is {0, 1, 2, 3, 4, 5, 6}.
Finding the Inequality
To represent this as an inequality, consider that 't' is greater than or equal to 0 and less than or equal to 6. This gives us the inequality 0 ≤ t ≤ 6. Here, the lower bound of 0 represents the earliest time Pablo can start teaching after 3 pm without working any hours, and the upper bound of 6 represents the latest time until which he can work starting from 3 pm until the closing time of 9 pm.