Step 1 :The empirical probability of an event is calculated by dividing the number of times the event occurs by the total number of trials. In this case, the total number of boat rentals is 42, and we are asked to find the empirical probability of renting a sunfish, a kayak, and a rowboat.
Step 2 :We can calculate these probabilities by dividing the number of each type of boat rental by the total number of rentals.
Step 3 :The empirical probability that the next boat rental is a sunfish is calculated as follows: \( \frac{22}{42} \) which simplifies to approximately 0.52.
Step 4 :The empirical probability that the next boat rental is a kayak is calculated as follows: \( \frac{6}{42} \) which simplifies to approximately 0.14.
Step 5 :The empirical probability that the next boat rental is a rowboat is calculated as follows: \( \frac{14}{42} \) which simplifies to approximately 0.33.
Step 6 :Final Answer: \n a) The empirical probability that the next boat rental is a sunfish is \( \boxed{\frac{22}{42}} \) or approximately \( \boxed{0.52} \).\n b) The empirical probability that the next boat rental is a kayak is \( \boxed{\frac{6}{42}} \) or approximately \( \boxed{0.14} \).\n c) The empirical probability that the next boat rental is a rowboat is \( \boxed{\frac{14}{42}} \) or approximately \( \boxed{0.33} \).