Step 1 :The problem provides the standard quotas for city council seats for the five boroughs as follows: Manhattan: 23.67, The Bronx: 8.95, Queens: 10.51, Brooklyn: 11.09, Staten Island: 2.53.
Step 2 :We are asked to use Adams's apportionment plan to round the quota given for Brooklyn. Adams's apportionment method is a type of apportionment method used to distribute seats proportionally. It works by iteratively decreasing a divisor until the rounded quotas sum to the total number of seats.
Step 3 :However, in this question, we are not given a total number of seats. We are only asked to round the quota for Brooklyn. Since we don't have a total number of seats, we can't apply the full Adams's method. But we can apply the rounding part of the method.
Step 4 :In Adams's method, quotas are always rounded down. So, we need to round down the quota for Brooklyn.
Step 5 :The quota for Brooklyn is 11.09. When we round down, we get 11.
Step 6 :Final Answer: The rounded quota for Brooklyn according to Adams's apportionment plan is \( \boxed{11} \).