Using proportions, it is found that the best estimate for the goose population is of 690.
A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, out of 460 geese, 34 had tags. How many geese are there when 51 have tags? The rule of three is given by:
34 tags - 460 geese
51 tags - n geese
Applying cross multiplication:
34n = 460 x 51
n = 460 x 51/34
n = 690.
The best estimate for the goose population is of 690.
More can be learned about proportions at https://brainly.com/question/24372153