Question

caden is a bird enthusiast and is trying to estimate the number of hawks living in his region. he traps 23 hawks and tags them. later, he traps 420 hawks, 14 of which are tagged. to the nearest whole number, what is the best estimate for the hawk population?

Explanation:

Step1: Set up proportion

Let \( N \) be the total hawk population. The proportion of tagged hawks in the first sample (tagged) to the total population should equal the proportion of tagged hawks in the second sample (trapped later) to the number trapped later. So we have \(\frac{23}{N}=\frac{14}{420}\).

Step2: Solve for \( N \)

Cross - multiply: \( 14N = 23\times420 \). First, calculate \( 23\times420=9660 \). Then, \( N=\frac{9660}{14} \).

Step3: Calculate the value

\(\frac{9660}{14} = 690\).

Answer:

690