Question

a country in africa is trying to restore its giraffe population and is carefully keeping track of how many giraffes are in the area. to do so, local wildlife authorities put tags on 20 giraffes and release them. later, they corral 570 giraffes; among these giraffes, 15 are tagged. to the nearest whole number, what is the best estimate for the giraffe population?

Explanation:

Step1: Set up proportion

Let \( N \) be the total giraffe population. The proportion of tagged giraffes in the sample should be equal to the proportion of tagged giraffes in the population. So we have \(\frac{20}{N}=\frac{15}{570}\).

Step2: Solve for \( N \)

Cross - multiply: \( 15N = 20\times570 \). Then \( N=\frac{20\times570}{15} \). First, calculate \( 20\times570 = 11400 \). Then divide by 15: \( N=\frac{11400}{15}=760 \).

Answer:

760