$$ 1 \leftarrow \begin{array}{l} ext { Biologists tagged } 119 ext { fish in a lake on January 1. On February 1, they returned } \ ext { and collected a random sample of } 22 ext { fish, } 11 ext { of which had been previously } \ ext { tagged. On the basis of this experiment, approximately how many fish does the } \ ext { lake have? }\end{array} \quad \begin{array}{l} ext { HW Score: } 42.19 \%, 16.88 ext { of } 40 ext { points } \ ext { Points: } 0 ext { of } 1\end{array} $$

Question

$$ 1 \leftarrow \begin{array}{l}	ext { Biologists tagged } 119 	ext { fish in a lake on January 1. On February 1, they returned } \ 	ext { and collected a random sample of } 22 	ext { fish, } 11 	ext { of which had been previously } \ 	ext { tagged. On the basis of this experiment, approximately how many fish does the } \ 	ext { lake have? }\end{array} \quad \begin{array}{l}	ext { HW Score: } 42.19 \%, 16.88 	ext { of } 40 	ext { points } \ 	ext { Points: } 0 	ext { of } 1\end{array} $$

UpStudy AI · Accepted Answer

Let $$ N $$ be the total number of fish in the lake.

1. Initially, $$ 119 $$ fish were tagged.
2. On February 1, a sample of $$ 22 $$ fish was captured and $$ 11 $$ of them were tagged.
3. Assuming the tagged fish are uniformly distributed throughout the lake, the proportion of tagged fish in the sample is the same as the proportion in the lake:

$$
   \frac{11}{22} = \frac{119}{N}
   $$

4. Simplify the left-hand side:

$$
   \frac{11}{22} = \frac{1}{2}
   $$

So the equation becomes:

$$
   \frac{1}{2} = \frac{119}{N}
   $$

5. Solve for $$ N $$:

$$
   N = 119 \times 2 = 238
   $$

Therefore, the lake has approximately $$ 238 $$ fish.
The lake has approximately 238 fish.

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