on monday biologists tagged 100 sunfish from a lake.on friday the biologists counted 12 tagged fish out of a sample of 400 sunfish from the same lake.estimate the total number of sunfish in the lake

total number of fish --- x

use a simple ratio:

x/100 = 400/12
x = 100(400/12) = appr 3333 fish

To estimate the total number of sunfish in the lake, we can use the concept of a proportion.

Let's assume that the ratio of tagged fish in the sample represents the same ratio in the entire population of sunfish in the lake.

Given that the biologists tagged 100 sunfish and found 12 tagged fish out of a sample of 400, we can set up the following proportion:

(12 tagged fish) / (400 total fish) = (100 tagged fish) / (x total fish in the lake)

Cross-multiplying, we have:

12 * x = 400 * 100

Simplifying, we get:

12x = 40,000

Dividing both sides by 12, we find:

x = 40,000 / 12

x ≈ 3333.33

Therefore, we can estimate that there are approximately 3333 sunfish in the lake.

To estimate the total number of sunfish in the lake, we can use a proportion.

Step 1: Determine the proportion of tagged fish in the sample.
To find the proportion of tagged fish in the sample, divide the number of tagged fish by the total number of fish in the sample:
Proportion of tagged fish = (Number of tagged fish in the sample) / (Total number of fish in the sample) = 12 / 400 = 0.03

Step 2: Apply the proportion to the total population.
Since the proportion of tagged fish in the sample represents the proportion of tagged fish in the entire population, we can set up a proportion using the known number of tagged fish and the estimated total number of sunfish in the lake.
Proportion of tagged fish = (Number of tagged fish in the sample) / (Total number of fish in the lake)

Let's use "x" to represent the total number of sunfish in the lake. We already know that there were 100 tagged fish in the lake.

0.03 = 100 / x

Step 3: Solve for x.
To find x (the total number of sunfish in the lake), we can cross-multiply and solve for x.

0.03x = 100
x = 100 / 0.03
x ≈ 3333.33

Therefore, we can estimate that there are approximately 3,333 sunfish in the lake.