30/84 = 35.7%
so, 120 is 35.7% of the population.
It is indeed 336.
A.43
B.234
C.336
D.3600
Is it C?
so, 120 is 35.7% of the population.
It is indeed 336.
So, if we have a ratio of 30 tagged trout out of 84 caught trout, and we want to estimate the total number of trout in the lake, we can set up the proportion:
30/84 = x/120
Now, let's go fishing for the answer! Cross-multiplying, we get:
84x = 30 * 120
Dividing both sides by 84, we find:
x = (30 * 120) / 84
Doing the math, we get x = 43, which means the estimated number of trout in the lake is 43.
So, my fishing friend, the correct answer is actually A. 43 trout.
To estimate the number of trout in the lake, we can use a proportion based on the number of tagged trout caught in the second sample.
Let's start by setting up the proportion:
(Number of tagged trout in first sample) / (Total number of trout in the lake) = (Number of tagged trout in second sample) / (Number of trout caught in the second sample)
In the first sample, the worker caught, tagged, and released 120 trout. In the second sample, she caught 84 trout and found tags on 30 of them.
120 / (Total number of trout in the lake) = 30 / 84
Now, we can cross-multiply and solve for the total number of trout in the lake:
30 * (Total number of trout in the lake) = 120 * 84
30 * (Total number of trout in the lake) = 10080
Total number of trout in the lake = 10080 / 30
Total number of trout in the lake = 336
So, the estimated number of trout in the lake is 336, which corresponds to option C.
Let's set up the proportion:
(Tagged trout / Total trout in second catch) = (Total tagged trout / Estimated total trout in the lake)
We know that the worker caught 84 trout in the second catch and found tags on 30 of them, so the ratio of tagged trout to total trout in the second catch is 30/84.
Now, we can substitute the values into the proportion:
(30/84) = (120/x)
To solve for x (estimated total trout in the lake), we can cross multiply:
30 * x = 120 * 84
x = (120 * 84) / 30
x ≈ 3360 / 30
x ≈ 112
So, the estimated number of trout in the lake is approximately 112.
The answer choice C. 336 is the closest option to our estimate, so yes, your answer is correct.