Wildlife biologists catch, tag, and release 32 bears at a game reserve. Later,10 bears are caught and 4 of them have tags. Estimate the total number of bears at the game reserve.
A.320
B.316
C.128
D.80
Is the answer D?
40% of the caught bears are tagged.
So, 32 is 40% of what number?
You are correct. It is 80.
No, the answer is not D. That would mean that bears are really good at playing hide and seek! But don't worry, I'm here to help you with the correct answer. Let's break it down:
We know that 32 bears were originally caught, tagged, and released. Later, 10 bears were caught and 4 of them had tags. This means that out of the 10 bears caught later, 4 of them were already tagged, so we can assume that they were part of the original 32 bears.
To estimate the total number of bears at the game reserve, we can use a proportion:
32 tagged bears / 10 total caught bears = x tagged bears / total number of bears in the reserve
Simplifying the proportion, we get:
32/10 = x/total number of bears
Cross multiplying, we get:
10x = 32 * total number of bears
10x = 32b
Now, solving for x, we divide both sides by 10:
x = (32b)/10
Since we want to estimate the total number of bears, we can assume that the proportion found above represents the entire population, so x would be equal to the total number of bears.
x = (32 * 10)/10
x = 32
Therefore, the estimated total number of bears at the game reserve is 32. So, the correct answer is not D, but rather C. I hope this clears things up for you!
No, the answer is not D. To estimate the total number of bears at the game reserve, we can use a proportion:
(Number of tagged bears in the second catch / Total number of bears in the second catch) = (Number of tagged bears in the first catch / Total number of bears in the first catch)
Let's plug in the given information:
(4 / 10) = (32 / X)
Cross-multiplying, we get:
4X = 10 * 32
4X = 320
X = 320 / 4
X = 80
Therefore, the estimate of the total number of bears at the game reserve is 80.
The correct answer is D.
To estimate the total number of bears at the game reserve, we can use a proportion based on the number of tagged bears in the second sample and the total number of bears in the reserve.
Let's set up the proportion:
(Number of tagged bears in the second sample) / (Total number of bears in the reserve) = (Number of tagged bears in the initial sample) / (Total number of bears in the initial sample)
We know that 10 bears were caught in the second sample and 4 of them had tags.
So the proportion becomes:
4 / (Total number of bears in the reserve) = 4 / 10
To solve for the total number of bears in the reserve, we can cross-multiply:
4 * 10 = 4 * (Total number of bears in the reserve)
40 = 4 * (Total number of bears in the reserve)
Now divide both sides of the equation by 4 to isolate the total number of bears in the reserve:
40 / 4 = (Total number of bears in the reserve)
10 = (Total number of bears in the reserve)
Therefore, the estimate for the total number of bears at the game reserve is 10.
The correct answer choice is not provided in the options given.