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zzz [600]
3 years ago
8

An ornithologist who specializes in cockatoos in Australia decides to estimate the cockatoo population in a certain region. To d

o so, he traps 54 cockatoos and marks them. After releasing the cockatoos and waiting a bit, he traps 290 cockatoos and observes that 29 of them are marked. To the nearest whole number, what is the best estimate for the cockatoo population?
Mathematics
2 answers:
Jet001 [13]3 years ago
8 0

Answer:

540

Step-by-step explanation:

Let the estimate total population=y

Initially, out of a total of y, 54 are marked.

Then out of a sample of 290 cockatoos, 29 of them are marked.

We take the ratio of the population to the sample and do same for the number of marked in each category.

y:290 = 54: 29

\frac{y}{290}=\frac{54}{29}

Cross multiplying

y X 29 = 290 X 54

Divide both sides by 29 to obtain y.

\frac{y X 29}{29}=\frac{290 X 54}{29}

y= 54 X 10 =540

The best estimate of the cuckatoo population is 540

gogolik [260]3 years ago
4 0

Answer:

the population size is 540 cockatoos

Step-by-step explanation:

Denoting P as the total population , since the person took the 54 cockatoos and mark them , after he released them there are a proportion of marked cockatoos in the population equal to

proportion of marked cockatoos = marked cockatoos / total number of cockatoos = 54 / P

then if he takes a sample , if we assume that the marked cockatoos are well mixed around the population and each cockatoo has the same probability of being trapped  , then if we take cockatoos at random , is almost likely that he traps cockatoos in the same proportion , then

proportion of marked cockatoos = 29/290 = 54/P

P= 54 * 290 / 29 = 540 cockatoos

Note

- Mathematically , is the same that saying that each sample has the the same probability of being chosen.

- Actually if the traps 290 cockatoos out of 540 , the actual probability can be calculated through an hypergeometric distribution whose most probable value of the population size is 540 cockatoos

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Troyanec [42]

Answer:

[\frac{\pi}{2},\frac{3\pi}{2}]

Step-by-step explanation:

Let me first state that I am assuming your function is

f(x)=7cos^2(x)-14sin(x)

If this is incorrect, then disregard this whole answer/explanation.

In order to find where the function is increasing or decreasing, we need to first find the first derivative, set it equal to 0, and then factor to find the values that cause the derivative to equal 0.  This is where you expect to find a max or a min value in the function itself.  But this function is not going to be easily solved for 0 once we find the derivative unless we make it in terms of either sin or cos right now, before taking the first derivative.  

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Rewriting:

f(x)=7(1-sin^2(x))-14sin(x) which simplifies to

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We will set that equal to zero and solve for the values that cause that derivative to equal 0.  But first we can simplify it a bit.  You can factor out a -14cos(x):

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Those intervals are

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f'(\pi)=+ so the function is increasing here.

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Equation

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