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vampirchik [111]
3 years ago
6

American kestrels live in More Mesa near your professor’s house. Suppose that there are 100 birds, of which a random sample of s

ize 20 your professor has captured and tagged (\simple random sample means that all 100 20 sets of 20 birds are equally likely). The captured birds are returned to the population, and then a new sample is drawn, this time with size 10. This is an important method that is used in ecology, known as capture-recapture. What is the probability that exactly 3 of the 10 birds in the new sample were previously tagged?
Mathematics
1 answer:
Ulleksa [173]3 years ago
5 0

Answer:

P(X=3) = 0.2013

Step-by-step explanation:

After taking and tagging the first 20 birds, then we have a proportion of 20% of tagged birds within the population, that is

p=\frac{n}{N}

p=\frac{20}{100}=0.20

Supposing that the probability (0.20) of capturing a bird <em>remains constant</em>, we may resolve it as it follows:

Capturing 10 birds can be considered as a binomial experiment with a success probability p = 0.2

Let, P(X=x)=nCx*p^{x}*(1-p)^{n-x} be the expression of the binomial distribution, for our case we have:

p=0.2

x = 3

n=10

Then,

P(X=3)=10C3*0.2^{3}*0.8^{10-3}

P(X=x)=0.2013

Therefore, the probability that exactly 3 of the 10 birds in the new sample were previously tagged is 20.13%

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Marizza181 [45]

Answer:

328 feet

Step-by-step explanation:

From a boat ont he lake, the angle of elevation to the top of a cliff is 11° 50'. If the base of the cliff is 1568 feet from the boat, how high is the cliff (to the nearest foot)

Step 1

Note that

that 11°50' is just 11 degrees and 50 minutes

60 minutes = 1 degree,

thus 50 minutes = x degree

50/60 degrees

= 0.83°

Hence: 11°50' = 11.83°.

Step 2

We solve using Trigonometric function of tan

tan theta = Opposite/Adjacent

theta = 11.83°

Adjacent = 1568 feet

Opposite = Height of the cliff = x

tan 11.83° = x/1568

Cross Multiply

x = tan 11.83 × 1568

x = 328.429195 feet

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The height of the cliff is 328 feet

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3 years ago
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Mkey [24]

Answer:

Step-by-step explanation:

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2 years ago
In triangle ABC, the size of angle B is 5 times the size of angle A, and the size of angle C is 7 less than 4 times the size of
kipiarov [429]
It sounds like everything is being described in reference to angle A, so a good starting point is to pick a variable to represent the measure of angle A. I'm going to use "a" for that.

Next, I'm going to take the verbal descriptions in the problem and "translate" them into "math language". They say angle B is 5 times angle A, so that means the measure of angle B is actually 5a. The size of angle C is 5 degrees less than 4 times the size of A, so that translates to 4a-5.

We now know the following:

Angle A: a
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Angle C: 4a-5

Now, to find the value of a, we need to remember that all the angles in a triangle add up to 180 degrees.

So we have: a+5a+4a-5 = 180

We can solve that equation by combining like terms to get: 10a-5=180

We can add 5 to both sides: 10a =185

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That tells us the measure of angle A! (It's 18.5 degrees). Now we can go back and find B by multiplying A by 5. We get 92.5 degrees for that.

Finally, we can find C by taking 4*18.5-5. We get 69 degrees for that.

One last thing-- let's check that they really do add up to 180! 69+92.5+18.5 = 180. Yep!

Hope that helps you!!
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3 years ago
Which expression represents five more than one-third y?
MaRussiya [10]

Answer:

1/3 y  +5

Step-by-step explanation:

five more than one-third y

1/3 y  +5

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I think is true

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