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yaroslaw [1]
3 years ago
15

Will give brainliest

Mathematics
1 answer:
EleoNora [17]3 years ago
8 0

Answer:

Because the sin function is positive in the first and second quadrants.

Step-by-step explanation:

We are told that sin(A) = 0.422

Thus;

A = sin^(-1) 0.422

A = 25°

Now,this is just for the first quadrant because this angle could very well be in another quadrant.

Usually in four quadrants of an x-y coordinate, the sin function is negative in the third and fourth quadrants because the x- values there are negative and sin is opposite/hypotenuse. That will lead to a negative value of Sin A since hypotenuse is always positive while the x-values in these quadrants are negative.

So, sin function is positive in the first and second quadrant.

In the first quadrant, it's 25°, however in the second quadrant where it is below the x-axis, the angle will now be: 180° - 25° = 155°

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5 0
2 years ago
Geologist has collected 10 specimens of basaltic rock and 10th specimens of granite. The geologist instructs a laboratory assist
olya-2409 [2.1K]

Answer:

p(5)=0.00136

(a) p(x)=\frac{(10Cx)*((10)C(15-x))}{20C10}

(b)p(10)+p(5)=0.00272

(c)p(7)+p(8)=0.0584

Step-by-step explanation:

If we have N elements with k elements that we consider success and N-k elements that we consider fail, and we take a sample of n elements, the probability that there are x successes in the sample follows a hypergeometric distribution, so it is calculated as:

p(x)=\frac{(kCx)*((N-k)C(n-x))}{NCn}

In this case, N is equal to 20, k is equal to 10 specimens of granite rock, N-k is equal to 10 specimens of basaltic rock and n is 15. So, the probability that there are x specimens of granite rock in the sample or the pmf of the number of granite specimens selected for analysis is:

p(x)=\frac{(10Cx)*((10)C(15-x))}{20C10}

Now, the probability of getting exactly 5 granite specimens selected for analysis is:

p(5)=\frac{(10C5)*((10)C(15-5))}{20C10}=0.00136

On the other hand, the probability that all specimens of one of the two types of rock are selected  for analysis is the probability to select 10 granite specimens or 10 basaltic specimens. Where the probability to take 10 basaltic specimens is equal to the probability to take 5 granite specimens.

Then, the probability that all specimens of one of the two types of rock are selected  for analysis is:

p(10)+p(5)=\frac{(10C10)*((10)C(15-10))}{20C10}+\frac{(10C5)*((10)C(15-5))}{20C10}\\p(10)+p(5)=0.00136+0.00136=0.00272

For the hypergeometric distribution, the mean E(x) and standard deviation S(x) are:

E(x)=\frac{nk}{N}=\frac{15*10}{20}=7.5\\S(x)=\sqrt{\frac{nk}{N}*(1-\frac{k}{N})*(\frac{N-n}{N-1})}\\S(x)=\sqrt{\frac{15*10}{20}*(1-\frac{10}{20})*(\frac{20-15}{20-1})}=0.9934

Then, the number of granite specimens within 1 standard deviation of its mean value is:

  E(x) - S(x) ≤ mean ≤ E(x) + S(x)

7.5-0.9934 ≤ mean ≤ 7.5+0.9934

     6.5066 ≤ mean ≤ 8.4934

               7 ≤ mean ≤ 8

Finally, the probability that the number of granite specimens selected for analysis is  within 1 standard deviation of its mean value is:

p(7)+p(8)=\frac{(10C7)*((10)C(15-7))}{20C10}+\frac{(10C8)*((10)C(15-8))}{20C10}\\p(10)+p(5)=0.0292+0.0292=0.0584

8 0
4 years ago
There are 65 chairs set up for a movie. they are arranged into 5. How many chairs are in each row
kati45 [8]
Answer;
13
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Answer:

3/2

Step-by-step explanation:

y2 - y1 / x2 - x1

1 - 7 / -5 - (-1)

-6 / -4

= 3/2

7 0
3 years ago
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Answer:

Both sides are equal so there are infinitely many  solutions.

Step-by-step explanation:

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2 years ago
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