Answer:
Step-by-step explanation:
Surface area of sphere = 125 sq.ft
4πr² = 125
4*3.14*r² = 125
r = 3.15 ft
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1 answer:
9514 1404 393
Answer:
(a) vertical compression by a factor of 1/3
Step-by-step explanation:
We can see that g(x) = 1/3f(x). Multiplying a function by a constant scales the graph vertically by that factor. When the magnitude of the factor is more than 1, we say the graph is "stretched." When it is less than 1, we say the graph is "compressed" by that factor.
Here, the scale factor is 1/3, so the graph is "vertically compressed by a factor of 1/3."
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<em>Additional comment</em>
My <em>personal</em> preference is for compression to be described by the factor the graph is divided by. I would call g(x) a compression of f(x) by a factor of 3. Modern curriculum authors disagree, calling it compression by a factor of 1/3.
Be careful. Using the currently accepted language, a <em>stretch</em> is always by a number <em>larger than 1</em>, and a <em>compression</em> is always by a number <em>less than 1</em>. This rules out choices C and D simply on the basis of the language used.
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For many graphs, vertical scaling and horizontal scaling can be interchanged. We note that g(x) is wider than f(x), so could be stretched horizontally by some factor. That factor would be √3. The equation using a horizontal stretch factor would be g(x) = (x/√3)^2. Replacing x by x/k is a stretch by a factor of k in the horizontal direction.
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Answer:
(a)
(b)
(c)
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:
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:
Now, the probability of getting exactly 5 granite specimens selected for analysis is:
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:
For the hypergeometric distribution, the mean E(x) and standard deviation S(x) are:
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: