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If the average (arithmetic mean) of x2 and y2 is 47, and xy = 3, what
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27 Dec 2021, 12:53
27 Dec 2021, 12:53
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If the average (arithmetic mean) of \(x^2\) and \(y^2\) is 47, and xy = 3, what is the average of the positive values of x and y?
(A) 1.5
(B) 3
(C) 5
(D) 10
(E) 15
(A) 1.5
(B) 3
(C) 5
(D) 10
(E) 15
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Re: If the average (arithmetic mean) of x2 and y2 is 47, and xy = 3, what
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27 Dec 2021, 20:49
27 Dec 2021, 20:49
1
Given that Average of \(x^2\) and \(y^2\) is 47 and xy = 3 and we need to find the average of x and y
Theory: Average = \(\frac{Sum Of All The Numbers In The Set }{ Total Number Of Numbers In The Set}\)
Average of x and y = \(\frac{x+y }{ 2}\)
Average of \(x^2\) and \(y^2\) = \(\frac{x^2 + y^2 }{ 2}\) = 47
=> \(x^2 + y^2\) = 47*2 = 94
and xy = 3
Now, we know that \((x+y)^2 = x^2 + y^2 + 2xy \)
=> \((x+y)^2\) = 94 + 2*3 = 94 + 6 = 100
=> x + y = \(\sqrt{100}\) = 10 (as we are asked about the positive values of x and y)
=> Average of x and y = \(\frac{x+y }{ 2}\) = \(\frac{10}{2}\) = 5
So, Answer will be C
Hope it helps!
Watch the following video to Learn the Basics of Statistics
Theory: Average = \(\frac{Sum Of All The Numbers In The Set }{ Total Number Of Numbers In The Set}\)
Average of x and y = \(\frac{x+y }{ 2}\)
Average of \(x^2\) and \(y^2\) = \(\frac{x^2 + y^2 }{ 2}\) = 47
=> \(x^2 + y^2\) = 47*2 = 94
and xy = 3
Now, we know that \((x+y)^2 = x^2 + y^2 + 2xy \)
=> \((x+y)^2\) = 94 + 2*3 = 94 + 6 = 100
=> x + y = \(\sqrt{100}\) = 10 (as we are asked about the positive values of x and y)
=> Average of x and y = \(\frac{x+y }{ 2}\) = \(\frac{10}{2}\) = 5
So, Answer will be C
Hope it helps!
Watch the following video to Learn the Basics of Statistics
Re: If the average (arithmetic mean) of x2 and y2 is 47, and xy = 3, what
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28 Oct 2023, 19:41
28 Oct 2023, 19:41
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