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Which of the following is equal to the average (arithmetic mean) of
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04 Aug 2021, 06:56
04 Aug 2021, 06:56
1
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Question Stats:
89% (00:40) correct
10% (00:47) wrong based on 29 sessions
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Which of the following is equal to the average (arithmetic mean) of \((x+3)^2\) and \((x-3)^2\) ?
A. \(x^2\)
B. \(x^2+3
\)
C. \(x^2+9\)
D. \(x^2+3x\)
E. \(x^2+9x
\)
A. \(x^2\)
B. \(x^2+3
\)
C. \(x^2+9\)
D. \(x^2+3x\)
E. \(x^2+9x
\)
Re: Which of the following is equal to the average (arithmetic mean) of
[#permalink]
04 Aug 2021, 07:00
04 Aug 2021, 07:00
1
(x + 3)^2 = x^2 + 9 + 6x
(x - 3)^2 = x^2 + 9 - 6x
((x + 3)^2 + (x - 3)^2)/2 = 2 * (x^2 + 9)/2 = (x^2 + 9)
(x - 3)^2 = x^2 + 9 - 6x
((x + 3)^2 + (x - 3)^2)/2 = 2 * (x^2 + 9)/2 = (x^2 + 9)
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Re: Which of the following is equal to the average (arithmetic mean) of
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04 Aug 2022, 00:04
04 Aug 2022, 00:04
Theory
The average (arithmetic mean) of \((x+3)^2\) and \((x-3)^2\)
Average = \(\frac{Sum}{2}\) = \(\frac{(x+3)^2 + (x-3)^2 }{ 2}\) = \(\frac{x^2 + 2*x*3 + 3^2 + x^2 - 2*x*3 + 3^2}{ 2}\) =\(\frac{ 2*(x^2 + 9)}{2}\) = \(x^2 + 9\)
So, Answer will be C.
Hope it helps!
Watch the following video to Learn the Basics of Statistics
- ➡ Average = Sum of all the Values / Total Number of Values
The average (arithmetic mean) of \((x+3)^2\) and \((x-3)^2\)
Average = \(\frac{Sum}{2}\) = \(\frac{(x+3)^2 + (x-3)^2 }{ 2}\) = \(\frac{x^2 + 2*x*3 + 3^2 + x^2 - 2*x*3 + 3^2}{ 2}\) =\(\frac{ 2*(x^2 + 9)}{2}\) = \(x^2 + 9\)
So, Answer will be C.
Hope it helps!
Watch the following video to Learn the Basics of Statistics
