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16 Sep 2014, 01:28
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If \(x^2 + 2x -15 = -m\), where \(x\) is an integer from -10 and 10, inclusive, what is the probability that \(m\) is greater than zero?
A. \(\frac{2}{7}\)
B. \(\frac{1}{3}\)
C. \(\frac{7}{20}\)
D. \(\frac{2}{5}\)
E. \(\frac{3}{7}\)
A. \(\frac{2}{7}\)
B. \(\frac{1}{3}\)
C. \(\frac{7}{20}\)
D. \(\frac{2}{5}\)
E. \(\frac{3}{7}\)
16 Sep 2014, 01:28
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Official Solution:
If \(x^2 + 2x -15 = -m\), where \(x\) is an integer from -10 and 10, inclusive, what is the probability that \(m\) is greater than zero?
A. \(\frac{2}{7}\)
B. \(\frac{1}{3}\)
C. \(\frac{7}{20}\)
D. \(\frac{2}{5}\)
E. \(\frac{3}{7}\)
Rearrange the equation given as follows: \(-x^2-2x+15=m\).
Given that \(x\) is an integer from -10 to 10, inclusive (a total of 21 values), we need to determine the probability that \(-x^2-2x+15\) is greater than zero. That is, we are looking for the probability where \(-x^2-2x+15 > 0\).
We can factorize the expression as \((x+5)(3-x) > 0\). This inequality holds true when \(-5 < x < 3\).
Since \(x\) is an integer, it can take on 7 values: -4, -3, -2, -1, 0, 1, and 2.
Therefore, the probability is \(\frac{7}{21}=\frac{1}{3}\).
Answer: B
If \(x^2 + 2x -15 = -m\), where \(x\) is an integer from -10 and 10, inclusive, what is the probability that \(m\) is greater than zero?
A. \(\frac{2}{7}\)
B. \(\frac{1}{3}\)
C. \(\frac{7}{20}\)
D. \(\frac{2}{5}\)
E. \(\frac{3}{7}\)
Rearrange the equation given as follows: \(-x^2-2x+15=m\).
Given that \(x\) is an integer from -10 to 10, inclusive (a total of 21 values), we need to determine the probability that \(-x^2-2x+15\) is greater than zero. That is, we are looking for the probability where \(-x^2-2x+15 > 0\).
We can factorize the expression as \((x+5)(3-x) > 0\). This inequality holds true when \(-5 < x < 3\).
Since \(x\) is an integer, it can take on 7 values: -4, -3, -2, -1, 0, 1, and 2.
Therefore, the probability is \(\frac{7}{21}=\frac{1}{3}\).
Answer: B
General Discussion
SingaravelChocks
Joined: 12 Feb 2019
Last visit: 01 Mar 2024
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Schools: ISB '23 CBS '23 IIMA PGPX'23 Wharton '22
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WE:Business Development (Computer Software)
14 Aug 2019, 18:47
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perfect!
