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If p2 – 13p + 40 = q , and p is a positive integer between 1 and 10, inclusive, what is the probability that   q < 0?
  • a)
    1/10
  • b)
    1/5
  • c)
    2/5
  • d)
    3/5
  • e)
    3/10
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If p2 – 13p + 40 = q , and p is a positive integer between 1 and...
If we factor the right side of the equation, we can come up with a more meaningful relationship between p and q : p2 – 13p + 40 = q so (p – 8)(p – 5) = q. We know that p is an integer between 1 and 10, inclusive, so there are ten possible values for p. We see from the factored equation that the sign of q will depend on the value of p . One way to solve this problem would be to check each possible value of p to see whether it yields a positive or negative q. However, we can also use some logic here. For q to be negative, the expressions (p – 8) and (p – 5) must have opposite signs. Which integers on the number line will yield opposite signs for the expressions (p – 8) and (p – 5)? Those integers in the range 5 < p < 8 (notice 5 and 8 are not included because they would both yield a value of zero and zero is a nonnegative integer). That means that there are only two integer values for p, 6 and 7, that would yield a negative q. With a total of 10 possible p values, only 2 yield a negative q, so the probability is 2/10 or 1/5.
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Most Upvoted Answer
If p2 – 13p + 40 = q , and p is a positive integer between 1 and...
Understanding the Problem
- We are given the equation p2 – 13p + 40 = q, where p is a positive integer between 1 and 10.
- We need to find the probability that q < />

Solution
- First, let's factor the equation p2 – 13p + 40 = q into (p – 5)(p – 8) = q.
- Since p is a positive integer between 1 and 10, the possible values for q are (1-5)(1-8), (2-5)(2-8), ..., (10-5)(10-8).
- Calculating the values, we get q = -4, -6, -6, -4, 0, 4, 12, 24, 40, 60.
- Out of these, only q = -4, -6, -6, -4 are < />
- Therefore, the probability that q < 0="" is="" 4="" out="" of="" 10="" possible="" values="" of="" />
- So, the probability is 4/10 = 1/5.
Therefore, the correct answer is option B) 1/5.
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If p2 – 13p + 40 = q , and p is a positive integer between 1 and 10, inclusive, what is the probability that q < 0?a)1/10b)1/5c)2/5d)3/5e)3/10Correct answer is option 'B'. Can you explain this answer?
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