M = {-6, -5, -4, -3, -2} T = {-2, -1, 0, 1, 2, 3} If an integer is to be randomly selected from set M above and an integer is to be randomly selected from set T above, what is the probability that the product of the two integers will be negative?
A. 0 B. 1/3 C. 2/5 D. 1/2 E. 3/5
Solution:
Set M has 5 integers in it, set T has 6. The question is asking for the probability that the product of any 2 integers is negative.
Total possibilities of products = 5 * 6 = 30
A negative product for 2 integers only can happen when a negative integer is multiplied by a positive one.
There are 3 positive integers in set T, and 5 in set M, so total number of possibilities = 5 * 3 = 15.
Hence, probability that 2 numbers chosen will have negative product = 15/30 = 1/2. Choice D.
On a recent trip, Cindy drove her car 290 miles, rounded to the nearest 10 miles, and used 12 gallons of gasoline, rounded to the nearest gallon. The actual number of miles per gallon that Cindy's car got on this trip must have been between
(A) 290/12.5 and 290/11.5 (B) 295/12 and 285/11.5 (C) 285/12 and 295/12 (D) 285/12.5 and 295/11.5 (E) 295/12.5 and 285/11.5
Solution:
Here's the inequality we could set up: 285/12.4 <= x <= 294/11.5 However, the question doesn't ask "which of the following is the range of possible mileage for the car" - it asks what the mileage "must have been between".
For "must have been between", a range bigger than the minimum range certainly fits. Let's look at a different question: If x=6, then x must be between which of the following: A) 2 and 3 B) 4 and 5 C) 5 and 6 D) 1 and 1000000 E) 6 and 7 Now, if x=6, it certainly must be between 1 and 1000000 - even though that range is bigger than absolutely necessary, it meets the requirements of the question (while none of the other choices do so). For this question, we need to recognize that: 285/12.5 is less than 285/12.4 (remember, when you increase the denominator, you decrease the fraction); and that 295/11.5 is greater than 294/11.5 (since increasing the numerator increases the fraction)
In order to see that the range in D is bigger than our inequality, and is therefore the correct answer to the question.
A. 0 B. 1/3 C. 2/5 D. 1/2 E. 3/5
Solution:
Set M has 5 integers in it, set T has 6. The question is asking for the probability that the product of any 2 integers is negative.
Total possibilities of products = 5 * 6 = 30
A negative product for 2 integers only can happen when a negative integer is multiplied by a positive one.
There are 3 positive integers in set T, and 5 in set M, so total number of possibilities = 5 * 3 = 15.
Hence, probability that 2 numbers chosen will have negative product = 15/30 = 1/2. Choice D.
On a recent trip, Cindy drove her car 290 miles, rounded to the nearest 10 miles, and used 12 gallons of gasoline, rounded to the nearest gallon. The actual number of miles per gallon that Cindy's car got on this trip must have been between
(A) 290/12.5 and 290/11.5 (B) 295/12 and 285/11.5 (C) 285/12 and 295/12 (D) 285/12.5 and 295/11.5 (E) 295/12.5 and 285/11.5
Solution:
Here's the inequality we could set up: 285/12.4 <= x <= 294/11.5 However, the question doesn't ask "which of the following is the range of possible mileage for the car" - it asks what the mileage "must have been between".
For "must have been between", a range bigger than the minimum range certainly fits. Let's look at a different question: If x=6, then x must be between which of the following: A) 2 and 3 B) 4 and 5 C) 5 and 6 D) 1 and 1000000 E) 6 and 7 Now, if x=6, it certainly must be between 1 and 1000000 - even though that range is bigger than absolutely necessary, it meets the requirements of the question (while none of the other choices do so). For this question, we need to recognize that: 285/12.5 is less than 285/12.4 (remember, when you increase the denominator, you decrease the fraction); and that 295/11.5 is greater than 294/11.5 (since increasing the numerator increases the fraction)
In order to see that the range in D is bigger than our inequality, and is therefore the correct answer to the question.
Hello, my name is Jack Sparrow. I'm a 50 year old self-employed Pirate from the Caribbean.
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