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Question: What is the probability that a randomly chosen positive integer less than or equal to 50 is a factor of 60?
Solution: First, we find all positive integers less than or equal to 50 that are factors of 60. The positive divisors of 60 are:
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
However, we only consider those less than or equal to 50. Removing 60, we are left with:
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30
There are 11 such numbers. Since there are 50 positive integers less than or equal to 50, the probability is:
\frac{11}{50} = \boxed{\frac{11}{50}}
Question: Solve for $ z $ in the equation $ 3(z - 4) + 7 = 2(4z + 1) $.
3z - 12 + 7 = 8z + 2
3z - 5 = 8z + 2
