answer:To count the number of positive integers less than or equal to 30 that are relatively prime to 30, we need to count the number of positive integers less than or equal to 30 that have no prime factors in common with 30. The prime factors of 30 are 2, 3, and 5, so we need to count the numbers that are not divisible by 2, 3, or 5. There are 15 positive integers less than or equal to 30 that are divisible by 2, 10 positive integers less than or equal to 30 that are divisible by 3, and 6 positive integers less than or equal to 30 that are divisible by 5. However, some numbers are divisible by more than one of these primes, so we need to subtract the numbers that are divisible by 2 and 3, the numbers divisible by 2 and 5, and the numbers divisible by 3 and 5. There are 5 positive integers less than or equal to 30 that are divisible by both 2 and 3, 3 positive integers less than or equal to 30 that are divisible by both 2 and 5, and 1 positive integer less than or equal to 30 that is divisible by both 3 and 5. Finally, we need to add back the number of positive integers less than or equal to 30 that are divisible by all three primes, which is just 1 (30 itself). So, the number of positive integers less than or equal to 30 that are relatively prime to 30 is 30-15-10-6+5+3+1=8. The probability is then frac{8}{30}=boxed{frac{4}{15}}. The answer is: frac{4}{15}

answer:Let's call the total number of people surveyed x. Out of those surveyed, 86.8% believed that rats carry diseases. This means that 86.8% of x people believed that rats carry diseases, or 0.868x people. Out of those who believed that rats carry diseases, 45.7% mistakenly believed that rats frequently carry rabies. This means that 45.7% of 0.868x people mistakenly believed that rats frequently carry rabies, or 0.457(0.868x) = 0.396076x people. We know that 21 people were incorrect in their belief about rats carrying rabies. Therefore, we can set up the equation 0.396076x = 21 and solve for x. Dividing both sides of the equation by 0.396076, we get x = frac{21}{0.396076} approx boxed{53}. The answer is: 53

answer:Let's assume the number of girls at the camp is G. Since there were 33 more boys than girls, the number of boys at the camp is G+33. The total number of people at the camp is the sum of the number of girls and boys, so G + (G+33) = 133. Combining like terms, we have 2G + 33 = 133. Subtracting 33 from both sides, we have 2G = 100. Dividing both sides by 2, we have G = 50. Therefore, there were 50 girls at the camp. 50 50 The answer is: 50

answer:Mo plans to give a Valentine to 30 x 60% = 18 students. Each card costs 2, so Mo will spend 18 x 2 = 36 on cards. Mo has a budget of 40, so he will spend 36 / 40 = 0.9, or 90% of his budget on Valentine's Day cards. 90 The answer is: 90