answer:Nadia walked x kilometers, which was twice as far as Hannah walked. So Hannah walked x/2 kilometers. The total distance walked by the two girls is the sum of the distances walked by Nadia and Hannah: x + x/2. We are given that the total distance walked is 27 kilometers, so we can write: x + x/2 = 27. To simplify the equation, we can multiply both sides by 2 to get rid of the fraction: 2x + x = 54. Combining like terms, we get: 3x = 54. Dividing both sides by 3, we get: x = 18. The value of x is 18. 18 The answer is: 18

answer:Let theta = arcsinleft(frac{2}{3}right). Since sintheta = frac{2}{3}, we can draw a right triangle with angle theta and opposite side length 2 and hypotenuse length 3. By the Pythagorean theorem, the adjacent side length is sqrt{3^2 - 2^2} = sqrt{5}. Therefore, costheta = frac{text{adjacent}}{text{hypotenuse}} = frac{sqrt{5}}{3}. Hence, the value of cosine of the arcsine of 2/3 is boxed{frac{sqrt{5}}{3}}. The answer is: frac{sqrt{5}}{3}

answer:We want to find the value of X in the given situation. To find the smallest positive integer with exactly X positive divisors, we need to consider the prime factorization of the number. The prime factorization of 192 is 2^6 * 3^1. To find the number of positive divisors, we can use the formula: Number of divisors = (Exponent of prime factor 1 + 1) * (Exponent of prime factor 2 + 1) * ... In this case, we have 2 prime factors: 2 and 3. The exponent of prime factor 2 is 6, and the exponent of prime factor 3 is 1. So, the number of positive divisors is: (6 + 1) * (1 + 1) = 7 * 2 = 14 Given that the number with exactly X positive divisors is 192, we can write: X = 14 The value of X is 14. The answer is: 14

answer:In a carton of 12 eggs, there are 12 yolks in total. Out of the 12 eggs, 5 have double yolks, which means there are 5 extra yolks. So the total number of yolks in the entire carton is 12 + 5 = 17. 17 The answer is: 17