answer:There are 10 possible choices for the first digit (0-9), 26 choices for the letter, and 10 choices for the second digit (0-9). So there are 10 cdot 26 cdot 10 = 2600 possible passwords. Out of these, there are 5 odd single-digit numbers (1, 3, 5, 7, 9), 26 choices for the letter, and 9 choices for the second digit (1-9). So there are 5 cdot 26 cdot 9 = 1170 passwords that consist of an odd single-digit number followed by a letter and a positive single-digit number. Therefore, the probability is frac{1170}{2600} = frac{117}{260} = boxed{frac{9}{20}}. The answer is: frac{9}{20}

answer:We know that Lucy can clean 2 aquariums in 3 hours, or 2/3 aquariums per hour. To find out how many aquariums she can clean in x hours, we can use the formula: number of aquariums = (number of hours) * (aquariums per hour) Substituting 2/3 for "aquariums per hour", we get: number of aquariums = x * (2/3) = (2/3) * x = 2x/3 We are given that the number of aquariums Lucy can clean is 16, so we can write: 2x/3 = 16 Multiplying both sides by 3, we get: 2x = 48 Dividing both sides by 2, we get: x = 24 The value of x is 24. 24 The answer is: 24

answer:We know that tan 60^circ = sqrt{3}, so we can use the tangent addition formula to find tan 120^circ. Using the formula tan(a+b) = frac{tan a + tan b}{1 - tan a tan b}, we have [tan 120^circ = tan (60^circ + 60^circ) = frac{tan 60^circ + tan 60^circ}{1 - tan 60^circ tan 60^circ}.] Since tan 60^circ = sqrt{3}, we can substitute that in to get [tan 120^circ = frac{sqrt{3} + sqrt{3}}{1 - sqrt{3} cdot sqrt{3}} = frac{2sqrt{3}}{1 - 3} = boxed{-sqrt{3}}.] The answer is: -sqrt{3}

answer:The tickets cost 100 each, so for James and Susan, it will be 100 + 100 = 200 in total. Dinner costs 120, and since James pays for everything, it will be an additional 120. To calculate the tip, we multiply the cost of dinner by the tip percentage: 120 * 0.30 = 36. So, the tip will be an additional 36. James also charters a limo for 6 hours at 80 per hour, so the cost will be 6 * 80 = 480. Adding up all the costs, the total will be 200 + 120 + 36 + 480 = 836. 836 The answer is: 836