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question:A cylindrical water tank's gauge indicates that there are 60 liters of water when the tank is 25% full. Additionally, each 5% of the tank's capacity corresponds to 12 liters. Determine the tank's full capacity in liters. A) 120 liters B) 200 liters C) 240 liters D) 300 liter
answer:1. Let x be the total capacity of the water tank in liters when it is full. 2. The problem states that 25% of the tank's capacity is 60 liters, which can be formulated as: [ 0.25x = 60 ] 3. Solve this equation to find x: [ x = frac{60}{0.25} = 240 ] 4. To confirm this, check the information that each 5% of the tank's capacity equals 12 liters. [ 0.05x = 12 quad Rightarrow quad x = frac{12}{0.05} = 240 ] 5. Both methods confirm the full capacity is consistent. Conclusion: The full capacity of the tank is 240 liters. The final answer is boxed{C}.
question:Rounded to 3 decimal places, what is frac{8}{11}?
answer:To solve the problem, first calculate the value of frac{8}{11}: frac{8}{11} = 8 div 11 approx 0.72727272ldots = 0.overline{72} Next, to round to 3 decimal places, look at the first three numbers in the decimal sequence and the fourth number to determine if rounding up is necessary: - First three numbers: 727 - Fourth number: 2 Since the fourth number is less than 5, we do not round up. Thus, rounded to 3 decimal places, frac{8}{11} is: boxed{0.727}
question:Calculate 2354 + 240 div 60 354 times 2.
answer:First, follow the order of operations, often remembered by PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). 1. **Division and Multiplication First**: [ 240 div 60 = 4, quad 354 times 2 = 708 ] 2. **Subsequent Addition and Subtraction**: [ 2354 + 4 - 708 = 2354 + 4 - 708 ] Combine the operations: [ 2354 + 4 = 2358, quad 2358 - 708 = 1650 ] 3. **Final Calculation**: [ boxed{1650} ]
question:The length of a rectangle is increased to 2 times its original size and its width is increased to 3 times its original size. The area of the original rectangle is 300 square meters. What is the area of the new rectangle?
answer:Let's denote the original length of the rectangle as L and the original width as W. The area of the original rectangle is given by: Area_original = L * W According to the problem, the area of the original rectangle is 300 square meters, so: L * W = 300 Now, the length of the rectangle is increased to 2 times its original size, and the width is increased to 3 times its original size. Therefore, the new length (L_new) is 2L and the new width (W_new) is 3W. The area of the new rectangle is given by: Area_new = L_new * W_new Area_new = (2L) * (3W) Area_new = 2 * 3 * L * W Area_new = 6 * (L * W) Since we know that L * W = 300, we can substitute this value into the equation: Area_new = 6 * 300 Area_new = 1800 Therefore, the area of the new rectangle is boxed{1800} square meters.