This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

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Step 1: Convert the percentage to a fraction by dividing by 100. Step 2: Simplify the fraction. The final answer is .
Step 1: Convert the whole number to a fraction with the same denominator. Step 2: Add the fractions. The final answer is .
Step 1: Recognize the relationship between the given multiplication and the required multiplication. Given: . We need to find . Notice that and . Step 2: Rewrite the expression using the given numbers and decimal factors. Step 3: Substitute the given product and multiply the decimal factors. The final answer is .
i) Step 1: List all the unique letters in the word ANURADHAPURA. The unique letters are A, N, U, R, D, H, P. The elements of the set B are .
ii) Step 1: Count the number of unique elements in the set B. There are 7 unique letters. So, n(B) = .
Step 1: Add the time difference to the Sri Lankan time. Sri Lanka time: 9:15 AM on 2025-06-15 Time difference: +10 hours Step 2: Convert the 24-hour format time to 12-hour format. 19:15 is 7:15 PM. The date remains the same. The time in Sydney will be .
Step 1: Find the square root of 576. We know that and . The number ends in 6, so its square root must end in 4 or 6. Let's test 24: The final answer is .
Step 1: Recall the conversion factor between tonnes (t) and kilograms (kg). Step 2: Multiply the given value in tonnes by the conversion factor. The final answer is .
Step 1: Calculate the cube of -2. Step 2: Perform the multiplication. The final answer is .
Step 1: Calculate the area of using the base BC and its corresponding height AE. Step 2: Use the calculated area and the other given height CD to find the length of its corresponding base AB. Step 3: Solve for AB. The final answer is .
Step 1: Identify the angles in the right-angled triangle. One angle is (right angle). One acute angle is . The other acute angle is . Step 2: Use the property that the sum of angles in a triangle is . Step 3: Solve for . The final answer is .
Step 1: Let the monthly salary be . According to the problem, 5% of the monthly salary is Rs. 4000. Step 2: Convert the percentage to a fraction and set up the equation. Step 3: Solve for . Mr. Perera's monthly salary is .
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Convert the percentage to a fraction by dividing by 100. 25\% = (25)/(100) Step 2: Simplify the fraction.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.