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.
ScanSolve AI Answer
Here are the solutions to the next set of problems: 7. 0.3 × 0.7 = 0.21. Solve 0.7 × 0.6 Step 1: Multiply the numbers as if they were whole numbers. 7 × 6 = 42. Step 2: Count the total number of decimal places in the original numbers. 0.7 has one decimal place. 0.6 has one decimal place. Total decimal places = 1 + 1 = 2. Step 3: Place the decimal point in the product. Starting from the right of 42, move the decimal point 2 places to the left. This gives 0.42. 0.42 8. The average of 1, 2 and 3 is 2. What is the average of 4, 5, 7, 8, and 11? Step 1: Sum the given numbers. Sum = 4 + 5 + 7 + 8 + 11 = 35. Step 2: Count how many numbers are in the set. There are 5 numbers. Step 3: Divide the sum by the count to find the average. Average = (35)/(5) = 7. 7 9. Two angles of a triangle are 60^ and 65^; Find the third angle. Step 1: Recall that the sum of angles in a triangle is 180^. Let the third angle be . Step 2: Add the two given angles. Sum of known angles = 60^ + 65^ = 125^. Step 3: Subtract the sum of known angles from 180^ to find the third angle. = 180^ - 125^ = 55^. 55^ 10. What is the next number in the sequence 4, 7, 10, 13, 16? Step 1: Find the difference between consecutive terms to identify the pattern. 7 - 4 = 3 10 - 7 = 3 13 - 10 = 3 16 - 13 = 3 The pattern is an addition of 3 to the previous term. Step 2: Add 3 to the last term in the sequence. Next number = 16 + 3 = 19. 19 11. A bag was bought for 5000 FRS and sold at a gain of 500frs. What is the % gain? Step 1: Identify the cost price and the gain. Cost Price (CP) = 5000 FRS. Gain = 500 FRS. Step 2: Use the formula for percentage gain. Percentage Gain = GainCost Price × 100\%. Step 3: Substitute the values and calculate. Percentage Gain = (500)/(5000) × 100\% = (1)/(10) × 100\% = 10\%. 10\% 12. The area of a square field is 64m^2. Find the dimension of the side of the field. Step 1: Recall the formula for the area of a square. Area = side × side = s^2. Step 2: Set up the equation with the given area. s^2 = 64m^2. Step 3: Solve for s by taking the square root of both sides. s = sqrt(64m)^2 = 8m. 8m 13. If 0.4 of my money is 3000 FRS. What is the total amount of my money? Step 1: Let the total amount of money be M. Set up the equation based on the given information. 0.4 × M = 3000. Step 2: Convert the decimal to a fraction for easier calculation. 0.4 = (4)/(10) = (2)/(5). So, (2)/(5) M = 3000. Step 3: Solve for M by multiplying both sides by the reciprocal of (2)/(5). M = 3000 × (5)/(2) = 1500 × 5 = 7500. The total amount of money is 7500 FRS. 7500 FRS 14. The difference between 7 and 3 is 4. What is the difference between 2.1 and 0.796? Step 1: Identify the numbers for which the difference is required. The numbers are 2.1 and 0.796. Step 2: Subtract the smaller number from the larger number. Difference = 2.1 - 0.796. Step 3: Perform the subtraction. r 2.100 \\ -0.796 \\ 1.304 \\ The difference is 1.304. 1.304 That's 2 down. 3 left today — send the next one.