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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alexnwabuike, let's knock this out. Question 11: Step 1: Add the given numbers. 3.25 + 2.573 + 4.6 Step 2: Align the decimal points and sum. c 3.250 \\ 2.573 \\ + 4.600 \\ 10.423 The sum is 10.423. Question 12: Step 1: Convert all fractions to have a common denominator. The least common multiple of 2, 4, and 8 is 8. (1)/(2) = (1 × 4)/(2 × 4) = (4)/(8) (1)/(4) = (1 × 2)/(4 × 2) = (2)/(8) (1)/(8) = (1)/(8) (3)/(4) = (3 × 2)/(4 × 2) = (6)/(8) (5)/(8) = (5)/(8) Step 2: Arrange the fractions in increasing order based on their numerators. (1)/(8), (2)/(8), (4)/(8), (5)/(8), (6)/(8) Step 3: Write the original fractions in increasing order. (1)/(8), (1)/(4), (1)/(2), (5)/(8), (3)/(4) The correct order is (1)/(8), (1)/(4), (1)/(2), (5)/(8), (3)/(4). Question 13: Step 1: Use the Pythagorean theorem, a^2 + b^2 = c^2, where c is the hypotenuse and a, b are the other two sides. Given one side a = 12 cm and hypotenuse c = 13 cm. We need to find the other side b. 12^2 + b^2 = 13^2 Step 2: Calculate the squares. 144 + b^2 = 169 Step 3: Solve for b^2. b^2 = 169 - 144 b^2 = 25 Step 4: Find the square root of b^2. b = sqrt(25) b = 5 cm The length of the other side is 5 cm. Question 14: Step 1: Use the formula for the area of a circle, A = r^2, to find the radius r. Given A = 2464 cm^2 and = (22)/(7). 2464 = (22)/(7) × r^2 Step 2: Solve for r^2. r^2 = (2464 × 7)/(22) r^2 = 112 × 7 r^2 = 784 Step 3: Find the radius r. r = sqrt(784) r = 28 cm Step 4: Calculate the diameter d = 2r. d = 2 × 28 cm d = 56 cm Step 5: Approximate to 2 significant figures. Since 56 already has two significant figures, no further rounding is needed. The diameter is 56 cm. Question 15: Step 1: Multiply the number of patients by the amount of milk each patient gets. Total milk = Number of patients × Milk per patient Total milk = 36 × (1)/(2) litres Step 2: Perform the multiplication. Total milk = (36)/(2) litres Total milk = 18 litres 18 litres of milk are needed. Question 16: Step 1: To divide by a fraction, multiply by its reciprocal. (1)/(4) ÷ (1)/(16) = (1)/(4) × (16)/(1) Step 2: Perform the multiplication. (1)/(4) × 16 = (16)/(4) = 4 The value is 4. Question 17: Step 1: The clock shows 1:10 p.m. and is 20 minutes fast. To find the correct time, subtract 20 minutes from 1:10 p.m. Step 2: Subtract 10 minutes from 1:10 p.m. to get 1:00 p.m. Step 3: Subtract the remaining 10 minutes (20 - 10) from 1:00 p.m. 1:00 p.m. - 10 minutes = 12:50 p.m. The correct time is 12:50 p.m. Question 18: Step 1: Convert the mixed number to an improper fraction. 1(1)/(2) = ((1 × 2) + 1)/(2) = (3)/(2) Step 2: Find a common denominator for 2, 4, and 3. The least common multiple is 12. (3)/(2) = (3 × 6)/(2 × 6) = (18)/(12) (1)/(4) = (1 × 3)/(4 × 3) = (3)/(12) (2)/(3) = (2 × 4)/(3 × 4) = (8)/(12) Step 3: Perform the operations. (18)/(12) - (3)/(12) + (8)/(12) = (18 - 3 + 8)/(12) = (15 + 8)/(12) = (23)/(12) The simplified value is (23)/(12). Question 19: Step 1: Calculate the total toll from buses. Toll from buses = 500 buses × N10/bus Toll from buses = N5000 Step 2: Calculate the total toll from trailers. Toll from trailers = 100 trailers × N50/trailer Toll from trailers = N5000 Step 3: Find the total amount collected. Total amount = N5000 + N5000 Total amount = N10,000 The total amount collected is N10,000.00. Question 20: Step 1: Find the factors of each number. Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 18: 1, 2, 3, 6, 9, 18 Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 Step 2: Identify the common factors. Common factors: 1, 2, 3, 6 Step 3: The greatest common factor is the largest number among the common factors. The greatest number is 6. Question 21: Step 1: Identify the first two significant figures in 3053.56. The first significant figure is 3, and the second is 0. Step 2: Look at the digit immediately after the second significant figure, which is 5. Step 3: Since 5 is 5 or greater, round up the second significant figure. The 0 becomes 1. Step 4: Replace all digits after the second significant figure with zeros to maintain the place value. 3053.56 ≈ 3100 The approximation to 2 significant figures is 3100. Send me the next one 📸