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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Here are the solutions to the questions you sent: 14. The volume of water in a tank is 2998673 m^3. What is the place value of digit 2 in the number? (2 marks) Step 1: Identify the number and the digit in question. The number is 2,998,673. The digit is 2. Step 2: Determine the place value of each digit from right to left. 3 is in the ones place. 7 is in the tens place. 6 is in the hundreds place. 8 is in the thousands place. 9 is in the ten thousands place. 9 is in the hundred thousands place. 2 is in the millions place. The place value of digit 2 is Millions. 15. Kimani's plot of land is in the shape below. Calculate its area in hectares. (3 marks) Step 1: Identify the shape and its dimensions. The plot is a right-angled triangle with base 600 m and height 800 m. The hypotenuse is 1000 m. Step 2: Calculate the area of the triangle in square meters. The formula for the area of a triangle is (1)/(2) × base × height. Area = (1)/(2) × 600 m × 800 m Area = 300 m × 800 m Area = 240000 m^2 Step 3: Convert the area from square meters to hectares. We know that 1 hectare = 10000 m^2. Area in hectares = 240000 m^210000 m^2/hectare Area in hectares = 24 hectares The area of the plot is 24 hectares. 16. Patrick spent (1)/(4) of his salary on rent and (2)/(3) on food. What was the total fraction spent? (3 marks) Step 1: Identify the fractions spent. Fraction on rent = (1)/(4) Fraction on food = (2)/(3) Step 2: Add the fractions to find the total fraction spent. To add fractions, find a common denominator. The least common multiple of 4 and 3 is 12. Total fraction spent = (1)/(4) + (2)/(3) Step 3: Convert the fractions to have the common denominator. (1)/(4) = (1 × 3)/(4 × 3) = (3)/(12) (2)/(3) = (2 × 4)/(3 × 4) = (8)/(12) Step 4: Add the fractions with the common denominator. Total fraction spent = (3)/(12) + (8)/(12) Total fraction spent = (3 + 8)/(12) Total fraction spent = (11)/(12) The total fraction spent was (11)/(12). Last free one today — make it count tomorrow, or type /upgrade for unlimited.