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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25. Calculate the area of a cuboid of length 11 cm, breadth 9 cm and height 5 cm. The question asks for "area" but the units in the options are cm^3, which are units for volume. Given the options, it is highly probable that the question intended to ask for the volume of the cuboid. Step 1: Identify the dimensions. Length l = 11 cm Breadth b = 9 cm Height h = 5 cm Step 2: Calculate the volume of the cuboid. Volume = l × b × h Volume = 11 cm × 9 cm × 5 cm Volume = 495 cm^3 The correct option is B. The volume is 495 cm^3. 26. How many notebooks sold at N150.00 each can a father purchase for N2550.00 for his ward? Step 1: Divide the total money by the cost per notebook. Number of notebooks = Total moneyCost per notebook Number of notebooks = N2550.00N150.00 Step 2: Perform the division. Number of notebooks = 17 The correct option is C. He can purchase 17 notebooks. 27. Reduce (105)/(225) to a fraction in its lowest term. Step 1: Find the greatest common divisor (GCD) of the numerator and denominator. Both 105 and 225 are divisible by 5. (105 ÷ 5)/(225 ÷ 5) = (21)/(45) Step 2: Continue dividing by common factors. Both 21 and 45 are divisible by 3. (21 ÷ 3)/(45 ÷ 3) = (7)/(15) The correct option is B. The fraction in its lowest term is (7)/(15). 28. Change 7 to a number in percentage. Given the options, it is highly probable that the question intended to ask for the percentage equivalent of (7)/(8). Step 1: Convert the fraction (7)/(8) to a percentage. Percentage = (7)/(8) × 100\% Step 2: Calculate the percentage. Percentage = 0.875 × 100\% = 87.5\% Percentage = 87(1)/(2)\% The correct option is C. The percentage is 87(1)/(2)\%. 29. The number 10,080,008 can be interpreted in words as: Step 1: Break down the number by place value. 10,000,000 Ten Million 80,000 Eighty Thousand 8 Eight Step 2: Combine the parts. Ten Million, Eighty Thousand and Eight. The correct option is B. The number is Ten Million, Eighty Thousand and Eight. 30. Which of the following angles is an obtuse angle? Step 1: Recall the definition of an obtuse angle. An obtuse angle is an angle that measures greater than 90^ but less than 180^. Step 2: Evaluate each option. A. 89^ is an acute angle (less than 90^). B. 92^ is an obtuse angle (greater than 90^ and less than 180^). C. 184^ is a reflex angle (greater than 180^). D. 0.237^ is an acute angle. The correct option is B. 92^ is an obtuse angle. 31. Express 117 as a product of its prime factors. Step 1: Divide 117 by the smallest prime numbers. 117 ÷ 3 = 39 39 ÷ 3 = 13 13 ÷ 13 = 1 Step 2: Write the prime factorization. 117 = 3 × 3 × 13 = 3^2 × 13 The correct option is D. The prime factors are 3^2 × 13. 32. Calculate the area of the triangle below: The diagram shows a right-angled triangle with a base of 8 cm and a height of 6 cm. Step 1: Identify the base and height. Base b = 8 cm Height h = 6 cm Step 2: Apply the formula for the area of a triangle. Area = (1)/(2) × base × height Area = (1)/(2) × 8 cm × 6 cm Area = 4 cm × 6 cm Area = 24 cm^2 The correct option is D. The area of the triangle is 24 cm^2. 33. Solve the simultaneous equations: (i) a + 6b = 13 (ii) 5a - 6b = 7 Adding the two equations as given results in 6a = 20, so a = (10)/(3), which is not an integer. Since all options are integers, there might be a typo in the second equation. Assuming the second equation was intended to be 5a - 6b = -7 to yield integer solutions matching the options: (i) a + 6b = 13 (ii) 5a - 6b = -7 Step 1: Add equation (i) and equation (ii) to eliminate b. (a + 6b) + (5a - 6b) = 13 + (-7) 6a = 6 Step 2: Solve for a. a = (6)/(6) = 1 Step 3: Substitute a=1 into equation (i) to solve for b. 1 + 6b = 13 6b = 13 - 1 6b = 12 b = (12)/(6) = 2 The correct option is C (assuming the typo in equation (ii) as 5a - 6b = -7). The solutions are a = 1 and b = 2. 34. Factorize the expression y^2 + 10y - 24 = 0. Step 1: Find two numbers that multiply to -24 and add to 10. The two numbers are 12 and -2, because 12 × (-2) = -24 and 12 + (-2) = 10. Step 2: Rewrite the middle term using these numbers and factor by grouping. y^2 + 12y - 2y - 24 = 0 y(y + 12) - 2(y + 12) = 0 (y + 12)(y - 2) = 0 Step 3: Solve for y. y + 12 = 0 y = -12 y - 2 = 0 y = 2 The correct option is B. The solutions are y = -12 or y = 2. Got more? Send 'em!