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 questions: Question 24: The distance between Ogoja and Nbube is 24km. If a driver covered the distance in 1(1)/(2) hours, what was his average speed for the journey? Step 1: Identify the given distance and time. Distance (D) = 24 km Time (T) = 1(1)/(2) hours = 1.5 hours Step 2: Use the formula for average speed. Average Speed = DistanceTime Step 3: Substitute the values and calculate the speed. Average Speed = 24 km1.5 hours = 16 km/h The average speed for the journey is 16 km/h. The correct option is (c). c) 16 km/h Question 25: Find the breadth of a rectangular field with area 648 cm^2 and length 40 cm. Step 1: Identify the given area and length. Area (A) = 648 cm^2 Length (L) = 40 cm Step 2: Use the formula for the area of a rectangle, A = L × B, where B is the breadth. Step 3: Rearrange the formula to solve for breadth and substitute the values. B = (A)/(L) = 648 cm^240 cm B = 16.2 cm The breadth of the rectangular field is 16.2 cm. The correct option is (b). b) 16.2 cm Question 26: Find the difference between the LCM and HCF of 10 and 12. Step 1: Find the prime factorization of 10 and 12. 10 = 2 × 5 12 = 2^2 × 3 Step 2: Calculate the HCF (Highest Common Factor). HCF(10, 12) = 2 Step 3: Calculate the LCM (Least Common Multiple). LCM(10, 12) = 2^2 × 3 × 5 = 4 × 3 × 5 = 60 Step 4: Find the difference between the LCM and HCF. Difference = 60 - 2 = 58 The difference is 58. The correct option is (d). d) 58 Question 27: Ayobami used 587kg of sugar to bake a cake and mixed 140kg sugar for coating the cake. How much of sugar content is used? Step 1: Identify the amounts of sugar used. Sugar for baking = 587 kg Sugar for coating = 140 kg Step 2: Add the amounts to find the total sugar content. Total sugar = 587 kg + 140 kg = 727 kg The total sugar content used is 727 kg. The correct option is (b). b) 727 kg Question 28: Simplify sqrt(4) + sqrt(9 - 25). Step 1: Simplify the innermost square root. sqrt(25) = 5 Step 2: Substitute and simplify the next part of the expression. sqrt(9 - 5) = sqrt(4) Step 3: Simplify the remaining square roots. sqrt(4) + sqrt(4) = 2 + 2 Step 4: Perform the final addition. 2 + 2 = 4 The simplified value is 4. The correct option is (a). a) 4 Question 29: Simplify 5(1)/(3) - 2(1)/(4) + (1)/(2). Step 1: Convert mixed numbers to improper fractions. 5(1)/(3) = (16)/(3) 2(1)/(4) = (9)/(4) Step 2: Rewrite the expression. (16)/(3) - (9)/(4) + (1)/(2) Step 3: Find the LCM of the denominators (3, 4, 2), which is 12. Convert fractions to have this common denominator. (16 × 4)/(3 × 4) - (9 × 3)/(4 × 3) + (1 × 6)/(2 × 6) = (64)/(12) - (27)/(12) + (6)/(12) Step 4: Perform the operations. (64 - 27 + 6)/(12) = (37 + 6)/(12) = (43)/(12) Step 5: Convert the improper fraction back to a mixed number. (43)/(12) = 3(7)/(12) The simplified value is 3(7)/(12). The correct option is (c). c) 3(7)/(12) Question 30: Add 3min. 25secs. and 2mins. 44secs. Step 1: Add the minutes and seconds separately. Minutes: 3 + 2 = 5 min Seconds: 25 + 44 = 69 secs Step 2: Convert the total seconds into minutes and remaining seconds. 69 secs = 1 min 9 secs (since 1 min = 60 secs) Step 3: Add the converted minutes to the total minutes. Total time = 5 min + 1 min 9 secs = 6 min 9 secs The sum is 6 mins. 9 secs. The correct option is (b). b) 6 mins. 9 secs. Question 31: What is the volume of a cylinder with base diameter 14cm and height 10cm? Step 1: Identify the given values and calculate the radius. Diameter (d) = 14 cm Radius (r) = (14)/(2) = 7 cm Height (h) = 10 cm Step 2: Use the formula for the volume of a cylinder, V = r^2 h. Use = (22)/(7). Step 3: Substitute the values and calculate the volume. V = (22)/(7) × (7 cm)^2 × 10 cm V = (22)/(7) × 49 cm^2 × 10 cm V = 22 × 7 cm^2 × 10 cm V = 1540 cm^3 The volume of the cylinder is 1540 cm^3. The correct option is (b). b) 1540 cm^3 Question 32: Find the value of P in the figure below. Step 1: Recognize that angles on a straight line sum to 180^. Step 2: Set up the equation based on the given angles. 110^ + 2P = 180^ Step 3: Solve for 2P. 2P = 180^ - 110^ 2P = 70^ Step 4: Solve for P. P = (70^)/(2) P = 35^ The value of P is 35^. The correct option is (c). c) 35^ Question 33: Change 3% to fraction in its lowest term. Step 1: Convert the percentage to a fraction by dividing by 100. 3\% = (3)/(100) Step 2: Check if the fraction can be simplified. The numerator (3) is a prime number. The denominator (100) is not divisible by 3. Therefore, the fraction is already in its lowest term. The correct option is (a). a) (3)/(100) Question 34: A line from the centre of a circle to any point on a circumference is called --- Step 1: Recall the definition of a radius. A radius is a line segment that connects the center of a circle to any point on its circumference. The correct option is (b). b) radius Question 35: Write 2019 in Roman numeral. Step 1: Break down the number 2019. 2019 = 2000 + 10 + 9 Step 2: Convert each part to its Roman numeral. 2000 = MM 10 = X 9 = IX Step 3: Combine the Roman numerals. 2019 = MMXIX The Roman numeral for 2019 is MMXIX. The correct option is (b). b) MMXIX Question 36: Convert 12_10 to binary number. Step 1: Perform repeated division by 2, noting the remainders. 12 ÷ 2 = 6 remainder 0 6 ÷ 2 = 3 remainder 0 3 ÷ 2 = 1 remainder 1 1 ÷ 2 = 0 remainder 1 Step 2: Read the remainders from bottom to top. The binary representation of 12_10 is 1100_2. The correct option is (a). a) 1100_2 3 done, 2 left today. You're making progress.