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
Hey Ngoh, good to see you again. Step 1: Solve Question 1. To write "twenty-three point seven five million" in figures, we multiply 23.75 by 1,000,000. 23.75 × 1,000,000 = 23,750,000 The number in figures is 23,750,000. Step 2: Solve Question 2. Michael Jackson died in 2009 at the age of 50. To find his birth year, subtract his age from the death year. Birth Year = Death Year - Age Birth Year = 2009 - 50 = 1959 The year he was born is 1959. Step 3: Solve Question 3. Total pupils = 20. Pupils who love football (F) = 13. Pupils who love handball (H) = 8. Pupils who love both (F and H) = 5. Pupils who love only football = 13 - 5 = 8. Pupils who love only handball = 8 - 5 = 3. Pupils who love at least one sport = (only F) + (only H) + (both F and H) 8 + 3 + 5 = 16 Pupils who love neither sport = Total pupils - Pupils who love at least one sport 20 - 16 = 4 Percentage of pupils who love neither sport = Number who love neitherTotal pupils × 100\% (4)/(20) × 100\% = (1)/(5) × 100\% = 20\% The percentage of pupils who love neither football nor handball is 20\%. Step 4: Solve Question 4. Quarter past 12 noon is 12:15. The minute hand moves 360^ in 60 minutes, so 6^ per minute. At 15 minutes, its angle from 12 is: 15 × 6^ = 90^ The hour hand moves 360^ in 12 hours, so 30^ per hour. It also moves 0.5^ per minute. At 12:15, its angle from 12 is: 12 × 30^ + 15 × 0.5^ = 360^ + 7.5^ Since 360^ is a full circle, the hour hand is at 7.5^ from the 12 mark. The angle between the minute hand and the hour hand is the absolute difference: |90^ - 7.5^| = 82.5^ The angle represented is 82.5^. Step 5: Solve Question 5. To convert the denary number 62 to a hexal (base 6) number, we perform successive divisions by 6 and record the remainders. 62 ÷ 6 = 10 remainder 2 10 ÷ 6 = 1 remainder 4 1 ÷ 6 = 0 remainder 1 Reading the remainders from bottom to top, the hexal number is 142_6. 62 in hexal is 142_6. Step 6: Solve Question 6. Let V be the total volume of the drum in liters. Initially, the drum is (4)/(5) full, so the volume of water is (4)/(5)V. After withdrawing 60 liters, the drum is (1)/(2) full, so the volume of water is (1)/(2)V. We can set up the equation: (4)/(5)V - 60 = (1)/(2)V To solve for V, first move the V terms to one side: (4)/(5)V - (1)/(2)V = 60 Find a common denominator for the fractions (which is 10): (8)/(10)V - (5)/(10)V = 60 (3)/(10)V = 60 Multiply both sides by (10)/(3): V = 60 × (10)/(3) V = 20 × 10 V = 200 The drum can hold 200 liters. Step 7: Solve Question 7. The man sold the article for 38,400 FRS and made a loss of 20%. This means the selling price (SP) is 80% of the cost price (CP). 0.80 × CP = 38,400 FRS CP = (38,400)/(0.80) CP = 48,000 FRS To gain 30%, the new selling price (New SP) should be 130% of the cost price. New SP = 1.30 × CP New SP = 1.30 × 48,000 New SP = 62,400 FRS He was supposed to sell it for 62,400 FRS. Step 8: Solve Question 8. A score is 20. Half a dozen is 6. To find what percentage of a score is half a dozen: Half a dozenA score × 100\% = (6)/(20) × 100\% (3)/(10) × 100\% = 30\% Half a dozen is 30\% of a score. Step 9: Solve Question 9. Johnson's mother gave birth to his junior brother in 2018. At that time, Johnson was 9 years old. The age difference between Johnson and his brother is constant. Age difference = Johnson's age when brother was born = 9 years. If the baby (junior brother) is 9 years old today, Johnson's current age would be 9 + 9 = 18 years. The difference in their ages is 9 years. Step 10: Solve Question 10. Number of seats in the bus = 70. The bus is full, so there are 70 passengers. Each passenger paid 7,000 FRS. Total amount raised = Number of passengers × Fare per passenger Total raised = 70 × 7,000 FRS Total raised = 490,000 FRS The amount raised from all the passengers is 490,000 FRS. Send me the next one 📸