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Solve the following questions: 1. Write "twenty-three point seven five million" in figures. 2. Michael Jackson died in 2009 aged 50. In what year was he born? 3. 20 pupils were asked about their favou

Mathematics

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  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=23,750,00023.75 \times 1,000,000 = 23,750,000

    The number in figures is 23,750,000\boxed{\text{23,750,000}}.

  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\text{Birth Year} = \text{Death Year} - \text{Age} Birth Year=2009−50=1959\text{Birth Year} = 2009 - 50 = 1959

    The year he was born is 1959\boxed{\text{1959}}.

  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=813 - 5 = 8.
    Pupils who love only handball = 8−5=38 - 5 = 3.
    Pupils who love at least one sport = (only F) + (only H) + (both F and H)

    8+3+5=168 + 3 + 5 = 16

    Pupils who love neither sport = Total pupils - Pupils who love at least one sport

    20−16=420 - 16 = 4

    Percentage of pupils who love neither sport = Number who love neitherTotal pupils×100%\frac{\text{Number who love neither}}{\text{Total pupils}} \times 100\%

    420×100%=15×100%=20%\frac{4}{20} \times 100\% = \frac{1}{5} \times 100\% = 20\%

    The percentage of pupils who love neither football nor handball is 20%\boxed{\text{20\%}}.

  4. Solve Question 4.

    Quarter past 12 noon is 12:15.
    The minute hand moves 360∘360^\circ in 60 minutes, so 6∘6^\circ per minute. At 15 minutes, its angle from 12 is:

    15×6∘=90∘15 \times 6^\circ = 90^\circ

    The hour hand moves 360∘360^\circ in 12 hours, so 30∘30^\circ per hour. It also moves 0.5∘0.5^\circ per minute. At 12:15, its angle from 12 is:

    12×30∘+15×0.5∘=360∘+7.5∘12 \times 30^\circ + 15 \times 0.5^\circ = 360^\circ + 7.5^\circ

    Since 360∘360^\circ is a full circle, the hour hand is at 7.5∘7.5^\circ from the 12 mark.
    The angle between the minute hand and the hour hand is the absolute difference:

    ∣90∘−7.5∘∣=82.5∘|90^\circ - 7.5^\circ| = 82.5^\circ

    The angle represented is \boxed{\text{82.5^\circ}}.

  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 262 \div 6 = 10 \text{ remainder } 2 10÷6=1 remainder 410 \div 6 = 1 \text{ remainder } 4 1÷6=0 remainder 11 \div 6 = 0 \text{ remainder } 1

    Reading the remainders from bottom to top, the hexal number is 1426142_6.
    62 in hexal is 1426\boxed{\text{142}_6}.

  6. Solve Question 6.

    Let VV be the total volume of the drum in liters.
    Initially, the drum is 45\frac{4}{5} full, so the volume of water is 45V\frac{4}{5}V.
    After withdrawing 60 liters, the drum is 12\frac{1}{2} full, so the volume of water is 12V\frac{1}{2}V.
    We can set up the equation:

    45V−60=12V\frac{4}{5}V - 60 = \frac{1}{2}V

    To solve for VV, first move the VV terms to one side:

    45V−12V=60\frac{4}{5}V - \frac{1}{2}V = 60

    Find a common denominator for the fractions (which is 10):

    810V−510V=60\frac{8}{10}V - \frac{5}{10}V = 60 310V=60\frac{3}{10}V = 60

    Multiply both sides by 103\frac{10}{3}:

    V=60×103V = 60 \times \frac{10}{3} V=20×10V = 20 \times 10 V=200V = 200

    The drum can hold 200 liters\boxed{\text{200 liters}}.

  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 FRS0.80 \times \text{CP} = 38,400 \text{ FRS} CP=38,4000.80\text{CP} = \frac{38,400}{0.80} CP=48,000 FRS\text{CP} = 48,000 \text{ FRS}

    To gain 30%, the new selling price (New SP) should be 130% of the cost price.

    New SP=1.30×CP\text{New SP} = 1.30 \times \text{CP} New SP=1.30×48,000\text{New SP} = 1.30 \times 48,000 New SP=62,400 FRS\text{New SP} = 62,400 \text{ FRS}

    He was supposed to sell it for 62,400 FRS\boxed{\text{62,400 FRS}}.

  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%=620×100%\frac{\text{Half a dozen}}{\text{A score}} \times 100\% = \frac{6}{20} \times 100\% 310×100%=30%\frac{3}{10} \times 100\% = 30\%

    Half a dozen is 30%\boxed{\text{30\%}} of a score.

  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=189 + 9 = 18 years.
    The difference in their ages is 9 years\boxed{\text{9 years}}.

  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 ×\times Fare per passenger

    Total raised=70×7,000 FRS\text{Total raised} = 70 \times 7,000 \text{ FRS} Total raised=490,000 FRS\text{Total raised} = 490,000 \text{ FRS}

    The amount raised from all the passengers is 490,000 FRS\boxed{\text{490,000 FRS}}.

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