We read your photo as:

Solve the following problems: Convert "twenty - three point seven five million" to figures. Calculate Michael Jackson's birth year if he died in 2009 at 50. Find the percentage of 20 pupils who love n

Mathematics

ScanSolve AI Answer

Step-by-step solution

10 steps
  1. Convert "twenty - three point seven five million" to figures.

    23.75 million=23.75×1,000,000=23,750,00023.75 \text{ million} = 23.75 \times 1,000,000 = 23,750,000

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

  2. Calculate Michael Jackson's birth year.

    Michael Jackson died in 2009 at the age of 50.

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

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

  3. Calculate the percentage of pupils who love neither football nor handball.

    Total pupils = 20.
    Pupils who love football (F) = 13.
    Pupils who love handball (H) = 8.
    Pupils who love both (F ∩\cap H) = 5.

    First, find the number of pupils who love at least one sport:

    ∣F∪H∣=∣F∣+∣H∣−∣F∩H∣|F \cup H| = |F| + |H| - |F \cap H| ∣F∪H∣=13+8−5|F \cup H| = 13 + 8 - 5 ∣F∪H∣=21−5=16|F \cup H| = 21 - 5 = 16

    Number of pupils who love neither sport:

    Neither=Total Pupils−∣F∪H∣\text{Neither} = \text{Total Pupils} - |F \cup H| Neither=20−16=4\text{Neither} = 20 - 16 = 4

    Percentage of pupils who love neither sport:

    Percentage=Number who love neitherTotal Pupils×100%\text{Percentage} = \frac{\text{Number who love neither}}{\text{Total Pupils}} \times 100\% Percentage=420×100%=15×100%=20%\text{Percentage} = \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. Calculate the angle represented by quarter past 12noon.

    Quarter past 12noon is 12:15.
    The hour hand moves 360∘360^\circ in 12 hours, so 30∘30^\circ per hour or 0.5∘0.5^\circ per minute.
    The minute hand moves 360∘360^\circ in 60 minutes, so 6∘6^\circ per minute.

    Angle of the hour hand at 12:15:

    Hour hand angle=(12×30∘)+(15×0.5∘)=360∘+7.5∘=367.5∘\text{Hour hand angle} = (12 \times 30^\circ) + (15 \times 0.5^\circ) = 360^\circ + 7.5^\circ = 367.5^\circ

    Since 360∘360^\circ is a full circle, this is equivalent to 7.5∘7.5^\circ from the 12.

    Angle of the minute hand at 12:15:

    Minute hand angle=15×6∘=90∘\text{Minute hand angle} = 15 \times 6^\circ = 90^\circ

    The angle between the hands is the absolute difference:

    Angle=∣90∘−7.5∘∣=82.5∘\text{Angle} = |90^\circ - 7.5^\circ| = 82.5^\circ

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

  5. Convert 62 (denary) to hexal (base 6).

    Divide 62 by 6:

    62÷6=10 remainder 262 \div 6 = 10 \text{ remainder } 2

    Divide 10 by 6:

    10÷6=1 remainder 410 \div 6 = 1 \text{ remainder } 4

    Divide 1 by 6:

    1÷6=0 remainder 11 \div 6 = 0 \text{ remainder } 1

    Reading the remainders from bottom to top, we get 142.
    So, 6210=142662_{10} = 142_6.
    The hexal number is 142\boxed{\text{142}}.

  6. Calculate the total volume of the drum.

    Let VV be the total volume of the drum in liters.
    Initially, the drum is 34\frac{3}{4} full, so the volume is 34V\frac{3}{4}V.
    After withdrawing 60 liters, the volume is 13\frac{1}{3} full, so the volume is 13V\frac{1}{3}V.
    Set up the equation:

    34V−60=13V\frac{3}{4}V - 60 = \frac{1}{3}V

    Subtract 13V\frac{1}{3}V from both sides and add 60 to both sides:

    34V−13V=60\frac{3}{4}V - \frac{1}{3}V = 60

    Find a common denominator for the fractions (12):

    912V−412V=60\frac{9}{12}V - \frac{4}{12}V = 60 512V=60\frac{5}{12}V = 60

    Multiply both sides by 125\frac{12}{5}:

    V=60×125V = 60 \times \frac{12}{5} V=12×12V = 12 \times 12 V=144 litersV = 144 \text{ liters}

    The drum can hold 144 liters\boxed{\text{144 liters}} when full.

  7. Calculate the selling price to gain 30%.

    The man sold the article for 38,400 FRS at a loss of 25%.
    This means 38,400 FRS represents 100%−25%=75%100\% - 25\% = 75\% of the cost price (CP).

    0.75×CP=38,4000.75 \times \text{CP} = 38,400 CP=38,4000.75\text{CP} = \frac{38,400}{0.75} CP=51,200 FRS\text{CP} = 51,200 \text{ FRS}

    To gain 30%, the new selling price (NSP) should be 100%+30%=130%100\% + 30\% = 130\% of the cost price.

    NSP=1.30×CP\text{NSP} = 1.30 \times \text{CP} NSP=1.30×51,200\text{NSP} = 1.30 \times 51,200 NSP=66,560 FRS\text{NSP} = 66,560 \text{ FRS}

    He was supposed to sell it for 66,560 FRS\boxed{\text{66,560 FRS}} to gain 30%.

  8. Calculate what percentage of a score is half a dozen.

    A score = 20.
    Half a dozen = 6.

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

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

  9. Calculate the difference in their ages.

    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 junior brother is constant and is 9 years.
    If the baby is 9 years old today, Johnson is 9+9=189 + 9 = 18 years old today.
    The difference in their ages is 9 years\boxed{\text{9 years}}.

  10. Calculate the total amount raised from all passengers.

    Number of seats = 70.
    The bus had a full load, so there were 70 passengers.
    Each passenger paid 7,000 FRS.

    Total raised=Number of passengers×Cost per passenger\text{Total raised} = \text{Number of passengers} \times \text{Cost 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 was 490,000 FRS\boxed{\text{490,000 FRS}}.

Was this helpful?

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question