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I. What is the size of the angle marked ‘variety’? ii. How many hours in a day do the station telecast news?

Mathematics

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Question 1:
This question is incomplete as there is no pie chart or context provided for 'variety' or 'telecast news'. Therefore, it cannot be solved.

Question 2:

i) What is the angle for rent?

  1. The sum of angles in a pie chart is 360∘360^\circ.

    Add the given angles and subtract from 360∘360^\circ to find the angle for rent (xx).

    x∘+105∘+36∘+30∘+84∘+65∘=360∘x^\circ + 105^\circ + 36^\circ + 30^\circ + 84^\circ + 65^\circ = 360^\circ x∘+320∘=360∘x^\circ + 320^\circ = 360^\circ x∘=360∘−320∘x^\circ = 360^\circ - 320^\circ x∘=40∘x^\circ = 40^\circ

    The angle for rent is 40∘\boxed{\text{40}^\circ}.

    ii) Calculate the amount Mr. Brown put in his saving account.

  2. The total monthly income is Gh¢5,400.00.

    The angle for savings is 84∘84^\circ.

  3. Calculate the amount saved using the proportion of the angle.

    Amount saved=Savings angleTotal angle×Total income\text{Amount saved} = \frac{\text{Savings angle}}{\text{Total angle}} \times \text{Total income} Amount saved=84∘360∘×Gh¢5,400.00\text{Amount saved} = \frac{84^\circ}{360^\circ} \times \text{Gh¢}5,400.00 Amount saved=0.2333...×Gh¢5,400.00\text{Amount saved} = 0.2333... \times \text{Gh¢}5,400.00 Amount saved=Gh¢1,260.00\text{Amount saved} = \text{Gh¢}1,260.00

    Mr. Brown put Gh¢1,260.00\boxed{\text{Gh¢1,260.00}} in his saving account.

    iii) What fraction of his income was spent on rent?

  4. The angle for rent is 40∘40^\circ (from part i).

  5. Express this angle as a fraction of the total angle in a circle.

    Fraction on rent=Rent angleTotal angle\text{Fraction on rent} = \frac{\text{Rent angle}}{\text{Total angle}} Fraction on rent=40∘360∘\text{Fraction on rent} = \frac{40^\circ}{360^\circ} Fraction on rent=19\text{Fraction on rent} = \frac{1}{9}

    The fraction of his income spent on rent is 19\boxed{\frac{1}{9}}.

    Question 3:

    i) Find the angle representing Toyota.

  6. The sum of angles in a pie chart is 360∘360^\circ.

    Add the given angles and subtract from 360∘360^\circ to find the angle for Toyota (xx).

    x∘+100∘+36∘+40∘+64∘=360∘x^\circ + 100^\circ + 36^\circ + 40^\circ + 64^\circ = 360^\circ x∘+240∘=360∘x^\circ + 240^\circ = 360^\circ x∘=360∘−240∘x^\circ = 360^\circ - 240^\circ x∘=120∘x^\circ = 120^\circ

    The angle representing Toyota is 120∘\boxed{\text{120}^\circ}.

    ii) How many Toyota cars were parked at the park?

  7. We are given that 9 Opel cars represent an angle of 36∘36^\circ.

  8. Determine the number of cars per degree.

    Cars per degree=9 cars36∘=0.25 cars/degree\text{Cars per degree} = \frac{9 \text{ cars}}{36^\circ} = 0.25 \text{ cars/degree}

  9. Multiply the cars per degree by the angle for Toyota (120∘120^\circ from part i).

    Number of Toyota cars=0.25 cars/degree×120∘\text{Number of Toyota cars} = 0.25 \text{ cars/degree} \times 120^\circ Number of Toyota cars=30 cars\text{Number of Toyota cars} = 30 \text{ cars}

    There were 30 Toyota cars\boxed{\text{30 Toyota cars}} parked at the park.

    iii) How many cars were parked at the park?

  10. Use the cars per degree calculated in part ii.

  11. Multiply the cars per degree by the total angle of the pie chart (360∘360^\circ).

    Total cars=0.25 cars/degree×360∘\text{Total cars} = 0.25 \text{ cars/degree} \times 360^\circ Total cars=90 cars\text{Total cars} = 90 \text{ cars}

    There were 90 cars\boxed{\text{90 cars}} parked at the park.

    iv) What percentage of the cars parked is Nissan?

  12. The angle for Nissan is 40∘40^\circ.

  13. Calculate the percentage by dividing the Nissan angle by the total angle and multiplying by 100%100\%.

    Percentage of Nissan cars=Nissan angleTotal angle×100%\text{Percentage of Nissan cars} = \frac{\text{Nissan angle}}{\text{Total angle}} \times 100\% Percentage of Nissan cars=40∘360∘×100%\text{Percentage of Nissan cars} = \frac{40^\circ}{360^\circ} \times 100\% Percentage of Nissan cars=19×100%\text{Percentage of Nissan cars} = \frac{1}{9} \times 100\% Percentage of Nissan cars≈11.11%\text{Percentage of Nissan cars} \approx 11.11\%

    Approximately 11.11%\boxed{\text{11.11\%}} of the cars parked are Nissan.

    Question 4:

    i) Find the value of x.

  14. The total number of people surveyed is 400.

    Sum the number of people for each newspaper and set it equal to the total.

    150+100+75+x+25=400150 + 100 + 75 + x + 25 = 400 350+x=400350 + x = 400 x=400−350x = 400 - 350 x=50x = 50

    The value of xx is 50\boxed{\text{50}}.

    ii) Draw a pie chart for the distribution.
    To draw a pie chart, we need to calculate the angle for each sector.

  15. Calculate the angle for each newspaper using the formula

    Angle=Number of peopleTotal people×360∘\text{Angle} = \frac{\text{Number of people}}{\text{Total people}} \times 360^\circ
    • Graphic: 150400×360∘=135∘\frac{150}{400} \times 360^\circ = 135^\circ
    • Ghanaian Times: 100400×360∘=90∘\frac{100}{400} \times 360^\circ = 90^\circ
    • Mirror: 75400×360∘=67.5∘\frac{75}{400} \times 360^\circ = 67.5^\circ
    • Daily Guide (x=50): 50400×360∘=45∘\frac{50}{400} \times 360^\circ = 45^\circ
    • Free Press: 25400×360∘=22.5∘\frac{25}{400} \times 360^\circ = 22.5^\circ

  16. Sum the angles to verify they add up to 360∘360^\circ.

    135∘+90∘+67.5∘+45∘+22.5∘=360∘135^\circ + 90^\circ + 67.5^\circ + 45^\circ + 22.5^\circ = 360^\circ.
    To draw the pie chart, use a compass to draw a circle. Then, use a protractor to measure and draw each angle from the center of the circle, labeling each sector with the newspaper name and its corresponding number of people or percentage.

    Question 5:

    i) Find angle y representing savings for the month.

  17. The sum of angles in a pie chart is 360∘360^\circ.

    Add the given angles and subtract from 360∘360^\circ to find the angle for savings (yy).

    y∘+108∘+84∘+72∘+60∘=360∘y^\circ + 108^\circ + 84^\circ + 72^\circ + 60^\circ = 360^\circ y∘+324∘=360∘y^\circ + 324^\circ = 360^\circ y∘=360∘−324∘y^\circ = 360^\circ - 324^\circ y∘=36∘y^\circ = 36^\circ

    The angle representing savings is 36∘\boxed{\text{36}^\circ}.

    ii) What's the man's salary for the month?

  18. We are given that Gh¢180.00 was spent on rent, and the angle for rent is 72∘72^\circ.

  19. Calculate the total salary using the proportion of the rent amount to its angle.

    Total salary=Total angleRent angle×Amount spent on rent\text{Total salary} = \frac{\text{Total angle}}{\text{Rent angle}} \times \text{Amount spent on rent} Total salary=360∘72∘×Gh¢180.00\text{Total salary} = \frac{360^\circ}{72^\circ} \times \text{Gh¢}180.00 Total salary=5×Gh¢180.00\text{Total salary} = 5 \times \text{Gh¢}180.00 Total salary=Gh¢900.00\text{Total salary} = \text{Gh¢}900.00

    The man's salary for the month is Gh¢900.00\boxed{\text{Gh¢900.00}}.

    iii) By how much does expenditure on others exceed that on clothing.

  20. Calculate the amount spent on "Others".

    The angle for "Others" is 84∘84^\circ.

    Amount on Others=84∘360∘×Gh¢900.00\text{Amount on Others} = \frac{84^\circ}{360^\circ} \times \text{Gh¢}900.00 Amount on Others=0.2333...×Gh¢900.00\text{Amount on Others} = 0.2333... \times \text{Gh¢}900.00 Amount on Others=Gh¢210.00\text{Amount on Others} = \text{Gh¢}210.00

  21. Calculate the amount spent on "Clothing".

    The angle for "Clothing" is 60∘60^\circ.

    Amount on Clothing=60∘360∘×Gh¢900.00\text{Amount on Clothing} = \frac{60^\circ}{360^\circ} \times \text{Gh¢}900.00 Amount on Clothing=16×Gh¢900.00\text{Amount on Clothing} = \frac{1}{6} \times \text{Gh¢}900.00 Amount on Clothing=Gh¢150.00\text{Amount on Clothing} = \text{Gh¢}150.00

  22. Find the difference between the expenditure on "Others" and "Clothing".

    Difference=Amount on Others−Amount on Clothing\text{Difference} = \text{Amount on Others} - \text{Amount on Clothing} Difference=Gh¢210.00−Gh¢150.00\text{Difference} = \text{Gh¢}210.00 - \text{Gh¢}150.00 Difference=Gh¢60.00\text{Difference} = \text{Gh¢}60.00

    Expenditure on others exceeds that on clothing by Gh¢60.00\boxed{\text{Gh¢60.00}}.

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