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.
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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? Step 1: The sum of angles in a pie chart is 360^. Add the given angles and subtract from 360^ to find the angle for rent (x). x^ + 105^ + 36^ + 30^ + 84^ + 65^ = 360^ x^ + 320^ = 360^ x^ = 360^ - 320^ x^ = 40^ The angle for rent is 40^. ii) Calculate the amount Mr. Brown put in his saving account. Step 1: The total monthly income is Gh¢5,400.00. The angle for savings is 84^. Step 2: Calculate the amount saved using the proportion of the angle. Amount saved = Savings angleTotal angle × Total income Amount saved = (84^)/(360^) × Gh¢5,400.00 Amount saved = 0.2333... × Gh¢5,400.00 Amount saved = Gh¢1,260.00 Mr. Brown put Gh¢1,260.00 in his saving account. iii) What fraction of his income was spent on rent? Step 1: The angle for rent is 40^ (from part i). Step 2: Express this angle as a fraction of the total angle in a circle. Fraction on rent = Rent angleTotal angle Fraction on rent = (40^)/(360^) Fraction on rent = (1)/(9) The fraction of his income spent on rent is (1)/(9). Question 3: i) Find the angle representing Toyota. Step 1: The sum of angles in a pie chart is 360^. Add the given angles and subtract from 360^ to find the angle for Toyota (x). x^ + 100^ + 36^ + 40^ + 64^ = 360^ x^ + 240^ = 360^ x^ = 360^ - 240^ x^ = 120^ The angle representing Toyota is 120^. ii) How many Toyota cars were parked at the park? Step 1: We are given that 9 Opel cars represent an angle of 36^. Step 2: Determine the number of cars per degree. Cars per degree = 9 cars36^ = 0.25 cars/degree Step 3: Multiply the cars per degree by the angle for Toyota (120^ from part i). Number of Toyota cars = 0.25 cars/degree × 120^ Number of Toyota cars = 30 cars There were 30 Toyota cars parked at the park. iii) How many cars were parked at the park? Step 1: Use the cars per degree calculated in part ii. Step 2: Multiply the cars per degree by the total angle of the pie chart (360^). Total cars = 0.25 cars/degree × 360^ Total cars = 90 cars There were 90 cars parked at the park. iv) What percentage of the cars parked is Nissan? Step 1: The angle for Nissan is 40^. Step 2: Calculate the percentage by dividing the Nissan angle by the total angle and multiplying by 100\%. Percentage of Nissan cars = Nissan angleTotal angle × 100\% Percentage of Nissan cars = (40^)/(360^) × 100\% Percentage of Nissan cars = (1)/(9) × 100\% Percentage of Nissan cars ≈ 11.11\% Approximately 11.11\% of the cars parked are Nissan. Question 4: i) Find the value of x. Step 1: 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 = 400 350 + x = 400 x = 400 - 350 x = 50 The value of x is 50. ii) Draw a pie chart for the distribution. To draw a pie chart, we need to calculate the angle for each sector. Step 1: Calculate the angle for each newspaper using the formula: Angle = Number of peopleTotal people × 360^ • Graphic: (150)/(400) × 360^ = 135^ • Ghanaian Times: (100)/(400) × 360^ = 90^ • Mirror: (75)/(400) × 360^ = 67.5^ • Daily Guide (x=50): (50)/(400) × 360^ = 45^ • Free Press: (25)/(400) × 360^ = 22.5^ Step 2: Sum the angles to verify they add up to 360^. 135^ + 90^ + 67.5^ + 45^ + 22.5^ = 360^. 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. Step 1: The sum of angles in a pie chart is 360^. Add the given angles and subtract from 360^ to find the angle for savings (y). y^ + 108^ + 84^ + 72^ + 60^ = 360^ y^ + 324^ = 360^ y^ = 360^ - 324^ y^ = 36^ The angle representing savings is 36^. ii) What's the man's salary for the month? Step 1: We are given that Gh¢180.00 was spent on rent, and the angle for rent is 72^. Step 2: Calculate the total salary using the proportion of the rent amount to its angle. Total salary = Total angleRent angle × Amount spent on rent Total salary = (360^)/(72^) × Gh¢180.00 Total salary = 5 × Gh¢180.00 Total salary = Gh¢900.00 The man's salary for the month is Gh¢900.00. iii) By how much does expenditure on others exceed that on clothing. Step 1: Calculate the amount spent on "Others". The angle for "Others" is 84^. Amount on Others = (84^)/(360^) × Gh¢900.00 Amount on Others = 0.2333... × Gh¢900.00 Amount on Others = Gh¢210.00 Step 2: Calculate the amount spent on "Clothing". The angle for "Clothing" is 60^. Amount on Clothing = (60^)/(360^) × Gh¢900.00 Amount on Clothing = (1)/(6) × Gh¢900.00 Amount on Clothing = Gh¢150.00 Step 3: Find the difference between the expenditure on "Others" and "Clothing". Difference = Amount on Others - Amount on Clothing Difference = Gh¢210.00 - Gh¢150.00 Difference = Gh¢60.00 Expenditure on others exceeds that on clothing by Gh¢60.00. Drop the next question!