c) The diagram shows a circle centre O. If POQ = x°, the diameter of the circle is 7cm and the area of the shaded portion is 27.5cm². Find, correct to the nearest degree, the value of x. [Take π = 22/7]

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Asked on June 3, 2026Mathematics

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.

Accepted Answer · 2026-06-03T06:10:42.680Z

c) Step 1: Find the radius of the circle. The diameter is 7 cm, so the radius r = (7)/(2) cm. Step 2: Calculate the area of the entire circle. The area of a circle is given by A = r^2. A = (22)/(7) × ((7)/(2))^2 A = (22)/(7) × (49)/(4) A = (22 × 7)/(4) = (154)/(4) = 38.5 cm^2 Step 3: Determine the area of the unshaded sector. The area of the shaded portion is 27.5 cm^2. Area of unshaded sector = Total area - Area of shaded portion Area of unshaded sector = 38.5 - 27.5 = 11 cm^2 Step 4: Use the area of the unshaded sector to find the angle x. The area of a sector with angle is given by ()/(360^) × r^2. Here, the angle of the unshaded sector is x^. 11 = (x)/(360) × 38.5 x = (11 × 360)/(38.5) x = (3960)/(38.5) x = 102.857... Step 5: Round the value of x to the nearest degree. x ≈ 103^ The value of x is 103^. a) Step 1: Calculate the import duty. Original cost of fish = GHe 400.00. Import duty = 15% of GHe 400.00. Import Duty = 0.15 × 400 = GHe 60.00 Step 2: Calculate the cost after import duty. Cost after duty = 400 + 60 = GHe 460.00 Step 3: Calculate the sales tax. Sales tax = 10% of the total cost including import duty. Sales Tax = 0.10 × 460 = GHe 46.00 Step 4: Calculate the total cost price (CP). CP = Cost after duty + Sales Tax CP = 460 + 46 = GHe 506.00 Step 5: Calculate the profit. Selling Price (SP) = GHe 660.00. Profit = SP - CP Profit = 660 - 506 = GHe 154.00 Step 6: Calculate the percentage profit. Percentage Profit = ProfitCP × 100\% Percentage Profit = (154)/(506) × 100\% Percentage Profit = 0.304347... × 100\% Percentage Profit ≈ 30.43\% The percentage profit is 30.43\%. b) Step 1: Define variables and total students. Number of boys = 1000. Let the number of girls be G. Total number of students = 1000 + G. Step 2: Calculate the number of successful students from boys and girls. Number of successful boys = 50% of 1000 = 0.50 × 1000 = 500. Number of successful girls = 40% of G = 0.40G. Total successful students = 500 + 0.40G. Step 3: Calculate the total number of successful students using the overall percentage. 48% of the total number of students were successful. Total successful students = 0.48 × (1000 + G). Step 4: Set up and solve the equation for G. 500 + 0.40G = 0.48(1000 + G) 500 + 0.40G = 480 + 0.48G Subtract 0.40G from both sides: 500 = 480 + 0.48G - 0.40G 500 = 480 + 0.08G Subtract 480 from both sides: 500 - 480 = 0.08G 20 = 0.08G Divide by 0.08: G = (20)/(0.08) G = 250 The number of girls in the school is 250. Send me the next one 📸

Accepted Answer · 2026-06-03T06:10:42.680Z

c) Step 1: Find the radius of the circle. The diameter is 7 cm, so the radius r = (7)/(2) cm. Step 2: Calculate the area of the entire circle. The area of a circle is given by A = r^2. A = (22)/(7) × ((7)/(2))^2 A = (22)/(7) × (49)/(4) A = (22 × 7)/(4) = (154)/(4) = 38.5 cm^2 Step 3: Determine the area of the unshaded sector. The area of the shaded portion is 27.5 cm^2. Area of unshaded sector = Total area - Area of shaded portion Area of unshaded sector = 38.5 - 27.5 = 11 cm^2 Step 4: Use the area of the unshaded sector to find the angle x. The area of a sector with angle is given by ()/(360^) × r^2. Here, the angle of the unshaded sector is x^. 11 = (x)/(360) × 38.5 x = (11 × 360)/(38.5) x = (3960)/(38.5) x = 102.857... Step 5: Round the value of x to the nearest degree. x ≈ 103^ The value of x is 103^. a) Step 1: Calculate the import duty. Original cost of fish = GHe 400.00. Import duty = 15% of GHe 400.00. Import Duty = 0.15 × 400 = GHe 60.00 Step 2: Calculate the cost after import duty. Cost after duty = 400 + 60 = GHe 460.00 Step 3: Calculate the sales tax. Sales tax = 10% of the total cost including import duty. Sales Tax = 0.10 × 460 = GHe 46.00 Step 4: Calculate the total cost price (CP). CP = Cost after duty + Sales Tax CP = 460 + 46 = GHe 506.00 Step 5: Calculate the profit. Selling Price (SP) = GHe 660.00. Profit = SP - CP Profit = 660 - 506 = GHe 154.00 Step 6: Calculate the percentage profit. Percentage Profit = ProfitCP × 100\% Percentage Profit = (154)/(506) × 100\% Percentage Profit = 0.304347... × 100\% Percentage Profit ≈ 30.43\% The percentage profit is 30.43\%. b) Step 1: Define variables and total students. Number of boys = 1000. Let the number of girls be G. Total number of students = 1000 + G. Step 2: Calculate the number of successful students from boys and girls. Number of successful boys = 50% of 1000 = 0.50 × 1000 = 500. Number of successful girls = 40% of G = 0.40G. Total successful students = 500 + 0.40G. Step 3: Calculate the total number of successful students using the overall percentage. 48% of the total number of students were successful. Total successful students = 0.48 × (1000 + G). Step 4: Set up and solve the equation for G. 500 + 0.40G = 0.48(1000 + G) 500 + 0.40G = 480 + 0.48G Subtract 0.40G from both sides: 500 = 480 + 0.48G - 0.40G 500 = 480 + 0.08G Subtract 480 from both sides: 500 - 480 = 0.08G 20 = 0.08G Divide by 0.08: G = (20)/(0.08) G = 250 The number of girls in the school is 250. Send me the next one 📸

c) The diagram shows a circle centre O. If POQ = x°, the diameter of the circle is 7cm and the area of the shaded portion is 27.5cm². Find, correct to the nearest degree, the value of x. [Take π = 22/7]

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c) The diagram shows a circle centre O. If POQ = x°, the diameter of the circle is 7cm and the area of the shaded portion is 27.5cm². Find, correct to the nearest degree, the value of x. [Take π = 22/7]

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