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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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3 partsStep-by-step solution
12 stepsPart c· 4 steps
Step 1: Find the radius of the circle.
The diameter is , so the radius .
Calculate the area of the entire circle.
The area of a circle is given by .
Determine the area of the unshaded sector.
The area of the shaded portion is .
Area of unshaded sector = Total area - Area of shaded portionUse the area of the unshaded sector to find the angle .
The area of a sector with angle is given by .
Here, the angle of the unshaded sector is .Round the value of to the nearest degree.
The value of is .
Part a
Step 1: Calculate the import duty.
Original cost of fish = GHe 400.00.
Import duty = 15% of GHe 400.00.
Calculate the cost after import duty.
Calculate the sales tax.
Sales tax = 10% of the total cost including import duty.
Calculate the total cost price (CP).
Calculate the profit.
Selling Price (SP) = GHe 660.00.
Calculate the percentage profit.
The percentage profit is .
Part b250
Step 1: Define variables and total students.
Number of boys = 1000.
Let the number of girls be .
Total number of students = .
Calculate the number of successful students from boys and girls.
Number of successful boys = 50% of 1000 = .
Number of successful girls = 40% of .
Total successful students = .Calculate the total number of successful students using the overall percentage.
48% of the total number of students were successful.
Total successful students = .Set up and solve the equation for .
Subtract from both sides:
Subtract 480 from both sides:
Divide by 0.08:
The number of girls in the school is .
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