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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You're on a roll — here are the solutions to your problems: Problem 1 (Left Column - Pie Chart): E-sheen was given ₦20000 for her pocket money and spent it as represented on a pie chart. The amounts spent are given as 2X, 3X, 4X, and X. a) Find X Step 1: Sum the proportions of money spent. The total amount spent is the sum of the given parts: 2X + 3X + 4X + X = 10X Step 2: Equate the total proportion to the total money. The total pocket money is ₦20000. 10X = 20000 Step 3: Solve for X. X = (20000)/(10) X = ₦2000 b) How much does she spend on each item? Step 1: Calculate the amount for each proportion using X = ₦2000. For 2X: 2X = 2 × 2000 = ₦4000 For 3X: 3X = 3 × 2000 = ₦6000 For 4X: 4X = 4 × 2000 = ₦8000 For X: X = ₦2000 She spends: ₦4000, ₦6000, ₦8000, and ₦2000 on each item. Problem 2 (Left Column - Exponents): Work out 5^3 × 5^-5. Step 1: Apply the exponent rule a^m × a^n = a^m+n. 5^3 × 5^-5 = 5^3 + (-5) 5^3 + (-5) = 5^3-5 5^3-5 = 5^-2 Step 2: Apply the exponent rule a^-n = (1)/(a^n). 5^-2 = (1)/(5^2) 5^-2 = (1)/(25) The result is (1)/(25). Problem 3 (Left Column - Percentage/Fraction): 12.5% of the people in town are traders. What fraction of the people are in town are traders? Step 1: Convert the percentage to a fraction by dividing by 100. 12.5\% = (12.5)/(100) Step 2: Eliminate the decimal by multiplying the numerator and denominator by 10. (12.5 × 10)/(100 × 10) = (125)/(1000) Step 3: Simplify the fraction. Divide both numerator and denominator by their greatest common divisor. (125 ÷ 125)/(1000 ÷ 125) = (1)/(8) The fraction of people who are traders is (1)/(8). Problem 4 (Left Column - Polygon): A regular polygon has one of its interior angles as 144^. a) Name the polygon. Step 1: Find the exterior angle. The sum of an interior angle and its corresponding exterior angle is 180^. Exterior Angle = 180^ - Interior Angle Exterior Angle = 180^ - 144^ = 36^ Step 2: Find the number of sides (n). For any regular polygon, the sum of its exterior angles is 360^. Therefore, each exterior angle is (360^)/(n). 36^ = (360^)/(n) n = (360^)/(36^) n = 10 A polygon with 10 sides is a decagon. b) Find the sum of its interior angles. Step 1: Use the formula for the sum of interior angles of an n-sided polygon: (n-2) × 180^. For n=10: Sum of Interior Angles = (10-2) × 180^ Sum of Interior Angles = 8 × 180^ Sum of Interior Angles = 1440^ The sum of its interior angles is 1440^. Problem 1 (Right Column - Simple Interest): A sum of ₦45000 is invested at 12% per annum simple interest. What is the total amount after 4 years? Step 1: Identify the given values. Principal (P) = ₦45000 Rate (R) = 12% = 0.12 Time (T) = 4 years Step 2: Calculate the simple interest (SI). SI = P × R × T SI = 45000 × 0.12 × 4 SI = 45000 × 0.48 SI = ₦21600 Step 3: Calculate the total amount (A). A = P + SI A = 45000 + 21600 A = ₦66600 The total amount after 4 years is ₦66600. Problem 2 (Right Column - Time Zone): The time in Accra is 9:00 am. What time is it in Buenos Aires, in the +3 time zone to the west? Step 1: Determine the time difference. "3 time zone to the west" means Buenos Aires is 3 hours behind Accra. Time difference = 3 hours. Step 2: Calculate the time in Buenos Aires. Time in Buenos Aires = Time in Accra - Time difference Time in Buenos Aires = 9:00 am - 3 hours Time in Buenos Aires = 6:00 am The time in Buenos Aires is 6:00 am. (The "Find the value of K" part of the question is unclear in this context and is not addressed.) Problem 3 (Right Column - Fraction Arithmetic): Evaluate (2)/(3) - (1)/(4) + (3)/(5). Step 1: Find the least common multiple (LCM) of the denominators (3, 4, 5). The LCM of 3, 4, and 5 is 3 × 4 × 5 = 60. Step 2: Convert each fraction to an equivalent fraction with a denominator of 60. (2)/(3) = 2