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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1. a) Identify each of them. (i) The first diagram is a circle. (ii) The second diagram is a rectangle. b) Find the area of each of the shape. For (i) Circle:* Step 1: Identify the radius. The diameter is given as 7 cm, so the radius r = (7)/(2) = 3.5 cm. Step 2: Apply the formula for the area of a circle. The area of a circle is given by A = r^2. Using ≈ (22)/(7). A = (22)/(7) × (3.5 cm)^2 A = (22)/(7) × (3.5 × 3.5) cm^2 A = (22)/(7) × 12.25 cm^2 A = 22 × 1.75 cm^2 A = 38.5 cm^2 The area of the circle is 38.5 cm^2. For (ii) Rectangle:* Step 1: Identify the length and width. Length L = 8.5 cm Width W = 3.5 cm Step 2: Apply the formula for the area of a rectangle. The area of a rectangle is given by A = L × W. A = 8.5 cm × 3.5 cm A = 29.75 cm^2 The area of the rectangle is 29.75 cm^2. 2. a) How many students are in JS3 class? Step 1: Sum the number of students from all classes. Total students = 20 + 16 + 21 + 25 + 17 + 15 + 11 Total students = 125 There are 125 students in JS3 class. b) Calculate the mean of the data. Step 1: Use the total number of students from part (a) and count the number of classes. Total students = 125 Number of classes = 7 (A, B, C, D, E, F, G) Step 2: Calculate the mean. Mean = Sum of studentsNumber of classes = (125)/(7) Mean ≈ 17.857 The mean of the data is (125)/(7) ≈ 17.86 (rounded to two decimal places). c) What percentages of the students are in F class? Step 1: Identify the number of students in F class and the total number of students. Students in F class = 15 Total students = 125 (from part a) Step 2: Calculate the percentage. Percentage = Students in F classTotal students × 100\% Percentage = (15)/(125) × 100\% Percentage = 0.12 × 100\% Percentage = 12\% 12\% of the students are in F class. 3. a) A book costs N750.00 and a pencil costs N45.00. If Collins wants to buy 6 books and 4 pencils, how much money does he need in total to pay? Step 1: Calculate the cost of 6 books. Cost of books = 6 × N750.00 = N4500.00 Step 2: Calculate the cost of 4 pencils. Cost of pencils = 4 × N45.00 = N180.00 Step 3: Calculate the total cost. Total cost = Cost of books + Cost of pencils Total cost = N4500.00 + N180.00 = N4680.00 Collins needs N4680.00 in total. b) A man invested N143500.00 at 5% simple interest for 4 years. At the end of the period, how much was his investment altogether? Step 1: Identify the principal, rate, and time. Principal P = N143500.00 Rate R = 5\% Time T = 4 years Step 2: Calculate the simple interest (SI). SI = (P × R × T)/(100) SI = (143500 × 5 × 4)/(100) SI = (143500 × 20)/(100) SI = 1435 × 20 SI = N28700.00 Step 3: Calculate the total investment (Amount). Amount = P + SI Amount = N143500.00 + N28700.00 Amount = N172200.00 His investment altogether was N172200.00. 4. a) Factorise x^2 - 4x - 21 = 0. Step 1: Find two numbers that multiply to -21 and add to -4. The numbers are -7 and 3. Step 2: Rewrite the middle term using these numbers. x^2 - 7x + 3x - 21 = 0 Step 3: Factor by grouping. x(x - 7) + 3(x - 7) = 0 (x - 7)(x + 3) = 0 Step 4: Solve for x. x - 7 = 0 x = 7 x + 3 = 0 x = -3 The factorised form is (x - 7)(x + 3) = 0, and the solutions are x = 7 or x = -3. b) Evaluate 9.95 × 10^-4 - 7.3 × 10^-5 and express your answer on standard form. Step 1: Convert both numbers to the same power of 10. Let's convert 7.3 × 10^-5 to a number with 10^-4. 7.3 × 10^-5 = 0.73 × 10^-4 Step 2: Perform the subtraction. 9.95 × 10^-4 - 0.73 × 10^-4 (9.95 - 0.73) × 10^-4 9.22 × 10^-4 Step 3: Express the answer in standard form (which it already is, as 9.22 is between 1 and 10). The result is 9.22 × 10^-4. What's next?