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.
ScanSolve AI Answer
Alright Noura — let's do this. Here are the solutions to the remaining questions: 2) A packet of sweets is shared between Amina, Pauline and Sharon in the ratio 2:3:5. If Pauline received 12 sweets, how many did Sharon receive? Step 1: Determine the value of one ratio part. The ratio for Amina : Pauline : Sharon is 2:3:5. Pauline's share corresponds to 3 parts of the ratio. Given that Pauline received 12 sweets, we can find the value of one part: 3 parts = 12 sweets 1 part = (12)/(3) = 4 sweets Step 2: Calculate Sharon's share. Sharon's share corresponds to 5 parts of the ratio. Sharon's sweets = 5 parts × 4 sweets/part Sharon's sweets = 20 sweets Sharon received 20 sweets. 3) A right circular cone has a base diameter of 12 cm and a height of 8 cm. Find the total surface area of the cone, leaving your answer to the nearest unit. Take = (22)/(7). Step 1: Determine the radius and calculate the slant height. The base diameter is 12 cm, so the radius r = (12)/(2) = 6 cm. The height h = 8 cm. The slant height l can be found using the Pythagorean theorem: l = sqrt(r^2 + h^2) l = sqrt(6^2 + 8^2) l = sqrt(36 + 64) l = sqrt(100) l = 10 cm Step 2: Calculate the area of the base. The area of the circular base is A_base = r^2. A_base = (22)/(7) × (6)^2 A_base = (22)/(7) × 36 A_base = (792)/(7) ≈ 113.14 cm^2 Step 3: Calculate the lateral surface area. The lateral surface area is A_lateral = r l. A_lateral = (22)/(7) × 6 × 10 A_lateral = (22)/(7) × 60 A_lateral = (1320)/(7) ≈ 188.57 cm^2 Step 4: Calculate the total surface area and round to the nearest unit. The total surface area (TSA) is the sum of the base area and the lateral surface area. TSA = A_base + A_lateral TSA = (792)/(7) + (1320)/(7) TSA = (2112)/(7) TSA ≈ 301.71 cm^2 Rounding to the nearest unit, the total surface area is 302 cm^2. 4) Complete the logic table. Step 1: Fill the ~Q column (negation of Q). Step 2: Fill the P ^ ~Q column (conjunction of P and ~Q). Step 3: Fill the P v (P ^ ~Q) column (disjunction of P and (P ^ ~Q)). | P | Q | ~Q | P ^ ~Q | P v (P ^ ~Q) | |---|---|----|--------|--------------| | T | T | F | F | T | | T | F | T | T | T | | F | T | F | F | F | | F | F | T | F | F | The completed logic table is shown above. What's next?