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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Hey Flora, good to see you again. Here are the solutions to your questions: 1. Pie Chart Analysis a) The pie chart shows the following angles: Goats: 120^ Sheep: 90^ Chicken: 60^ The total angle in a pie chart is 360^. Step 1: Sum the known angles. 120^ + 90^ + 60^ = 270^ Step 2: Subtract the sum from 360^ to find the angle for cattle. 360^ - 270^ = 90^ The angle representing cattle is 90 degrees. b) The question states there were 15 more sheep than goats, but based on the degrees, goats (120^) are more than sheep (90^). We will interpret "15 more sheep than goat" as the absolute difference in the number of animals corresponding to the difference in their angles. Step 1: Find the difference in degrees between goats and sheep. 120^ (Goats) - 90^ (Sheep) = 30^ Step 2: Determine the number of animals per degree. Since 30^ corresponds to 15 animals, 1^ = 15 animals30^ = 0.5 animals per degree Step 3: Calculate the number of cattle and chicken. Cattle: 90^ × 0.5 animals/degree = 45 animals Chicken: 60^ × 0.5 animals/degree = 30 animals Step 4: Find how many more cattle than chicken. 45 (Cattle) - 30 (Chicken) = 15 animals There were 15 more cattle than chicken. 2. Straight Line Equation The equation of a straight line is 2y = x + 11. We need to find the value of x when y = 2. Step 1: Substitute y = 2 into the equation. 2(2) = x + 11 Step 2: Simplify and solve for x. 4 = x + 11 x = 4 - 11 x = -7 The value of x when y=2 is -7. 3. Ratios Given a:b = 4:3 and b:c = 4:5. We need to find the ratio a:c. Step 1: Write the given ratios. a:b = 4:3 b:c = 4:5 Step 2: Find a common multiple for the 'b' terms (3 and 4). The least common multiple is 12. Step 3: Adjust the ratios so that the 'b' term is 12 in both. For a:b = 4:3, multiply both parts by 4: a:b = (4 × 4) : (3 × 4) = 16:12 For b:c = 4:5, multiply both parts by 3: b:c = (4 × 3) : (5 × 3) = 12:15 Step 4: Combine the ratios to find a:c. Now we have a:b:c = 16:12:15. Therefore, a:c = 16:15. The ratio a:c is 16:15. 4. Percentage Loss Juan sold a jacket for 1800 and made a 10% loss. We need to find the original cost price. Step 1: Let the cost price be C. The selling price (S) is 1800. A 10% loss means the selling price is 100\% - 10\% = 90\% of the cost price. S = 0.90 × C Step 2: Substitute the selling price and solve for C. 1800 = 0.90 × C C = (1800)/(0.90) C = (18000)/(9) C = 2000 Juan had bought the jacket for 2000. 5. Length of Wire for Fencing The figure shows a sector of a circle with a radius of 140 m and an angle of 80^. The farm was fenced using two strands of wire. Step 1: Calculate the length of the arc (L) of the sector. The formula for arc length is L = ()/(360^) × 2 r. Given = 80^ and r = 140 m. L = (80)/(360) × 2 × × 140 L = (2)/(9) × 280 L = (560)/(9) m Step 2: Calculate the perimeter of one strand of fence. The perimeter of the sector includes the two radii and the arc length. Perimeter (one strand) = 2r + L P = 2(140) + (560)/(9) P = 280 + (560)/(9) m Step 3: Calculate the total length of wire for two strands. Total length = 2 × P Total length = 2 × (280 + (560)/(9)) Total length = 560 + (1120)/(9) m Step 4: Approximate the numerical value (using ≈ 3.142). Total length ≈ 560 + (1120 × 3.142)/(9) Total length ≈ 560 + (3519.04)/(9) Total length ≈ 560 + 391.004 Total length ≈ 951.004 m The total length of wire that was used is approximately 951.0 m. Send me the next one 📸