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This is a geometric sequence with first term a = 40, ratio r = 1.12, n = 5 terms.Sum = a(r^n - 1)/(r - 1) = 40(1.12^5 - 1)/(0.12)1.12^5 ≈ 1.76234Sum ≈ 40(1.76234 - 1)/0.12 = 40(0.76234)/0.12 ≈ 40 × 6.35283 ≈ <<40*6.35283=254.1332>>254.13 km#### 254.13An anthropologist analyzes ritual participation in 6 villages. Village A has 200 people, B has 300, C has 150, D has 400, E has 250, and F has 350. She randomly selects one village and then randomly selects 10% of its population for a survey. What is the expected number of people surveyed across all villages?For each village, the number surveyed is 10% of its population.Expected value per village = 0.1 × populationSum over villages: 0.1 × (200 + 300 + 150 + 400 + 250 + 350) = 0.1 × 1650 = <<0.1*1650=165>>165.A robotics engineer designs a production line with 3 types of robotic arms: 4 precision arms, 3 welding arms, and 2 assembly arms. Each robot requires exactly one arm of each type. How many distinct configurations of a full robot can be built using real, available arms?