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(3,500 + 1,800) / 2 + 1,704 + ($5.58 + 55.82) / 2 + (10.28 + 22.62) / 2 + (18.51 + 19.88) / 2 + (1.37 + 2.74) / 2 + 2.06 + (6.86 + 13.71) / 2 + (15.00 + 30.00) / 2 + (0 + 3.45) / 2 + (50 + 75) / 2 x 6 13.52 + 20.28) / 2 + (6.76 + 20.28) / 2 + (13.52 + 20.28) / 2 + 135 + 390 + (6.76 + 13.52) / 2 + 250 + 100 + 148.16 + (13.47 + 33.67) / 2 + (13.47 + 134.69) / 2 + (20.20 + 29.93) / 2 =

1 answer

To simplify the expression step by step, we first break it down into individual calculations:

  1. Calculate the averages:
    • \( (3,500 + 1,800) / 2 = 2,650 \)
    • \( (5.58 + 55.82) / 2 = 30.70 \)
    • \( (10.28 + 22.62) / 2 = 16.28 \)
    • \( (18.51 + 19.88) / 2 = 19.195 \)
    • \( (1.37 + 2.74) / 2 = 2.055 \)
    • \( (6.86 + 13.71) / 2 = 10.285 \)
    • \( (15.00 + 30.00) / 2 = 22.50 \)
    • \( (0 + 3.45) / 2 = 1.725 \)
    • \( (50 + 75) / 2 = 62.5 \)
    • \( (13.52 + 20.28) / 2 = 16.90 \)
    • \( (6.76 + 20.28) / 2 = 13.52 \)
    • \( (13.52 + 20.28) / 2 = 16.90 \)
    • \( (6.76 + 13.52) / 2 = 10.26 \)
    • \( (13.47 + 33.67) / 2 = 23.57 \)
    • \( (13.47 + 134.69) / 2 = 74.08 \)
    • \( (20.20 + 29.93) / 2 = 25.965 \)

Next, we can aggregate these calculated values:

  1. Substitute the averages back into the expression, replacing the calculations step by step:

    • \( 2,650 + 1,704 + 30.70 + 16.28 + 19.195 + 2.055 + 2.06 + 10.285 + 22.50 + 1.725 + (62.5 \times 6) + 16.90 + 13.52 + 16.90 + 135 + 390 + 10.26 + 250 + 100 + 148.16 + 23.57 + 74.08 + 25.965 \)

  2. Break it down into simpler additions:

    • First part: \( 2,650 + 1,704 = 4,354 \)
    • Add the next part: \( 4,354 + 30.70 + 16.28 + 19.195 + 2.055 + 2.06 + 10.285 + 22.50 + 1.725 \) \( = 4,354 + 30.70 + 16.28 + 19.195 + 2.055 + 2.06 + 10.285 + 22.50 + 1.725 \approx 4,496.745 \)
    • Add the part calculating \(62.5 \times 6 = 375\), \( 4,496.745 + 375 = 4,871.745 \)
    • For the next additions: \( 4,871.745 + 16.90 + 13.52 + 16.90 + 135 + 390 + 10.26 + 250 + 100 + 148.16 + 23.57 + 74.08 + 25.965 \)
    • This adds up as follows:
      • Start from \( 4,871.745 + 16.90 + 13.52 + 16.90 + 135 + 390 + 10.26 + 250 + 100 + 148.16 + 23.57 + 74.08 + 25.965 \)
      • Sequentially add each small part.

Continuing this process results in:

  • \( 4,871.745 + 16.90 = 4,888.645 \)
  • \( 4,888.645 + 13.52 = 4,902.165 \)
  • \( 4,902.165 + 16.90 = 4,919.065 \)
  • \( 4,919.065 + 135 = 5,054.065 \)
  • \( 5,054.065 + 390 = 5,444.065 \)
  • \( 5,444.065 + 10.26 = 5,454.325 \)
  • \( 5,454.325 + 250 = 5,704.325 \)
  • \( 5,704.325 + 100 = 5,804.325 \)
  • \( 5,804.325 + 148.16 = 5,952.485 \)
  • \( 5,952.485 + 23.57 = 5,976.055 \)
  • \( 5,976.055 + 74.08 = 6,050.135 \)
  • \( 6,050.135 + 25.965 = 6,076.1 \)

Finally, the result is approximately: 6,076.10