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Calculate rounded to the nearest 100, the missing value B, the estimated total number of copies made for 2026.

Mathematics

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3 parts
a

16 04216\,042

b
0.3333
c

195 300195\,300

Step-by-step solution

8 steps

Part a· 2 steps

  1. Identify the number of copies made in April for each year from 2021 to 2026.

    The values for April are:
    2021: 18 083
    2022: 17 719
    2023: 16 280
    2024: 17 323
    2025: 16 848
    2026: 16 042

  2. Find the lowest number among these values.

    The lowest number is 16 042.
    The lowest number of copies made in April over the 6-year period is 16 042\boxed{16\,042}.

Part b0.3333

  1. Identify the number of copies made in each month of 2022 and count how many are more than 18 500.

    The values for 2022 are:
    Jan: 17 978 (not > 18 500)
    Feb: 16 821 (not > 18 500)
    Mar: 18 416 (not > 18 500)
    Apr: 17 719 (not > 18 500)
    May: 18 907 (> 18 500)
    Jun: 18 851 (> 18 500)
    Jul: 18 826 (> 18 500)
    Aug: 19 231 (> 18 500)
    Sep: 16 871 (not > 18 500)
    Oct: 17 797 (not > 18 500)
    Nov: 17 291 (not > 18 500)
    Dec: 16 183 (not > 18 500)
    There are 4 months in 2022 with more than 18 500 copies.

  2. Calculate the probability as a decimal.

    The total number of months in a year is 12.

    Probability=Number of months with copies>18 500Total number of months\text{Probability} = \frac{\text{Number of months with copies} > 18\,500}{\text{Total number of months}} Probability=412=13\text{Probability} = \frac{4}{12} = \frac{1}{3} Probability≈0.33333...\text{Probability} \approx 0.33333...

    Rounded to four decimal places, the probability is 0.3333\boxed{0.3333}.

Part c

195 300195\,300

  1. Calculate the sum of copies made in the first five months of 2026.

    Jan: 16 030
    Feb: 15 082
    Mar: 16 745
    Apr: 16 042
    May: 17 471

    Sum=16 030+15 082+16 745+16 042+17 471=81 370\text{Sum} = 16\,030 + 15\,082 + 16\,745 + 16\,042 + 17\,471 = 81\,370

  2. Calculate the mean number of copies for the first five months of 2026.

    Mean=SumNumber of months=81 3705=16 274\text{Mean} = \frac{\text{Sum}}{\text{Number of months}} = \frac{81\,370}{5} = 16\,274

  3. Estimate the total number of copies for 2026 by assuming the mean is maintained throughout the year.

    Estimated Total=Mean×12 months\text{Estimated Total} = \text{Mean} \times 12 \text{ months} Estimated Total=16 274×12=195 288\text{Estimated Total} = 16\,274 \times 12 = 195\,288

  4. Round the estimated total to the nearest 100 to find the missing value B.

    B=195 288≈195 300\text{B} = 195\,288 \approx 195\,300

    The missing value B, the estimated total number of copies made for 2026, rounded to the nearest 100, is 195 300\boxed{195\,300}.

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