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Home » Daily growth: 2% of the current proficiency - Abbey Badges

Daily growth: 2% of the current proficiency - Abbey Badges

📅 February 26, 2026 👤 scraface

Feb 26, 2026

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📌 Solution: The arithmetic mean is calculated by summing the values and dividing by the count: $\frac{10 + 14 + 16}{3} = \frac{40}{3} \approx 13.\overline{3}$. The exact average is $\boxed{\dfrac{40}{3}}$.

📌 Question: The average of $4y - 3$, $2y + 5$, and $y + 7$ is 10. Find $y$.

📌 Solution: Sum the expressions: $(4y - 3) + (2y + 5) + (y + 7) = 7y + 9$. Divide by 3 and set equal to 10: $\frac{7y + 9}{3} = 10$. Multiply both sides by 3: $7y + 9 = 30$. Subtract 9: $7y = 21$. Divide by 7: $y = \boxed{3}$.

📌 Question: How many whole numbers lie between $3π$ and $5π$?

📌 Solution: Approximate $3π \approx 9.42$ and $5π \approx 15.71$. Whole numbers between them are 10, 11, 12, 13, 14, 15. Counting these gives $\boxed{6}$ numbers.A environmental scientist measures the concentration of PM2.5 in a city. If the concentration decreases by 5% every year due to emission controls, starting from 80 µg/m³, what will be the concentration after 5 years?

📌 The concentration after 5 years is calculated using exponential decay: 80 × (1 - 0.05)^5 = 80 × (0.95)^5 ≈ 80 × 0.7738 ≈ 61.90 µg/m³.

📌 #### 61.90

📌 An archaeologist excavates a site with 12 layers, each 0.5 meters thick. If the team removes 3 meters of soil per day, how many days will it take to expose all layers?

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