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Home » Epic Back-to-School Vibes: Free School Bus Clipart You Can Customize Today! - 500apps

Epic Back-to-School Vibes: Free School Bus Clipart You Can Customize Today! - 500apps

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 Question: What is the sum of all values of $b$ for which $\sqrt{(b-3)^2} = 5$?

📌 Solution: The equation simplifies to $|b - 3| = 5$, so $b - 3 = 5$ or $b - 3 = -5$. Solving gives $b = 8$ or $b = -2$. Sum: $8 + (-2) = 6$. $\boxed{6}$

📌 Question: How many numbers are in the list $ 2, 5, 8, \ldots, 32 $?

📌 Solution: The sequence increases by 3 each time. The nth term is $2 + (n-1) \times 3 = 3n - 1$. Set $3n - 1 = 32$: $3n = 33$, so $n = 11$. $\boxed{11}$### Question 1

📌 A scientist is studying the population growth of a species of bacteria. The population doubles every 3 hours. If the initial population is 500 bacteria, how many bacteria will there be after 24 hours?

📌 Determine the number of doubling periods in 24 hours:

📌 \( \frac{24 \text{ hours}}{3 \text{ hours/doubling period}} = 8 \text{ doubling periods} \).

📌 Calculate the final population using the formula for exponential growth:

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