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what are the winning lottery numbers for powerball - Decision Point

📅 May 5, 2026 👤 scraface

May 05, 2026

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📌 Solution: Let the score at level $ n $ be $ S_n = S_1 \cdot 2^{n-1} $. Given $ S_3 = S_1 \cdot 4 = 128 \Rightarrow S_1 = 32 $. Then $ S_5 = 32 \cdot 2^{4} = 32 \cdot 16 = 512 $. oxed{512}

📌 Question: An ornithologist records bird sightings in a pattern where the number of species observed each week increases by 2 each week. If 8 species are observed in week 1, how many species are observed in week 7?

📌 Solution: The sequence is arithmetic with $ a_1 = 8 $ and $ d = 2 $. The 7th term is $ a_7 = a_1 + 6d = 8 + 12 = 20 $. oxed{20}

📌 Question: A bridgeâs stability ratio requires 5 bolts for every 2 support beams. If the bridge uses 30 bolts, how many beams are needed?

📌 Solution: The ratio $ rac{5 ext{ bolts}}{2 ext{ beams}} $ implies $ rac{30 ext{ bolts}}{x ext{ beams}} = rac{5}{2} $. Cross-multiplying: $ 5x = 60 \Rightarrow x = 12 $. oxed{12}**1.

📌 A cylindrical tank has a radius of 5 meters and a height of 10 meters. Calculate the volume of the tank in cubic meters. Use the formula for the volume of a cylinder, \( V = \pi r^2 h \).

📌 First, calculate \( r^2 \): \( 5^2 = 25 \).

📌 Then, multiply by the height: \( 25 imes 10 = 250 \).

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