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Home » This is a geometric series: first term a = 3, ratio r = 0.95, n = 10 terms. - Dyverse

This is a geometric series: first term a = 3, ratio r = 0.95, n = 10 terms. - Dyverse

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 A technology consultant takes 25 attempts to optimize a system, with 64% success. After 7 more attempts, his success rate improves to 68%. How many of the additional attempts were successful?

📌 Initially, the number of successful attempts is:

📌 \times 25 = 16

📌 Let \( x \) be the number of successful additional attempts out of the 7. The total number of attempts is now \( 25 + 7 = 32 \), and the new success rate is 68%:

📌 \frac{16 + x}{32} = 0.68

📌 Solving for \( x \):

📌 + x = 0.68 \times 32

📌 + x = 21.76

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a \sin(c) = 0 \implies \sin(c) = 0 \implies c = 0 \quad \text{(since s...
Thus, \( a = 3 \), \( b = 2 \), \( c = 0 \), \( d = 0 \).
The function becomes \( f(x) = 3\sin(2x) \), which satisfies all condi...
Final values:
a = 3, \quad b = 2, \quad c = 0, \quad d = 0
\boxed{a = 3,\ b = 2,\ c = 0,\ d = 0}
Question:** During a workshop on AI ethics, a facilitator uses a geome...
Two vectors are perpendicular if their dot product is zero.
Compute the dot product:
\vec{v} \cdot \vec{w} = (2)(x) + (-1)(4) = 2x - 4

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