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Home » Average speed \( v \) is given by distance divided by time: - Veritas Home Health

Average speed \( v \) is given by distance divided by time: - Veritas Home Health

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 A ladder 13 feet long leans against a wall, with its base 5 feet from the wall. How high up the wall does the ladder reach?

📌 Using the Pythagorean theorem: \( h^2 + 5^2 = 13^2 \).

📌 \( h^2 + 25 = 169 \), so \( h^2 = 144 \), \( h = 12 \) feet.

📌 A bag contains 5 red, 7 blue, and 8 green marbles. Two marbles are drawn without replacement. What is the probability both are green?

📌 Total marbles: \( 5 + 7 + 8 = 20 \).

📌 Probability first green: \( \frac{8}{20} = \frac{2}{5} \).

📌 Probability second green: \( \frac{7}{19} \).

📌 Combined: \( \frac{2}{5} \times \frac{7}{19} = \frac{14}{95} \).

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\binom{8 - 3 + 1}{3} = \binom{6}{3} = 20
This formula counts the number of ways to place $k$ non-adjacent indis...
So, there are 20 ways to choose positions for the 3 A’s such that no t...
Step 2: Assign labels to the remaining 5 positions.
Each of the 5 non-A positions can be labeled U, C, or G (3 choices eac...
Therefore, total number of valid sequences is:
\times 243 = 4860
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