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Home » Total number of ways to choose 4 theories from 12: - DNSFLEX

Total number of ways to choose 4 theories from 12: - DNSFLEX

📅 March 12, 2026 👤 scraface

Mar 12, 2026

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📌 The volume of the sphere is calculated using the formula \( \frac{4}{3} \pi r^3 \). For a radius of 2 meters, the sphere's volume is \( \frac{4}{3} \pi (2)^3 = \frac{32}{3} \pi \) cubic meters. This volume matches the rise in water level in the tank.

📌 #### \(\frac{32}{3} \pi\)

📌 A company sells two products: A and B. Product A costs $50, and 40% of sales are Product A. Product B costs $70. If total revenue from 100 units sold is $6,500, how many units of Product B were sold?

📌 Let \( x \) be the number of Product B units sold. Then, \( 100 - x \) units are Product A. Revenue equation: \( 50(100 - x) + 70x = 6500 \). Solving: \( 5000 - 50x + 70x = 6500 \) simplifies to \( 20x = 1500 \), so \( x = 75 \).

📌 A bank account earns 5% annual interest, compounded annually. If $2,000 is deposited, how much will the account hold after 3 years?

📌 Use the compound interest formula \( A = P(1 + r)^n \). Here, \( A = 2000(1 + 0.05)^3 = 2000(1.157625) = 2315.25 \).

📌 Since \( 7^2 + 24^2 = 25^2 \), it is a right triangle. The area is \( \frac{1}{2} \times 7 \times 24 = 84 \) square units.

📌 A box contains 5 red, 4 blue, and 6 green marbles. If two marbles are drawn at random without replacement, what is the probability that both are green?

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