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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?
Total marbles = 15. Probability of first green = \( \frac{6}{15} \). Probability of second green = \( \frac{5}{14} \). Combined probability = \( \frac{6}{15} \times \frac{5}{14} = \frac{1}{7} \).
#### \(\frac{1}{7}\)
A circle is inscribed in a square with a side length of 10 cm. What is the area of the circle?
The diameter of the circle equals the square's side, so the radius is 5 cm. The area is \( \pi \times 5^2 = 25\pi \) square cm.
#### 25\pi
