Study questions platform-wide or filter by specific tests with correct answers revealed.
The 'Theory of Surplus Value' is a key component of:
Marx used this theory to explain the exploitation of labor by capitalists.
The time period of a pendulum is $T = 2\pi\sqrt{\frac{L}{g}}$, so $L \propto T^2$.
- Initial length: $L = kT^2$
- New length: $L + \Delta L = k T_M^2$
- Strain: $\frac{\Delta L}{L} = \frac{T_M^2 - T^2}{T^2} = (\frac{T_M}{T})^2 - 1$
- From $Y = \frac{\text{Stress}}{\text{Strain}} = \frac{Mg/A}{\Delta L/L}$
- Therefore, $\frac{1}{Y} = \frac{\Delta L/L}{Mg/A} = [(\frac{T_M}{T})^2 - 1]\frac{A}{Mg}$
A bag has 4 red and 6 black balls. One ball is drawn, observed, and returned along with 2 more balls of the same colour. A second ball is then drawn. Find the probability that the second ball drawn is red.
Initially: 4 red, 6 black (10 total).
Case 1 — First ball is red (prob $= \frac{4}{10}$):
Bag becomes: 6 red, 6 black (12 total). $P(\text{red 2nd}) = \frac{6}{12} = \frac{1}{2}$.
Case 2 — First ball is black (prob $= \frac{6}{10}$):
Bag becomes: 4 red, 8 black (12 total). $P(\text{red 2nd}) = \frac{4}{12} = \frac{1}{3}$.
Total: $\dfrac{4}{10}\cdot\dfrac{1}{2}+\dfrac{6}{10}\cdot\dfrac{1}{3} = \dfrac{2}{10}+\dfrac{2}{10} = \dfrac{4}{10} = \dfrac{2}{5}$
Sign in to join the conversation and share your thoughts.
Log In to Comment