A construction project requires mixing concrete. Mixer A can produce $5 \text{ m}^3$ of concrete per hour. Mixer B can produce $7 \text{ m}^3$ of concrete per hour.
If both mixers operate together for 4 hours, what is the total volume of concrete produced?
A new, larger "Mixing Unit C" is designed to be as productive as Mixer A and Mixer B combined. What is its production rate in cubic meters per hour?
The formula to calculate the power $P$ (in watts) in an electrical circuit is $P = V \times I$, where $V$ is voltage (in volts) and $I$ is current (in amperes). Calculate the power $P$ if $V = 12 \text{ volts}$ and $I = 2.5 \text{ amperes}$.
A manufacturing process involves three sequential steps. The output value $Z$ is determined as follows:
Step 1: $X = (15 - 3) \times 2$
Step 2: $Y = X / 4 + 5$
Step 3: $Z = Y - 2^3$
Calculate the final output value $Z$.
A sensor "module" is designed to measure a length of $80 \text{ cm}$. It provides a reading of $78 \text{ cm}$. Calculate the percentage error of the sensor reading. Use the formula: \[ \text{Percentage Error} = \frac{|\text{Actual Value} - \text{Measured Value}|}{\text{Actual Value}} \times 100\% \]
The efficiency $E$ of an engine is given by a simplified formula $E = \left(1 - \frac{T_{\text{cold}}}{T_{\text{hot}}}\right) \times 100\%$, where $T_{\text{cold}}$ is the cold reservoir temperature and $T_{\text{hot}}$ is the hot reservoir temperature (in Kelvin).
Calculate the efficiency if $T_{\text{cold}} = 300 \text{ K}$ and $T_{\text{hot}} = 600 \text{ K}$.
What if, due to improved insulation (a change in a "thermal module"), $T_{\text{cold}}$ is reduced to $270 \text{ K}$ while $T_{\text{hot}}$ remains $600 \text{ K}$? What is the new efficiency?