Sure, let's go through the steps to calculate the cost to run the TV for 30 days.
1. Determine the power consumption in watts (W):
- Power (P) is calculated using the formula \( P = I \times V \), where \( I \) is the current in amperes (A) and \( V \) is the voltage in volts (V).
- Given that \( I = 3.0 \) A and \( V = 120 \) V, we can calculate the power:
[tex]\[
P = 3.0 \, \text{A} \times 120 \, \text{V} = 360 \, \text{W}
\][/tex]
2. Convert power to kilowatts (kW):
- Since 1 kW = 1000 W, we convert the power from watts to kilowatts by dividing by 1000:
[tex]\[
\text{Power in kW} = \frac{360 \, \text{W}}{1000} = 0.36 \, \text{kW}
\][/tex]
3. Calculate the total energy consumption in kilowatt-hours (kWh):
- We need to find the total energy consumed by the TV over 30 days. We do this by multiplying the power in kW by the number of hours the TV is operated each day and the number of days.
- Assume the TV is operated 24 hours a day for 30 days.
[tex]\[
\text{Total energy} = 0.36 \, \text{kW} \times 24 \, \text{hours/day} \times 30 \, \text{days} = 259.20 \, \text{kWh}
\][/tex]
4. Calculate the cost to run the TV for 30 days:
- To find the cost, multiply the total energy consumption by the cost per kilowatt-hour.
- Given that the cost per kWh is $0.15:
[tex]\[
\text{Total cost} = 259.20 \, \text{kWh} \times 0.15 \, \text{\[tex]$/kWh} = 38.88 \, \text{\$[/tex]}
\][/tex]
Thus, the cost to run the TV for 30 days is $38.88.
None of the given answers (\[tex]$6.46, \$[/tex]10.95, \[tex]$12.96, \$[/tex]8.64) match the calculated cost of \$38.88. Therefore, it seems there might be an error or mismatch in the provided options.
