Question
Knowing that you use 245 KWH between 7:00 a.m. and 7:00 p.m. and 165 KWH between 7:00 p.m. and 7:00 a.m., answer the follow questions using the chart below.
Constant Usage
$0.05324/ KWH
Daytimer (Most usage between 7:00 a.m. and 7:00 p.m.)
· As long as most power used is between 7:00 am and 7:00 p.m., then you receive a 20% discount on power usage between 7:00 p.m. and 7:00 a.m.
$0.05456/ KWH
NightTimer (Most usage between 7:00 p.m. and 7:00 a.m.)
· If more than 50% of power usage is outside of 7:00 p.m. to 7:00 a.m., then you have to pay the Daytimer rate for all power used between 7:00 a.m. and 7:00 p.m.
$0.05281/ KWH
How much would you have paid on the NightTimer plan?
(1 point)
Responses
$21.83
$21.83
$21.65
$21.65
$22.37
$22.37
$22.08
Constant Usage
$0.05324/ KWH
Daytimer (Most usage between 7:00 a.m. and 7:00 p.m.)
· As long as most power used is between 7:00 am and 7:00 p.m., then you receive a 20% discount on power usage between 7:00 p.m. and 7:00 a.m.
$0.05456/ KWH
NightTimer (Most usage between 7:00 p.m. and 7:00 a.m.)
· If more than 50% of power usage is outside of 7:00 p.m. to 7:00 a.m., then you have to pay the Daytimer rate for all power used between 7:00 a.m. and 7:00 p.m.
$0.05281/ KWH
How much would you have paid on the NightTimer plan?
(1 point)
Responses
$21.83
$21.83
$21.65
$21.65
$22.37
$22.37
$22.08
Answers
GPT-4o mini
To calculate the cost of power used under the NightTimer plan, we will first identify the usage during the two time periods:
- **From 7:00 a.m. to 7:00 p.m.**: 245 KWH
- **From 7:00 p.m. to 7:00 a.m.**: 165 KWH
Total usage:
- Total KWH = 245 KWH + 165 KWH = 410 KWH
Next, we'll determine the percentage of power used during the two time periods:
- Percentage during the day (7 a.m. to 7 p.m.):
\[
\frac{245 \text{ KWH}}{410 \text{ KWH}} \times 100 \approx 59.80\%
\]
Since 59.80% of the usage is during the day, it exceeds the 50% threshold required to be classified as predominantly night usage. Therefore, the NightTimer plan means that all power used during the day will be charged at the Daytimer rate and doesn't qualify for the discounted nighttime rates.
### Costs Calculation:
1. **Daytime Usage (245 KWH)**:
- Rate: $0.05456/KWH
\[
\text{Cost during the day} = 245 \text{ KWH} \times 0.05456 = 13.36
\]
2. **Nighttime Usage (165 KWH)**:
- Rate: $0.05281/KWH
\[
\text{Cost during the night} = 165 \text{ KWH} \times 0.05281 = 8.71
\]
### Total Cost:
\[
\text{Total Cost} = \text{Cost during the day} + \text{Cost during the night} = 13.36 + 8.71 = 22.07
\]
It seems there is a rounding in the steps. Let’s check the original options:
#### Compare Total Calculated Cost with Given Options:
- Nearby choice: **$22.08** which we can assume is reasonable considering rounding issues in billing systems.
### Final Answer:
The amount paid under the NightTimer plan is **$22.08**.
- **From 7:00 a.m. to 7:00 p.m.**: 245 KWH
- **From 7:00 p.m. to 7:00 a.m.**: 165 KWH
Total usage:
- Total KWH = 245 KWH + 165 KWH = 410 KWH
Next, we'll determine the percentage of power used during the two time periods:
- Percentage during the day (7 a.m. to 7 p.m.):
\[
\frac{245 \text{ KWH}}{410 \text{ KWH}} \times 100 \approx 59.80\%
\]
Since 59.80% of the usage is during the day, it exceeds the 50% threshold required to be classified as predominantly night usage. Therefore, the NightTimer plan means that all power used during the day will be charged at the Daytimer rate and doesn't qualify for the discounted nighttime rates.
### Costs Calculation:
1. **Daytime Usage (245 KWH)**:
- Rate: $0.05456/KWH
\[
\text{Cost during the day} = 245 \text{ KWH} \times 0.05456 = 13.36
\]
2. **Nighttime Usage (165 KWH)**:
- Rate: $0.05281/KWH
\[
\text{Cost during the night} = 165 \text{ KWH} \times 0.05281 = 8.71
\]
### Total Cost:
\[
\text{Total Cost} = \text{Cost during the day} + \text{Cost during the night} = 13.36 + 8.71 = 22.07
\]
It seems there is a rounding in the steps. Let’s check the original options:
#### Compare Total Calculated Cost with Given Options:
- Nearby choice: **$22.08** which we can assume is reasonable considering rounding issues in billing systems.
### Final Answer:
The amount paid under the NightTimer plan is **$22.08**.