Certainly! Let's break down the solution step-by-step:
### Step 1: Calculate the Energy Used by the Washer
1. Power of washer: 450 watts
2. Time for washing: 1 hour
The formula to convert power and time to energy in joules is:
[tex]\[ \text{Energy} = \text{Power} \times \text{Time} \times 3600 \][/tex]
(since 1 hour = 3600 seconds)
So, for the washer:
[tex]\[ \text{Energy}_{\text{washer}} = 450 \, \text{W} \times 1 \, \text{hour} \times 3600 \, \text{s/hour} \][/tex]
[tex]\[ \text{Energy}_{\text{washer}} = 450 \times 3600 \][/tex]
[tex]\[ \text{Energy}_{\text{washer}} = 1,620,000 \, \text{joules} \][/tex]
### Step 2: Calculate the Energy Used by the Dryer
1. Power of dryer: 3000 watts
2. Time for drying: 1.5 hours
Again, using the energy formula:
[tex]\[ \text{Energy} = \text{Power} \times \text{Time} \times 3600 \][/tex]
So, for the dryer:
[tex]\[ \text{Energy}_{\text{dryer}} = 3000 \, \text{W} \times 1.5 \, \text{hours} \times 3600 \, \text{s/hour} \][/tex]
[tex]\[ \text{Energy}_{\text{dryer}} = 3000 \times 1.5 \times 3600 \][/tex]
[tex]\[ \text{Energy}_{\text{dryer}} = 3000 \times 5400 \][/tex]
[tex]\[ \text{Energy}_{\text{dryer}} = 16,200,000 \, \text{joules} \][/tex]
### Step 3: Calculate the Total Energy Used
Now, we combine the energy used by both the washer and the dryer:
[tex]\[ \text{Total Energy} = \text{Energy}_{\text{washer}} + \text{Energy}_{\text{dryer}} \][/tex]
[tex]\[ \text{Total Energy} = 1,620,000 \, \text{J} + 16,200,000 \, \text{J} \][/tex]
[tex]\[ \text{Total Energy} = 17,820,000 \, \text{joules} \][/tex]
### Step 4: Select the Correct Answer
Convert 17,820,000 joules to scientific notation:
[tex]\[ 1.782 \times 10^7 \, \text{J} \][/tex]
The correct answer from the provided options is:
[tex]\[ \boxed{A. \, 1.78 \times 10^7 \, \text{J}} \][/tex]
