Let's solve the problem step by step.
### Step 1: Determine the number of earthquakes in State A
State A has a land area of 163,696 square miles and a seismic activity density of 0.0299 earthquakes per square mile.
To find the number of earthquakes in State A, we multiply the land area by the seismic activity density:
[tex]\[ \text{Earthquakes in State A} = \text{Land Area of State A} \times \text{Seismic Activity Density of State A} \][/tex]
[tex]\[ \text{Earthquakes in State A} = 163696 \, \text{mi}^2 \times 0.0299 \, \frac{\text{earthquakes}}{\text{mi}^2} \][/tex]
[tex]\[ \text{Earthquakes in State A} = 4894.5104 \, \text{earthquakes} \][/tex]
### Step 2: Determine the number of earthquakes in State B
State B has a land area of 10,931 square miles and a seismic activity density of 0.1402 earthquakes per square mile.
To find the number of earthquakes in State B, we multiply the land area by the seismic activity density:
[tex]\[ \text{Earthquakes in State B} = \text{Land Area of State B} \times \text{Seismic Activity Density of State B} \][/tex]
[tex]\[ \text{Earthquakes in State B} = 10931 \, \text{mi}^2 \times 0.1402 \, \frac{\text{earthquakes}}{\text{mi}^2} \][/tex]
[tex]\[ \text{Earthquakes in State B} = 1532.5262 \, \text{earthquakes} \][/tex]
### Step 3: Calculate the difference in the number of earthquakes between the two states
Now, we determine the difference in the number of earthquakes between State A and State B.
[tex]\[ \text{Difference AB} = \text{Earthquakes in State A} - \text{Earthquakes in State B} \][/tex]
[tex]\[ \text{Difference AB} = 4894.5104 - 1532.5262 \][/tex]
[tex]\[ \text{Difference AB} = 3361.9842 \][/tex]
### Step 4: State which of the given statements is true
From the calculations, the difference between the number of earthquakes in State A and State B is approximately 3362.
Therefore, the true statement is:
- State A had approximately 3,362 more earthquakes than State B.
