The seismic activity density of a region is the ratio of the number of earthquakes during a given time span to the land area affected. The table shows the land area and seismic activity density.

\begin{tabular}{|r|r|r|}
\hline
& Land Area [tex]$\left( \text{mi}^2 \right)$[/tex] & Seismic Activity Density \\
\hline
State A & 163,696 & 0.0299 \\
\hline
State B & 10,931 & 0.1402 \\
\hline
\end{tabular}

Which statement about the number of earthquakes the states had for the given time span is true?

A. State A had approximately 1,533 more earthquakes than State B.
B. State B had approximately 1,533 more earthquakes than State A.
C. State A had approximately 3,362 more earthquakes than State B.
D. State B had approximately 3,362 more earthquakes than State A.



Answer :

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.