Answer :
Let's approach this problem step by step to determine which statements regarding the four states are true.
### Step 1: Calculate Population Densities
First, we need to calculate the population density of each state. Population density is given by the formula:
[tex]\[ \text{Population Density} = \frac{\text{Population}}{\text{Area}} \][/tex]
Using the provided data:
#### State A:
[tex]\[ \text{Density}_A = \frac{1,055,173}{2,677} \approx 394.16 \, \text{people per km}^2 \][/tex]
#### State B:
[tex]\[ \text{Density}_B = \frac{1,333,089}{36,418} \approx 36.61 \, \text{people per km}^2 \][/tex]
#### State C:
[tex]\[ \text{Density}_C = \frac{3,596,677}{5,543} \approx 648.87 \, \text{people per km}^2 \][/tex]
#### State D:
[tex]\[ \text{Density}_D = \frac{6,745,408}{10,555} \approx 638.93 \, \text{people per km}^2 \][/tex]
### Step 2: Identify Populations and Their Order
Let's list the states in order of their populations:
1. State A: \(1,055,173\)
2. State B: \(1,333,089\)
3. State C: \(3,596,677\)
4. State D: \(6,745,408\)
From this list:
- The state with the lowest population is State A.
- The state with the second-lowest population is State B.
- The state with the second-greatest population is State C.
### Step 3: Evaluate Each Statement
#### Statement 1:
The state with the lowest population has the greatest population density.
- State A (lowest population) has a density of \(394.16 \, \text{people per km}^2\).
- The greatest population density is \(648.87 \, \text{people per km}^2\), which belongs to State C.
This statement is False.
#### Statement 2:
The state with the second-lowest population has the lowest population density.
- State B (second-lowest population) has a density of \(36.61 \, \text{people per km}^2\).
- The lowest population density is indeed \(36.61 \, \text{people per km}^2\), which belongs to State B.
This statement is True.
#### Statement 3:
The state with the lowest population has the lowest population density.
- State A (lowest population) has a density of \(394.16 \, \text{people per km}^2\).
- The lowest population density is \(36.61 \, \text{people per km}^2\), which belongs to State B.
This statement is False.
#### Statement 4:
The state with the second-greatest population has the lowest population density.
- State C (second-greatest population) has a density of \(648.87 \, \text{people per km}^2\).
- The lowest population density is \(36.61 \, \text{people per km}^2\), which belongs to State B.
This statement is False.
### Conclusion
The correct statement is:
The state with the second lowest population has the lowest population density.
### Step 1: Calculate Population Densities
First, we need to calculate the population density of each state. Population density is given by the formula:
[tex]\[ \text{Population Density} = \frac{\text{Population}}{\text{Area}} \][/tex]
Using the provided data:
#### State A:
[tex]\[ \text{Density}_A = \frac{1,055,173}{2,677} \approx 394.16 \, \text{people per km}^2 \][/tex]
#### State B:
[tex]\[ \text{Density}_B = \frac{1,333,089}{36,418} \approx 36.61 \, \text{people per km}^2 \][/tex]
#### State C:
[tex]\[ \text{Density}_C = \frac{3,596,677}{5,543} \approx 648.87 \, \text{people per km}^2 \][/tex]
#### State D:
[tex]\[ \text{Density}_D = \frac{6,745,408}{10,555} \approx 638.93 \, \text{people per km}^2 \][/tex]
### Step 2: Identify Populations and Their Order
Let's list the states in order of their populations:
1. State A: \(1,055,173\)
2. State B: \(1,333,089\)
3. State C: \(3,596,677\)
4. State D: \(6,745,408\)
From this list:
- The state with the lowest population is State A.
- The state with the second-lowest population is State B.
- The state with the second-greatest population is State C.
### Step 3: Evaluate Each Statement
#### Statement 1:
The state with the lowest population has the greatest population density.
- State A (lowest population) has a density of \(394.16 \, \text{people per km}^2\).
- The greatest population density is \(648.87 \, \text{people per km}^2\), which belongs to State C.
This statement is False.
#### Statement 2:
The state with the second-lowest population has the lowest population density.
- State B (second-lowest population) has a density of \(36.61 \, \text{people per km}^2\).
- The lowest population density is indeed \(36.61 \, \text{people per km}^2\), which belongs to State B.
This statement is True.
#### Statement 3:
The state with the lowest population has the lowest population density.
- State A (lowest population) has a density of \(394.16 \, \text{people per km}^2\).
- The lowest population density is \(36.61 \, \text{people per km}^2\), which belongs to State B.
This statement is False.
#### Statement 4:
The state with the second-greatest population has the lowest population density.
- State C (second-greatest population) has a density of \(648.87 \, \text{people per km}^2\).
- The lowest population density is \(36.61 \, \text{people per km}^2\), which belongs to State B.
This statement is False.
### Conclusion
The correct statement is:
The state with the second lowest population has the lowest population density.
