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The populations and areas of four states are shown.

\begin{tabular}{|l|r|r|}
\hline
& Population & Area [tex]$\left( km^2\right)$[/tex] \\
\hline
State A & [tex]$1,055,173$[/tex] & 2,677 \\
\hline
State B & [tex]$1,333,089$[/tex] & 36,418 \\
\hline
State C & [tex]$3,596,677$[/tex] & 5,543 \\
\hline
State D & [tex]$6,745,408$[/tex] & 10,555 \\
\hline
\end{tabular}

Which statement regarding these four states is true?

A. The state with the lowest population has the greatest population density.
B. The state with the second lowest population has the lowest population density.
C. The state with the lowest population has the lowest population density.
D. The state with the second greatest population has the lowest population density.

Sagot :

GinnyAnswer
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.
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