Answer :
To solve this problem, we first need to analyze the given data in the table. The table provides the populations and areas of four states. We are tasked with determining which of the provided statements is true regarding these states' population densities.
Let's break down the solution step-by-step:
1. Calculate the Population Densities:
Population density is defined as the population divided by the area. Let’s calculate the population density for each state.
[tex]\[ \text{Population density of State A} = \frac{\text{Population of State A}}{\text{Area of State A}} = \frac{1,055,173}{2,677} \approx 394.16 \, \text{people per km}^2 \][/tex]
[tex]\[ \text{Population density of State B} = \frac{\text{Population of State B}}{\text{Area of State B}} = \frac{1,333,089}{36,418} \approx 36.61 \, \text{people per km}^2 \][/tex]
[tex]\[ \text{Population density of State C} = \frac{\text{Population of State C}}{\text{Area of State C}} = \frac{3,596,677}{5,543} \approx 648.87 \, \text{people per km}^2 \][/tex]
[tex]\[ \text{Population density of State D} = \frac{\text{Population of State D}}{\text{Area of State D}} = \frac{6,745,408}{10,555} \approx 639.07 \, \text{people per km}^2 \][/tex]
The population densities are:
- State A: [tex]\(394.16 \, \text{people per km}^2\)[/tex]
- State B: [tex]\(36.61 \, \text{people per km}^2\)[/tex]
- State C: [tex]\(648.87 \, \text{people per km}^2\)[/tex]
- State D: [tex]\(639.07 \, \text{people per km}^2\)[/tex]
2. Determine the States with the Lowest and Second Lowest Populations:
The populations of the states are:
- State A: 1,055,173
- State B: 1,333,089
- State C: 3,596,677
- State D: 6,745,408
Sorting these in ascending order:
- State A: 1,055,173 (lowest population)
- State B: 1,333,089 (second lowest population)
3. Evaluate the Statements:
- Statement 1: The state with the lowest population (State A) has the greatest population density.
[tex]\[ \text{State A: } 394.16 \][/tex]
[tex]\[ \text{Greatest population density: State C, with } 648.87 \][/tex]
This statement is False.
- Statement 2: The state with the second lowest population (State B) has the lowest population density.
[tex]\[ \text{State B: } 36.61 \][/tex]
[tex]\[ \text{Lowest population density: } 36.61 \][/tex]
This statement is True.
- Statement 3: The state with the lowest population (State A) has the lowest population density.
[tex]\[ \text{State A: } 394.16 \][/tex]
[tex]\[ \text{Lowest population density: State B, with } 36.61 \][/tex]
This statement is False.
Conclusion:
Only the second statement is true: "The state with the second lowest population has the lowest population density." This matches the detailed step-by-step calculations we performed above.
Let's break down the solution step-by-step:
1. Calculate the Population Densities:
Population density is defined as the population divided by the area. Let’s calculate the population density for each state.
[tex]\[ \text{Population density of State A} = \frac{\text{Population of State A}}{\text{Area of State A}} = \frac{1,055,173}{2,677} \approx 394.16 \, \text{people per km}^2 \][/tex]
[tex]\[ \text{Population density of State B} = \frac{\text{Population of State B}}{\text{Area of State B}} = \frac{1,333,089}{36,418} \approx 36.61 \, \text{people per km}^2 \][/tex]
[tex]\[ \text{Population density of State C} = \frac{\text{Population of State C}}{\text{Area of State C}} = \frac{3,596,677}{5,543} \approx 648.87 \, \text{people per km}^2 \][/tex]
[tex]\[ \text{Population density of State D} = \frac{\text{Population of State D}}{\text{Area of State D}} = \frac{6,745,408}{10,555} \approx 639.07 \, \text{people per km}^2 \][/tex]
The population densities are:
- State A: [tex]\(394.16 \, \text{people per km}^2\)[/tex]
- State B: [tex]\(36.61 \, \text{people per km}^2\)[/tex]
- State C: [tex]\(648.87 \, \text{people per km}^2\)[/tex]
- State D: [tex]\(639.07 \, \text{people per km}^2\)[/tex]
2. Determine the States with the Lowest and Second Lowest Populations:
The populations of the states are:
- State A: 1,055,173
- State B: 1,333,089
- State C: 3,596,677
- State D: 6,745,408
Sorting these in ascending order:
- State A: 1,055,173 (lowest population)
- State B: 1,333,089 (second lowest population)
3. Evaluate the Statements:
- Statement 1: The state with the lowest population (State A) has the greatest population density.
[tex]\[ \text{State A: } 394.16 \][/tex]
[tex]\[ \text{Greatest population density: State C, with } 648.87 \][/tex]
This statement is False.
- Statement 2: The state with the second lowest population (State B) has the lowest population density.
[tex]\[ \text{State B: } 36.61 \][/tex]
[tex]\[ \text{Lowest population density: } 36.61 \][/tex]
This statement is True.
- Statement 3: The state with the lowest population (State A) has the lowest population density.
[tex]\[ \text{State A: } 394.16 \][/tex]
[tex]\[ \text{Lowest population density: State B, with } 36.61 \][/tex]
This statement is False.
Conclusion:
Only the second statement is true: "The state with the second lowest population has the lowest population density." This matches the detailed step-by-step calculations we performed above.
