In this problem, we are given the population data for four states: North Dakota, South Dakota, Nebraska, and Kansas. We also have information about the approximate areas of these states. Our goal is to determine which state has the greatest population density.
Population density is defined as the number of people per unit area. Mathematically, it is given by:
[tex]\[ \text{Population Density} = \frac{\text{Population}}{\text{Area}} \][/tex]
Let's list down the population and areas of the given states:
- North Dakota: Population = 780,000, Area = 70,700 square miles
- South Dakota: Population = 887,000, Area = 77,100 square miles
- Nebraska: Population = 1,960,000, Area = 77,330 square miles
- Kansas: Population = 2,940,000, Area = 82,278 square miles
Now, we calculate the population density for each state:
1. North Dakota:
[tex]\[ \text{Population Density} = \frac{780,000}{70,700} \approx 11.03 \text{ people per square mile} \][/tex]
2. South Dakota:
[tex]\[ \text{Population Density} = \frac{887,000}{77,100} \approx 11.50 \text{ people per square mile} \][/tex]
3. Nebraska:
[tex]\[ \text{Population Density} = \frac{1,960,000}{77,330} \approx 25.35 \text{ people per square mile} \][/tex]
4. Kansas:
[tex]\[ \text{Population Density} = \frac{2,940,000}{82,278} \approx 35.73 \text{ people per square mile} \][/tex]
Comparing the population densities of the four states, we find:
- North Dakota: 11.03 people per square mile
- South Dakota: 11.50 people per square mile
- Nebraska: 25.35 people per square mile
- Kansas: 35.73 people per square mile
The state with the greatest population density is Kansas with a population density of approximately 35.73 people per square mile.
Therefore, the correct answer is:
D. Kansas
