Select the correct answer.

The estimated population of four states is listed.

\begin{tabular}{|c|l|l|l|l|}
\hline
State & North Dakota & South Dakota & Nebraska & Kansas \\
\hline
Population & 780,000 & 887,000 & [tex]$1,960,000$[/tex] & [tex]$2,940,000$[/tex] \\
\hline
\end{tabular}

Use estimation to decide which state has the greatest population density.



Answer :

To determine which state has the greatest population density, we need to calculate the population density for each state. Population density is given by the formula:

[tex]\[ \text{Population Density} = \frac{\text{Population}}{\text{Area}} \][/tex]

Here are the populations and approximate areas of the four states:

1. North Dakota
- Population: 780,000
- Area: ~70,698 square miles

2. South Dakota
- Population: 887,000
- Area: ~77,116 square miles

3. Nebraska
- Population: 1,960,000
- Area: ~77,348 square miles

4. Kansas
- Population: 2,940,000
- Area: ~82,278 square miles

Now, let's calculate the population density for each state:

1. North Dakota

[tex]\[ \frac{780,000}{70,698} \approx 11.03 \,\text{people per square mile} \][/tex]

2. South Dakota

[tex]\[ \frac{887,000}{77,116} \approx 11.50 \,\text{people per square mile} \][/tex]

3. Nebraska

[tex]\[ \frac{1,960,000}{77,348} \approx 25.34 \,\text{people per square mile} \][/tex]

4. Kansas

[tex]\[ \frac{2,940,000}{82,278} \approx 35.73 \,\text{people per square mile} \][/tex]

According to our calculations, the population densities are:

- North Dakota: approximately 11.03 people per square mile
- South Dakota: approximately 11.50 people per square mile
- Nebraska: approximately 25.34 people per square mile
- Kansas: approximately 35.73 people per square mile

Thus, the state with the greatest population density is Kansas, with a population density of approximately 35.73 people per square mile.