Sure! Let's analyze each statement step by step:
1. The population density for Montana can be found using the ratio [tex]\( 1,005,141 : 145,552 \)[/tex].
Population density is found by dividing the population by the area. For Montana, we calculate:
[tex]\[
\text{Montana Density} = \frac{1,005,141}{145,552} \approx 6.9057 \text{ people per square mile}
\][/tex]
This statement is true.
2. The population density for Oregon can be found using the ratio [tex]\( 95,997 : 3,899,353 \)[/tex].
This statement incorrectly describes the population density calculation. The ratio provided should be the other way around. The correct way is:
[tex]\[
\text{Oregon Density} = \frac{3,899,353}{95,997} \approx 40.6195 \text{ people per square mile}
\][/tex]
Thus, this statement is false.
3. The population density for Hawaii is greater than the population density for Florida.
Let's compare the densities of Hawaii and Florida:
- Hawaii Density:
[tex]\[
\frac{1,392,313}{6,423} \approx 216.7038 \text{ people per square mile}
\][/tex]
- Florida Density:
[tex]\[
\frac{19,317,568}{53,927} \approx 358.26 \text{ people per square mile}
\][/tex]
The population density of Hawaii (216.7038) is not greater than the population density of Florida (358.26), so this statement is false.
4. The state with the smallest population density is Oregon.
We need to compare the population densities:
- Montana Density: [tex]\( 6.9057 \)[/tex]
- Oregon Density: [tex]\( 40.6195 \)[/tex]
- Hawaii Density: [tex]\( 216.7038 \)[/tex]
- Florida Density: [tex]\( 358.26 \)[/tex]
From these values, it's clear that Montana has the smallest population density, not Oregon. So, this statement is false.
5. The state with the smallest population density is Montana.
As verified in the comparison above, Montana indeed has the smallest population density. Therefore, this statement is true.
In conclusion, the two true statements are:
- The population density for Montana can be found using the ratio [tex]\( 1,005,141 : 145,552 \)[/tex].
- The state with the smallest population density is Montana.
