Answer :
Let's analyze each statement and determine its validity using the given population and area data for Florida, Hawaii, Montana, and Oregon.
1. The population density for Montana can be found using the ratio [tex]\(1,005,141: 145,552\)[/tex]
Population density is calculated as the population divided by the area. For Montana:
[tex]\[ \text{Population Density} = \frac{1,005,141}{145,552} \approx 6.91 \text{ people/mi}^2 \][/tex]
This calculation is correct, so 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 inverts the usual ratio format. The correct ratio should be the population divided by the area.
[tex]\[ \frac{3,899,353}{95,997} = 40.62 \text{ people/mi}^2 \][/tex]
Since the statement has the ratio reversed, it is false.
3. The population density for Hawaii is greater than the population density for Florida.
Let's calculate the population densities for Hawaii and Florida:
For Hawaii:
[tex]\[ \text{Population Density} = \frac{1,392,313}{6,423} = 216.77 \text{ people/mi}^2 \][/tex]
For Florida:
[tex]\[ \text{Population Density} = \frac{19,317,568}{53,927} = 358.22 \text{ people/mi}^2 \][/tex]
As seen, Hawaii's population density (216.77 people/mi²) is less than Florida's population density (358.22 people/mi²). So, this statement is false.
4. The state with the smallest population density is Oregon.
We have calculated population densities as follows:
- Montana: 6.91 people/mi²
- Oregon: 40.62 people/mi²
- Hawaii: 216.77 people/mi²
- Florida: 358.22 people/mi²
Montana has the smallest population density at 6.91 people/mi². Therefore, this statement is false.
5. The state with the smallest population density is Montana.
From the above calculations:
- Montana: 6.91 people/mi² (the smallest)
- Oregon: 40.62 people/mi²
- Hawaii: 216.77 people/mi²
- Florida: 358.22 people/mi²
Thus, Montana indeed has the smallest population density. This statement is true.
Summary:
- True: The population density for Montana can be found using the ratio [tex]\(1,005,141: 145,552\)[/tex].
- False: The population density for Oregon can be found using the ratio [tex]\(95,997: 3,899,353\)[/tex].
- False: The population density for Hawaii is greater than the population density for Florida.
- False: The state with the smallest population density is Oregon.
- True: The state with the smallest population density is Montana.
1. The population density for Montana can be found using the ratio [tex]\(1,005,141: 145,552\)[/tex]
Population density is calculated as the population divided by the area. For Montana:
[tex]\[ \text{Population Density} = \frac{1,005,141}{145,552} \approx 6.91 \text{ people/mi}^2 \][/tex]
This calculation is correct, so 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 inverts the usual ratio format. The correct ratio should be the population divided by the area.
[tex]\[ \frac{3,899,353}{95,997} = 40.62 \text{ people/mi}^2 \][/tex]
Since the statement has the ratio reversed, it is false.
3. The population density for Hawaii is greater than the population density for Florida.
Let's calculate the population densities for Hawaii and Florida:
For Hawaii:
[tex]\[ \text{Population Density} = \frac{1,392,313}{6,423} = 216.77 \text{ people/mi}^2 \][/tex]
For Florida:
[tex]\[ \text{Population Density} = \frac{19,317,568}{53,927} = 358.22 \text{ people/mi}^2 \][/tex]
As seen, Hawaii's population density (216.77 people/mi²) is less than Florida's population density (358.22 people/mi²). So, this statement is false.
4. The state with the smallest population density is Oregon.
We have calculated population densities as follows:
- Montana: 6.91 people/mi²
- Oregon: 40.62 people/mi²
- Hawaii: 216.77 people/mi²
- Florida: 358.22 people/mi²
Montana has the smallest population density at 6.91 people/mi². Therefore, this statement is false.
5. The state with the smallest population density is Montana.
From the above calculations:
- Montana: 6.91 people/mi² (the smallest)
- Oregon: 40.62 people/mi²
- Hawaii: 216.77 people/mi²
- Florida: 358.22 people/mi²
Thus, Montana indeed has the smallest population density. This statement is true.
Summary:
- True: The population density for Montana can be found using the ratio [tex]\(1,005,141: 145,552\)[/tex].
- False: The population density for Oregon can be found using the ratio [tex]\(95,997: 3,899,353\)[/tex].
- False: The population density for Hawaii is greater than the population density for Florida.
- False: The state with the smallest population density is Oregon.
- True: The state with the smallest population density is Montana.
