Answer :
To answer this question, we need to calculate the population density for each city and evaluate the given statements based on these population densities.
Here is a step-by-step solution:
1. Calculate the population density for each city.
- City A:
[tex]\[ \text{Population Density} = \frac{\text{Population}}{\text{Area}} = \frac{2,195,914}{1,553} \approx 1413.98 \, \text{people per km}^2 \][/tex]
- City B:
[tex]\[ \text{Population Density} = \frac{\text{Population}}{\text{Area}} = \frac{48,592}{26} \approx 1868.92 \, \text{people per km}^2 \][/tex]
- City C:
[tex]\[ \text{Population Density} = \frac{\text{Population}}{\text{Area}} = \frac{1,257,676}{999} \approx 1258.93 \, \text{people per km}^2 \][/tex]
- City D:
[tex]\[ \text{Population Density} = \frac{\text{Population}}{\text{Area}} = \frac{196,429}{258} \approx 761.35 \, \text{people per km}^2 \][/tex]
2. Evaluate the given statements:
- Statement 1: The population density for City B can be found using the ratio 48,592 : 26.
[tex]\[ \text{Calculation: } \frac{48,592}{26} \approx 1868.92 \][/tex]
This matches the population density calculated for City B, so this statement is true.
- Statement 2: The population density for City D can be found using the ratio 258: 196,429.
[tex]\[ \text{Calculation: } \frac{196,429}{258} \approx 761.35 \][/tex]
This matches the population density calculated for City D, so this statement is true.
- Statement 3: City A has the greatest population density of the four cities.
[tex]\[ \text{Population Densities: } \begin{align*} \text{City A: } & 1413.98 \\ \text{City B: } & 1868.92 \\ \text{City C: } & 1258.93 \\ \text{City D: } & 761.35 \end{align*} \][/tex]
Since the population density of City B (1868.92) is greater than that of City A (1413.98), this statement is false.
- Statement 4: The population density of City B is greater than that of City C.
[tex]\[ \text{Comparison: } 1868.92 > 1258.93 \][/tex]
This is correct, so the statement is true.
- Statement 5: City D has the lowest population density of the four cities.
[tex]\[ \text{Population Densities: } \begin{align*} \text{City A: } & 1413.98 \\ \text{City B: } & 1868.92 \\ \text{City C: } & 1258.93 \\ \text{City D: } & 761.35 \end{align*} \][/tex]
City D does indeed have the lowest population density, so this statement is true.
3. Summary of the evaluated statements:
- The population density for City B can be found using the ratio 48,592 : 26. (True)
- The population density for City D can be found using the ratio 258: 196,429. (True)
- City A has the greatest population density of the four cities. (False)
- The population density of City B is greater than that of City C. (True)
- City D has the lowest population density of the four cities. (True)
Selecting the three true options, they are:
- The population density for City B can be found using the ratio 48,592 : 26.
- The population density for City D can be found using the ratio 258: 196,429.
- The population density of City B is greater than that of City C.
Therefore, the correct answer choices are the first, second, and fourth statements.
Here is a step-by-step solution:
1. Calculate the population density for each city.
- City A:
[tex]\[ \text{Population Density} = \frac{\text{Population}}{\text{Area}} = \frac{2,195,914}{1,553} \approx 1413.98 \, \text{people per km}^2 \][/tex]
- City B:
[tex]\[ \text{Population Density} = \frac{\text{Population}}{\text{Area}} = \frac{48,592}{26} \approx 1868.92 \, \text{people per km}^2 \][/tex]
- City C:
[tex]\[ \text{Population Density} = \frac{\text{Population}}{\text{Area}} = \frac{1,257,676}{999} \approx 1258.93 \, \text{people per km}^2 \][/tex]
- City D:
[tex]\[ \text{Population Density} = \frac{\text{Population}}{\text{Area}} = \frac{196,429}{258} \approx 761.35 \, \text{people per km}^2 \][/tex]
2. Evaluate the given statements:
- Statement 1: The population density for City B can be found using the ratio 48,592 : 26.
[tex]\[ \text{Calculation: } \frac{48,592}{26} \approx 1868.92 \][/tex]
This matches the population density calculated for City B, so this statement is true.
- Statement 2: The population density for City D can be found using the ratio 258: 196,429.
[tex]\[ \text{Calculation: } \frac{196,429}{258} \approx 761.35 \][/tex]
This matches the population density calculated for City D, so this statement is true.
- Statement 3: City A has the greatest population density of the four cities.
[tex]\[ \text{Population Densities: } \begin{align*} \text{City A: } & 1413.98 \\ \text{City B: } & 1868.92 \\ \text{City C: } & 1258.93 \\ \text{City D: } & 761.35 \end{align*} \][/tex]
Since the population density of City B (1868.92) is greater than that of City A (1413.98), this statement is false.
- Statement 4: The population density of City B is greater than that of City C.
[tex]\[ \text{Comparison: } 1868.92 > 1258.93 \][/tex]
This is correct, so the statement is true.
- Statement 5: City D has the lowest population density of the four cities.
[tex]\[ \text{Population Densities: } \begin{align*} \text{City A: } & 1413.98 \\ \text{City B: } & 1868.92 \\ \text{City C: } & 1258.93 \\ \text{City D: } & 761.35 \end{align*} \][/tex]
City D does indeed have the lowest population density, so this statement is true.
3. Summary of the evaluated statements:
- The population density for City B can be found using the ratio 48,592 : 26. (True)
- The population density for City D can be found using the ratio 258: 196,429. (True)
- City A has the greatest population density of the four cities. (False)
- The population density of City B is greater than that of City C. (True)
- City D has the lowest population density of the four cities. (True)
Selecting the three true options, they are:
- The population density for City B can be found using the ratio 48,592 : 26.
- The population density for City D can be found using the ratio 258: 196,429.
- The population density of City B is greater than that of City C.
Therefore, the correct answer choices are the first, second, and fourth statements.
