To answer this question, we need to break it down into several steps to determine the population densities for each city and evaluate the statements accordingly.
First, let's define population density. Population density is defined as the population of a city divided by its area.
Given the data:
- City A:
- Population: 2,195,914
- Area: 1,553 square kilometers
- Population Density: [tex]\( \frac{2,195,914}{1,553} \approx 1413.98 \)[/tex] people per square kilometer
- City B:
- Population: 48,592
- Area: 26 square kilometers
- Population Density: [tex]\( \frac{48,592}{26} \approx 1868.92 \)[/tex] people per square kilometer
- City C:
- Population: 1,257,676
- Area: 999 square kilometers
- Population Density: [tex]\( \frac{1,257,676}{999} \approx 1258.93 \)[/tex] people per square kilometer
- City D:
- Population: 196,429
- Area: 258 square kilometers
- Population Density: [tex]\( \frac{196,429}{258} \approx 761.35 \)[/tex] people per square kilometer
Next, let's evaluate each statement:
1. The population density for City B can be found using the ratio 48,592: 26.
- This is true because the population density of a city is calculated as the population divided by the area. Therefore, the ratio [tex]\( 48,592: 26 \)[/tex] correctly provides the population density for City B.
2. The population density for City D can be found using the ratio 258: 196,429.
- This is false because the correct ratio should be the population divided by the area, not the other way around. The correct ratio should be [tex]\( 196,429: 258 \)[/tex].
3. City A has the greatest population density of the four cities.
- This is false. Comparing the densities:
- City A: 1413.98
- City B: 1868.92
- City C: 1258.93
- City D: 761.35
City B has the greatest population density, not City A.
4. The population density of City B is greater than that of City C.
- This is true.
- Population density of City B: 1868.92
- Population density of City C: 1258.93
So, [tex]\( 1868.92 > 1258.93 \)[/tex] indicates that City B has greater population density than City C.
5. City D has the lowest population density of the four cities.
- This is true. Comparing the densities:
- City A: 1413.98
- City B: 1868.92
- City C: 1258.93
- City D: 761.35
Clearly, City D has the lowest population density.
So, the three true statements are:
- The population density for City B can be found using the ratio [tex]\( 48,592: 26 \)[/tex].
- The population density of City B is greater than that of City C.
- City D has the lowest population density of the four cities.
