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Sagot :
To solve the problem, let's go through the calculations and conclusions step-by-step:
1. Determine the land areas of each city:
- Delhi (India):
[tex]\[ \text{Area of Delhi} = \frac{\text{Population of Delhi}}{\text{Pop. Density of Delhi}} = \frac{22,826,000}{30,400} \approx 750.86 \quad \text{sq mi} \][/tex]
- Manila (Philippines):
[tex]\[ \text{Area of Manila} = \frac{\text{Population of Manila}}{\text{Pop. Density of Manila}} = \frac{21,241,000}{38,300} \approx 554.60 \quad \text{sq mi} \][/tex]
- Karachi (Pakistan):
[tex]\[ \text{Area of Karachi} = \frac{\text{Population of Karachi}}{\text{Pop. Density of Karachi}} = \frac{20,877,000}{67,300} \approx 310.21 \quad \text{sq mi} \][/tex]
- New York (US):
[tex]\[ \text{Area of New York} = \frac{\text{Population of New York}}{\text{Pop. Density of New York}} = \frac{20,673,000}{4,600} \approx 4494.13 \quad \text{sq mi} \][/tex]
2. Analyze the conclusions based on the calculated areas:
- Conclusion 1:
"The land areas of Karachi and New York must be very similar in size."
- Karachi: [tex]\( 310.21 \ \text{sq mi} \)[/tex]
- New York: [tex]\( 4494.13 \ \text{sq mi} \)[/tex]
These areas are not similar in size. So, this conclusion is false.
- Conclusion 2:
"The population of Manila is greater than the population of New York."
- Manila: [tex]\( 21,241,000 \)[/tex]
- New York: [tex]\( 20,673,000 \)[/tex]
Manila's population is indeed greater than New York's. So, this conclusion is true.
- Conclusion 3:
"New York has a smaller land area than Delhi or Manila."
- New York: [tex]\( 4494.13 \ \text{sq mi} \)[/tex]
- Delhi: [tex]\( 750.86 \ \text{sq mi} \)[/tex]
- Manila: [tex]\( 554.60 \ \text{sq mi} \)[/tex]
New York has a larger land area compared to both Delhi and Manila. So, this conclusion is false.
- Conclusion 4:
"New York has a larger land area than Delhi or Manila."
- New York: [tex]\( 4494.13 \ \text{sq mi} \)[/tex]
- Delhi: [tex]\( 750.86 \ \text{sq mi} \)[/tex]
- Manila: [tex]\( 554.60 \ \text{sq mi} \)[/tex]
New York indeed has a larger land area compared to both Delhi and Manila. So, this conclusion is true.
Therefore, based on the calculations:
- The correct conclusions from the table are:
1. The population of Manila is greater than the population of New York.
2. New York has a larger land area than Delhi or Manila.
1. Determine the land areas of each city:
- Delhi (India):
[tex]\[ \text{Area of Delhi} = \frac{\text{Population of Delhi}}{\text{Pop. Density of Delhi}} = \frac{22,826,000}{30,400} \approx 750.86 \quad \text{sq mi} \][/tex]
- Manila (Philippines):
[tex]\[ \text{Area of Manila} = \frac{\text{Population of Manila}}{\text{Pop. Density of Manila}} = \frac{21,241,000}{38,300} \approx 554.60 \quad \text{sq mi} \][/tex]
- Karachi (Pakistan):
[tex]\[ \text{Area of Karachi} = \frac{\text{Population of Karachi}}{\text{Pop. Density of Karachi}} = \frac{20,877,000}{67,300} \approx 310.21 \quad \text{sq mi} \][/tex]
- New York (US):
[tex]\[ \text{Area of New York} = \frac{\text{Population of New York}}{\text{Pop. Density of New York}} = \frac{20,673,000}{4,600} \approx 4494.13 \quad \text{sq mi} \][/tex]
2. Analyze the conclusions based on the calculated areas:
- Conclusion 1:
"The land areas of Karachi and New York must be very similar in size."
- Karachi: [tex]\( 310.21 \ \text{sq mi} \)[/tex]
- New York: [tex]\( 4494.13 \ \text{sq mi} \)[/tex]
These areas are not similar in size. So, this conclusion is false.
- Conclusion 2:
"The population of Manila is greater than the population of New York."
- Manila: [tex]\( 21,241,000 \)[/tex]
- New York: [tex]\( 20,673,000 \)[/tex]
Manila's population is indeed greater than New York's. So, this conclusion is true.
- Conclusion 3:
"New York has a smaller land area than Delhi or Manila."
- New York: [tex]\( 4494.13 \ \text{sq mi} \)[/tex]
- Delhi: [tex]\( 750.86 \ \text{sq mi} \)[/tex]
- Manila: [tex]\( 554.60 \ \text{sq mi} \)[/tex]
New York has a larger land area compared to both Delhi and Manila. So, this conclusion is false.
- Conclusion 4:
"New York has a larger land area than Delhi or Manila."
- New York: [tex]\( 4494.13 \ \text{sq mi} \)[/tex]
- Delhi: [tex]\( 750.86 \ \text{sq mi} \)[/tex]
- Manila: [tex]\( 554.60 \ \text{sq mi} \)[/tex]
New York indeed has a larger land area compared to both Delhi and Manila. So, this conclusion is true.
Therefore, based on the calculations:
- The correct conclusions from the table are:
1. The population of Manila is greater than the population of New York.
2. New York has a larger land area than Delhi or Manila.
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