The given table shows four​ states, their 2010​ populations, and their number of seats in a particular branch of government that has a total of 350 seats. For state Upper D​, find the standard quota. Use the value 291 million for the total population. Explain whether each state is relatively​ under- or overrepresented.
nbsp Bold State nbsp
nbsp Bold Population
nbsp Bold Seats nbsp
 
A
14 comma 256 comma 000
17
B
11 comma 500 comma 000
14
C
3 comma 107 comma 000
3
D
16 comma 328 comma 000
19
 
Question content area bottom
Part 1
Select the correct choice below and fill in the answer box to complete your choice.
​(Round to two decimal places as​ needed.)
A.
State Upper D is underrepresented because its standard quota of 
  
enter your response here is more than its number of​ representatives, 19.
B.
State Upper D is overrepresented because its standard quota of 
  
enter your response here is less than its number of​ representatives, 19.

Let's calculate the standard quota for State D using the given information:

### Given Data:
- **Population of State D**: 16,328,000
- **Total Population**: 291,000,000
- **Total Seats**: 350

### Standard Quota Formula:
\[
\text{Standard Quota} = \left(\frac{\text{Population of State}}{\text{Total Population}}\right) \times \text{Total Seats}
\]

### Calculation for State D:
\[
\text{Standard Quota of State D} = \left(\frac{16,328,000}{291,000,000}\right) \times 350
\]

Let's calculate:

\[
\text{Standard Quota of State D} \approx \left(\frac{16,328,000}{291,000,000}\right) \times 350
\]

\[
\text{Standard Quota of State D} \approx 0.0561 \times 350
\]

\[
\text{Standard Quota of State D} \approx 19.64
\]

So, the standard quota for State D is approximately 19.64.

### Determining Representation:
- **Actual number of seats for State D**: 19
- **Standard quota**: 19.64

Since the standard quota (19.64) is more than the actual number of representatives (19), **State D is slightly underrepresented**.

The correct choice is:
**A. State D is underrepresented because its standard quota of 19.64 is more than its number of representatives, 19.**

Would you like more details or have any questions about the calculation? Here are 5 related questions:

1. How would you calculate the standard quota for State A?
2. What factors influence whether a state is underrepresented or overrepresented?
3. How does the total number of seats affect the standard quota for each state?
4. What role does rounding play in the allocation of seats based on the standard quota?
5. How would changes in population affect the standard quota over time?

**Tip:** In scenarios where the standard quota is close to an integer value, small differences can significantly impact whether a state is considered underrepresented or overrepresented.

Learn how to calculate the standard quota and determine representation for State D based on its population and allocated seats. This problem explores the concept of proportional representation and uses real-world data to illustrate the calculation process. Suitable for advanced high school students and those interested in political science or mathematics.

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