1. By predicting fertility and divorce rates as well as life-styles economic, demographers attempt to forecast the economy during the next decade and beyond -- predicting which industries will flourish and which will falter. The following table gives a distribution of age groups in the U.S. for the year 2030. Age Group Relative Age Group Relative frequency frequency 0-9.5 0.12 49.5-59.5 0.12 9.5-19.5 -0.14 59.5-69.5 19.5-29.5 k 69.5-79.5 29.5-39.5 0.16 79.5-89.5 39.5-49.5 Find the value of k. a 0.16 0.08 0.06 0.03
1. By predicting fertility and divorce rates as well as life-styles economic, demographers attempt to forecast the economy during the next decade and beyond -- predicting which industries will flourish and which will falter. The following table gives a distribution of age groups in the U.S. for the year 2030. Age Group Relative Age Group Relative frequency frequency 0-9.5 0.12 49.5-59.5 0.12 9.5-19.5 -0.14 59.5-69.5 19.5-29.5 k 69.5-79.5 29.5-39.5 0.16 79.5-89.5 39.5-49.5 Find the value of k. a 0.16 0.08 0.06 0.03
MATLAB: An Introduction with Applications
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![### Predicting Economic Trends Through Demographic Analysis
By predicting fertility and divorce rates as well as lifestyle changes, demographers attempt to forecast the economy during the next decade and beyond. This involves predicting which industries will flourish and which will falter. The following table provides a distribution of age groups in the U.S. for the year 2030:
#### Age Distribution Table for 2030
| Age Group | Relative Frequency |
|---------------|--------------------|
| 0-9.5 | 0.12 |
| 9.5-19.5 | 0.14 |
| 19.5-29.5 | k |
| 29.5-39.5 | 0.16 |
| 39.5-49.5 | 0.16 |
| 49.5-59.5 | 0.12 |
| 59.5-69.5 | 0.08 |
| 69.5-79.5 | 0.06 |
| 79.5-89.5 | 0.03 |
**Task:**
a) Find the value of k.
**Solution:**
To find the value of k, we use the fact that the sum of all the relative frequencies must equal 1. Summing the given relative frequencies:
\[
0.12 + 0.14 + k + 0.16 + 0.16 + 0.12 + 0.08 + 0.06 + 0.03 = 1
\]
Combining the known values:
\[
0.87 + k = 1
\]
Solving for k:
\[
k = 1 - 0.87 = 0.13
\]
Thus, the value of \( k \) is \( 0.13 \).
This information helps predict economic trends by understanding the distribution of different age groups within the population.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8afc82ac-131b-4872-93f6-baa956562cd6%2F3b3d53f1-1a22-44b3-97b7-0d3222ef199d%2Fwfrp0uc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Predicting Economic Trends Through Demographic Analysis
By predicting fertility and divorce rates as well as lifestyle changes, demographers attempt to forecast the economy during the next decade and beyond. This involves predicting which industries will flourish and which will falter. The following table provides a distribution of age groups in the U.S. for the year 2030:
#### Age Distribution Table for 2030
| Age Group | Relative Frequency |
|---------------|--------------------|
| 0-9.5 | 0.12 |
| 9.5-19.5 | 0.14 |
| 19.5-29.5 | k |
| 29.5-39.5 | 0.16 |
| 39.5-49.5 | 0.16 |
| 49.5-59.5 | 0.12 |
| 59.5-69.5 | 0.08 |
| 69.5-79.5 | 0.06 |
| 79.5-89.5 | 0.03 |
**Task:**
a) Find the value of k.
**Solution:**
To find the value of k, we use the fact that the sum of all the relative frequencies must equal 1. Summing the given relative frequencies:
\[
0.12 + 0.14 + k + 0.16 + 0.16 + 0.12 + 0.08 + 0.06 + 0.03 = 1
\]
Combining the known values:
\[
0.87 + k = 1
\]
Solving for k:
\[
k = 1 - 0.87 = 0.13
\]
Thus, the value of \( k \) is \( 0.13 \).
This information helps predict economic trends by understanding the distribution of different age groups within the population.
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