A university admissions committee anticipates an enrollment of 8000 students in its freshman class next year. To satisfy admission quotas, incoming students have been categorized accordin sex and place of residence. The number of students in each category is given by the matrix A. Male Female In-state 2700 28001 A= Out-of-state 900 800 Foreign 400 400 By using data accumulated in previous years, the admissions committee has determined that these students will elect to enter the College of Letters and Science, the College of Fine Arts, the Business Administration, and the School of Engineering according to the percentages that appear in the following matrix. AB= B = Male Female L. & S. Fine Arts Bus. Ad. Eng. 0.25 0.20 0.30 0.25 0.30 0.35 0.25 0.10 Find the matrix AB that shows the number of in-state, out-of-state, and foreign students expected to enter each discipline. ↓1
A university admissions committee anticipates an enrollment of 8000 students in its freshman class next year. To satisfy admission quotas, incoming students have been categorized accordin sex and place of residence. The number of students in each category is given by the matrix A. Male Female In-state 2700 28001 A= Out-of-state 900 800 Foreign 400 400 By using data accumulated in previous years, the admissions committee has determined that these students will elect to enter the College of Letters and Science, the College of Fine Arts, the Business Administration, and the School of Engineering according to the percentages that appear in the following matrix. AB= B = Male Female L. & S. Fine Arts Bus. Ad. Eng. 0.25 0.20 0.30 0.25 0.30 0.35 0.25 0.10 Find the matrix AB that shows the number of in-state, out-of-state, and foreign students expected to enter each discipline. ↓1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Expected Enrollment Distribution in Various Disciplines
**University Admissions Overview**
A university admissions committee anticipates an enrollment of 8000 students in its freshman class next year. To satisfy admission quotas, incoming students have been categorized according to their sex and place of residence. The number of students in each category is given by the matrix \( A \):
\[ A = \begin{pmatrix}
2700 & 2800 \\
900 & 800 \\
400 & 400
\end{pmatrix} \]
Here, the numbers represent:
- **In-state:** 2700 males and 2800 females
- **Out-of-state:** 900 males and 800 females
- **Foreign:** 400 males and 400 females
**Discipline Selection Matrix**
By using data accumulated in previous years, the admissions committee has determined that these students will elect to enter the College of Letters and Science, the College of Fine Arts, the School of Business Administration, and the School of Engineering according to the percentages that appear in the following matrix \( B \):
\[ B = \begin{pmatrix}
0.25 & 0.20 & 0.30 & 0.25 \\
0.30 & 0.35 & 0.25 & 0.10
\end{pmatrix} \]
Here, the percentages represent the distribution of male and female students choosing each discipline:
- **Letters & Science (L. & S.)**
- **Fine Arts**
- **Business Administration (Bus. Ad.)**
- **Engineering (Eng.)**
**Calculating the Expected Numbers**
To find the matrix \( AB \) that shows the number of in-state, out-of-state, and foreign students expected to enter each discipline, perform matrix multiplication:
\[ AB = \begin{pmatrix}
2700 & 2800 \\
900 & 800 \\
400 & 400
\end{pmatrix}
\times
\begin{pmatrix}
0.25 & 0.20 & 0.30 & 0.25 \\
0.30 & 0.35 & 0.25 & 0.10
\end{pmatrix} \]
The resulting matrix \( AB \) will have the following structure, where each cell represents the number of students in a specific category entering a specific discipline:
\[ AB = \begin{pmatrix}
\text{...} & \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F77247d15-844d-4e77-b205-212be8c6419e%2Fe00a3784-95e8-4aa3-86f5-8fc0c1cd6bb8%2Fvtxxvbd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Expected Enrollment Distribution in Various Disciplines
**University Admissions Overview**
A university admissions committee anticipates an enrollment of 8000 students in its freshman class next year. To satisfy admission quotas, incoming students have been categorized according to their sex and place of residence. The number of students in each category is given by the matrix \( A \):
\[ A = \begin{pmatrix}
2700 & 2800 \\
900 & 800 \\
400 & 400
\end{pmatrix} \]
Here, the numbers represent:
- **In-state:** 2700 males and 2800 females
- **Out-of-state:** 900 males and 800 females
- **Foreign:** 400 males and 400 females
**Discipline Selection Matrix**
By using data accumulated in previous years, the admissions committee has determined that these students will elect to enter the College of Letters and Science, the College of Fine Arts, the School of Business Administration, and the School of Engineering according to the percentages that appear in the following matrix \( B \):
\[ B = \begin{pmatrix}
0.25 & 0.20 & 0.30 & 0.25 \\
0.30 & 0.35 & 0.25 & 0.10
\end{pmatrix} \]
Here, the percentages represent the distribution of male and female students choosing each discipline:
- **Letters & Science (L. & S.)**
- **Fine Arts**
- **Business Administration (Bus. Ad.)**
- **Engineering (Eng.)**
**Calculating the Expected Numbers**
To find the matrix \( AB \) that shows the number of in-state, out-of-state, and foreign students expected to enter each discipline, perform matrix multiplication:
\[ AB = \begin{pmatrix}
2700 & 2800 \\
900 & 800 \\
400 & 400
\end{pmatrix}
\times
\begin{pmatrix}
0.25 & 0.20 & 0.30 & 0.25 \\
0.30 & 0.35 & 0.25 & 0.10
\end{pmatrix} \]
The resulting matrix \( AB \) will have the following structure, where each cell represents the number of students in a specific category entering a specific discipline:
\[ AB = \begin{pmatrix}
\text{...} & \
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