Homework Help is Here – Start Your Trial Now!
Math
Algebra
Two subjects, Pure Mathematies and Applied Mathematics, are offered in the first semester of a university science course. The matrix N lists the number of students enrolled in each subject. 540 Pure 360 Applied The matrix G lists the proportion of these students expected to be awarded grades 4, B, C, D or E in cach subject. B C DE G=[ 0.05 0.125 0.175 045 0.20 ] a. Write down the orders of matrices N and G. The final results matrix (R) shows the final number of students achieving each grade for b. cach Mathematics subject, and is calculated as follows : R= NG. i. Evaluate the matrix R, showing results correct to the nearest integer. ii. Explain what the matrix element R13 represents. iii. If an E grade is considered a fail, how many students, in total, will have failed these subjects at the end of the semester.

Two subjects, Pure Mathematies and Applied Mathematics, are offered in the first semester of a university science course. The matrix N lists the number of students enrolled in each subject. 540 Pure 360 Applied The matrix G lists the proportion of these students expected to be awarded grades 4, B, C, D or E in cach subject. B C DE G=[ 0.05 0.125 0.175 045 0.20 ] a. Write down the orders of matrices N and G. The final results matrix (R) shows the final number of students achieving each grade for b. cach Mathematics subject, and is calculated as follows : R= NG. i. Evaluate the matrix R, showing results correct to the nearest integer. ii. Explain what the matrix element R13 represents. iii. If an E grade is considered a fail, how many students, in total, will have failed these subjects at the end of the semester.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
See similar textbooks
icon
Related questions
Question
Two subjects, Pure Mathematies and Applied Mathematics, are offered in the first semester of a university science course. The matrix N lists the number of students enrolled in each subject. 540 Pure 360 Applied The matrix G lists the proportion of these students expected to be awarded grades 4, B, C, D or E in cach subject. A B C D E G=[ 0.05 0.125 0.175 045 0.20 ] a. Write down the orders of matrices N and G. The final results matrix (R) shows the final number of students achieving each grade for each Mathematics subject, and is calculated as follows : R= NG. b. i. Evaluate the matrix R, showing results correct to the nearest integer. ii. Explain what the matrix element R13 represents. If an E grade is considered a fail, how many students, in total, will have failed these ii. subjects at the end of the semester. Students enrolled in Pure Mathematics have to pay a course fee of $110, while students enrolled in Applied Mathematics pay a course fee of $150. These course fees cover the course of printed notes and access to a variety of resources. i. Write down a clearly labelled row matrix, called F, that lists these fees. ii. Show a matrix calculation that will give the total course fees, C, paid in dollars by the students enrolled in Pure and Applied Mathematics. Find this amount.
Transcribed Image Text:Two subjects, Pure Mathematies and Applied Mathematics, are offered in the first semester of a university science course. The matrix N lists the number of students enrolled in each subject. 540 Pure 360 Applied The matrix G lists the proportion of these students expected to be awarded grades 4, B, C, D or E in cach subject. A B C D E G=[ 0.05 0.125 0.175 045 0.20 ] a. Write down the orders of matrices N and G. The final results matrix (R) shows the final number of students achieving each grade for each Mathematics subject, and is calculated as follows : R= NG. b. i. Evaluate the matrix R, showing results correct to the nearest integer. ii. Explain what the matrix element R13 represents. If an E grade is considered a fail, how many students, in total, will have failed these ii. subjects at the end of the semester. Students enrolled in Pure Mathematics have to pay a course fee of $110, while students enrolled in Applied Mathematics pay a course fee of $150. These course fees cover the course of printed notes and access to a variety of resources. i. Write down a clearly labelled row matrix, called F, that lists these fees. ii. Show a matrix calculation that will give the total course fees, C, paid in dollars by the students enrolled in Pure and Applied Mathematics. Find this amount.
The following transition matrix, 7, is used to help predict class attendance of Pure Mathematics students at the university on a lecture-by-lecture basis. this lecture attend not attend T- 085 0.25 0.15 0.75 attend next lecture not attend So is the attendance matrix for the Pure Mathematics information session. 510 attend 30 not attend So indicates that 510 Pure Mathematics students attended the information session and 30 Pure Mathematics students did not attend the information session. d. Use T'and So to i. determine S1 the attendance matrix for the first lecture, writing your answers correct to the nearest integer. ii. predict the number of Pure Mathematics students attending the third lecture, writing your answer correct to the nearest integer. Write down a matrix equation for S, in terms of T, n and So, that would enable us to predict the number of students attending any of the 52 lectures scheduled for Pure Mathematies in Semester One. To cut down on cleaning costs, the Pure Mathematics lecture will be transferred to a smaller lecture theatre when the number of students predicted to attend falls below 350. 1. For which lecture can this first be done? Predict, correct to the nearest integer, the number of students who will be attending the Pure Mathematies lectures : i. one-quarter of the way through the course ii. one-half of the way through the course
Transcribed Image Text:The following transition matrix, 7, is used to help predict class attendance of Pure Mathematics students at the university on a lecture-by-lecture basis. this lecture attend not attend T- 085 0.25 0.15 0.75 attend next lecture not attend So is the attendance matrix for the Pure Mathematics information session. 510 attend 30 not attend So indicates that 510 Pure Mathematics students attended the information session and 30 Pure Mathematics students did not attend the information session. d. Use T'and So to i. determine S1 the attendance matrix for the first lecture, writing your answers correct to the nearest integer. ii. predict the number of Pure Mathematics students attending the third lecture, writing your answer correct to the nearest integer. Write down a matrix equation for S, in terms of T, n and So, that would enable us to predict the number of students attending any of the 52 lectures scheduled for Pure Mathematies in Semester One. To cut down on cleaning costs, the Pure Mathematics lecture will be transferred to a smaller lecture theatre when the number of students predicted to attend falls below 350. 1. For which lecture can this first be done? Predict, correct to the nearest integer, the number of students who will be attending the Pure Mathematies lectures : i. one-quarter of the way through the course ii. one-half of the way through the course
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Markov Processes and Markov chain
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education
SEE MORE TEXTBOOKS