Semester Grades A professor bases semester grades on four 100-point items: homework, quizzes, a midterm exam, and a final exam. Students may choose one of three schemes summarized in the accompanying matrix for weighting the points from the four items. Use matrix multiplication to determine the most advantageous weighting scheme for a student who earned 97 points on homework, 72 points on the quizzes, 83 points on the midterm exam, and 75 points on the final exam. Items HW Qu ME FE Scheme I Scheme II Scheme III [ .10 .10 .30 .50 .10 .20 .30 .40 .15 .15 .35 .35 ]
Semester Grades A professor bases semester grades on four 100-point items: homework, quizzes, a midterm exam, and a final exam. Students may choose one of three schemes summarized in the accompanying matrix for weighting the points from the four items. Use matrix multiplication to determine the most advantageous weighting scheme for a student who earned 97 points on homework, 72 points on the quizzes, 83 points on the midterm exam, and 75 points on the final exam. Items HW Qu ME FE Scheme I Scheme II Scheme III [ .10 .10 .30 .50 .10 .20 .30 .40 .15 .15 .35 .35 ]
Solution Summary: The author explains that the most advantageous weighting scheme is calculated by multiplying the scheme with points a student got.
Semester Grades A professor bases semester grades on four 100-point items: homework, quizzes, a midterm exam, and a final exam. Students may choose one of three schemes summarized in the accompanying matrix for weighting the points from the four items. Use matrix multiplication to determine the most advantageous weighting scheme for a student who earned 97 points on homework, 72 points on the quizzes, 83 points on the midterm exam, and 75 points on the final exam.
Items
HW
Qu
ME
FE
Scheme
I
Scheme
II
Scheme
III
[
.10
.10
.30
.50
.10
.20
.30
.40
.15
.15
.35
.35
]
Robyn owns and operates two souvenir shops. At his Sabina Park shop, sweatshirts cost $4500 and T-shirts cost $2000. At his National Arena shop, sweatshirts cost $5000 and T- shirts cost $1500. Today Robyn sold 200 sweatshirts and 250 T-shirts at each shop.
Use matrix multiplication to find the total amount in daily sales at each souvenir stand.
Sally went to the store and purchased 4 skirts, 4 dresses and 5 shirts. Anna went to the store and purchased 3 skirts, 3 dresses and 6 shirts.
Each skirt costs $10, each dress cost $15, and each shirt costs $16.
a) Write a 2 × 3 matrix summarizing the purchases made by Sally and Anna. (Keep the order of information).
b) Write a 3 x 1 matrix summarizing the cost (in dollars) of the items. (Keep the order of information).
c) Use matrix multiplication to find a 2 × 1 matrix summarizing the total amount (in dollars) spent by Sally and Anna.
Using Matrices, solve the following: A practical Humber student invested 20,000in two stocks. The two stocks yielded 7% and 11% simple interest in the first year. The total interest received was $1,880. How much does the student invested in each stock?
Chapter 2 Solutions
Finite Mathematics & Its Applications (12th Edition)
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