Vector - Total score from course record. The record for each student in a class is given as a 10-
vector r, where r1, . . . , r8 are the grades for the 8 homework assignments, each on a 0–10
scale, r9 is the midterm exam grade on a 0–120 scale, and r10 is final exam score on a
0–160 scale. The student’s total course score s, on a 0–100 scale, is based 25% on the
homework, 35% on the midterm exam, and 40% on the final exam. Determine s such that the student's final grade is given by the inner product of s and r.
Please help, is my approach correct?
I reduced the 10-vector r to (80,120,160), supposing that the student had mastered all grades.
In order to find the vector s, I made the following equations based on each score scale:
80A=0.25
120B=0.35
160C=0.40
Therefore the 3-vector s would be (0.0031,0.0029,0.0025), and the inner product of s and r would give the student's final grade.
 A: Your solution seems close to correct; I take it you have taken $A$ to be the sum of all homework scores? In that case, I see only two minor problems:


*

*Your scores now end up on a scale of $0$ to $1$. This is of course easily fixed by multiplying the vector by $100$.

*You use rounded values for the vector, which can lead to the wrong results. This can be avoided by using fractions instead of decimals, or otherwise by rounding a few decimals further to avoid significant impact on the grades. 


You should then end up with the vector
$$\left(\frac{25}{80},\frac{35}{120},\frac{40}{160}\right)=(0.3125,0.291666\ldots,0.25).$$
As a side note,  here's a how I originally approached the problem:
The total course score is on a $0$ to $100$ scale. The homework is $25\%$ of the score, so this is on a $0$ to $25$ scale. There are $8$ assignments, so each is on a scale of $0$ to $\tfrac{25}{8}=3.125$. So to convert the original homework scores from their $0$ to $10$ scales, multiply them by $0.3125$ to get them on a $0$ to $3.125$ scale.
The midterm and the final can be done in the same way, and then you can add up all the scores.
