Anais, a math teacher, noticed that the average grade, [tex]G[/tex], on an exam given that [tex]n[/tex] students watch the related video can be given by the function [tex]G(n) = 50 + 1.5n[/tex]. She also noticed that the number, [tex]S[/tex], of students who watch an [tex]m[/tex] minute video can be modeled by the function [tex]S(m) = 30 - m[/tex].

Which expression gives the average grade on an exam if the related video is [tex]m[/tex] minutes?

Choose one answer:

A. [tex]95 - m[/tex]

B. [tex]1.5m - 20[/tex]

C. [tex]-1.5m - 20[/tex]

D. [tex]95 - 1.5m[/tex]

We are given two functions:

1. The average exam grade when [tex]$n$[/tex] students watch the video:
[tex]$$G(n) = 50 + 1.5n.$$[/tex]

2. The number of students watching an [tex]$m$[/tex] minute video:
[tex]$$S(m) = 30 - m.$$[/tex]

Since the number of students [tex]$n$[/tex] is given by [tex]$S(m)$[/tex], we substitute [tex]$n = 30 - m$[/tex] into [tex]$G(n)$[/tex] to express the average grade in terms of [tex]$m$[/tex]. This gives:

[tex]$$
G(S(m)) = 50 + 1.5(30 - m).
$$[/tex]

Now, follow these steps:

1. Multiply [tex]$1.5$[/tex] by [tex]$30$[/tex]:
[tex]$$1.5 \times 30 = 45.$$[/tex]

2. Substitute back into the equation:
[tex]$$G(S(m)) = 50 + 45 - 1.5m.$$[/tex]

3. Combine the constants [tex]$50$[/tex] and [tex]$45$[/tex]:
[tex]$$50 + 45 = 95.$$[/tex]

Thus, the average grade in terms of [tex]$m$[/tex] is:

[tex]$$
G(S(m)) = 95 - 1.5m.
$$[/tex]

So the expression that gives the average grade on an exam if the related video is [tex]$m$[/tex] minutes is

[tex]$$\boxed{95 - 1.5m}.$$[/tex]

This corresponds to option (D).