Good read as always, here's the homework.

Spoiler:
6 Outs

Semi-Bluffing
1) Our opponent folds (40 percent), we win the pot of $30.
2) Our opponent calls (60 percent), we hit our draw (6/46), we win the $30 pot and the $25 call.
3) Our opponent calls (60 percent), we miss our draw (40/46), we lose our $25 bet.

<Semi-Bluff> = (0.4)(30) + (0.6)(6/46)(30+25) + (0.6)(40/46)(-25)
<Semi-Bluff> = 12 + 4.3 - 13.04
<Semi-Bluff> = $3.26

Checking
1 )Miss our draw (40/46), no win or loss.
2) Hit our draw (6/46), no extra money goes in (95 percent), win the pot of $30.
3) Hit our draw (6/46), get stacks in (5 percent), win the pot of $30 and the $25 bet.

<Check> = (40/46)(0) + (6/46)(0.95)(30) + (6/46)(0.05)(25+30)
<Check> = 0 + 3.72 + 0.36
<Check> = $4.08

This shows that the more outs that we have to the nuts the better our EV for both checking and semi-bluffing assuming all other variables stay the same. Whilst checking is still the better option in this scenario the EV of semi-bluffing has increase by more than the EV of checking. So I would assume that there is a tipping point where <Semi-Bluffing> is better than <Checking>.

8 Outs

Semi-Bluffing
1) Our opponent folds (40 percent), we win the pot of $30.
2) Our opponent calls (60 percent), we hit our draw (8/46), we win the $30 pot and the $25 call.
3) Our opponent calls (60 percent), we miss our draw (38/46), we lose our $25 bet.

<Semi-Bluff> = (0.4)(30) + (0.6)(8/46)(30+25) + (0.6)(38/46)(-25)
<Semi-Bluff> = 12 + 5.74 + 12.39
<Semi-Bluff> = $5.35

Checking
1 )Miss our draw (38/46), no win or loss.
2) Hit our draw (8/46), no extra money goes in (95 percent), win the pot of $30.
3) Hit our draw (8/46), get stacks in (5 percent), win the pot of $30 and the $25 bet.

<Check> = (38/46)(0) + (8/46)(0.95)(30) + (8/46)(0.05)(25+30)
<Check> = 0 + 4.96 + 0.48
<Check> = $5.43

Once again we see that the EV of Semi-bluffing has increased more than that of checking but has still not caught up to the EV of checking.

Extra Credit
If x is the % of the time we hit the nuts

<Semi-Bluff> = (0.4)(30) + (0.6)(x)(30+25) + (0.6)(1-x)(-25)
<Semi-Bluff> = 12 + 33x - 15 + 15x
<Semi-Bluff> = 48x - 3

<Check> = x[(0.95)(30) + (0.05)(55)]
<Check> = x[28.5 + 2.75]
<Check> = 31.25x

<Semi-Bluff> = <Check>

48x - 3 = 31.25x
192x - 12 = 125x
67x = 12
x = 12/67 (0.179)

8/46 = 0.1739
9/46 = 0.1957

So the point at which semi-bluffing becomes better than checking in this scenario is when we have 9 outs to the nuts.

Assuming I've not made a silly mistake.