The phases of the moon are periodic and repetitive. A new moon occurs when no moon is visible to an observer on Earth. During the first quarter, half of the side of the moon facing the Earth is visible. During a full moon the entire side of the moon is visible. During the last quarter the other half of the side of the moon facing Earth is visible. The U. S. Naval Observatory lists the following dates for phases of the Moon in the year 2008.

Date
Moon Phase
x: Days since Jan. 8
y: The Amount of Moon Visible
Jan 8
New
0
0
Jan 15
1st quarter
7
0.5
Jan 22
Full
13
1
Jan 30
Last quarter
22
0.5
Feb 7
New
30
0
Feb 14
1st quarter
37
0.5
Feb 21
Full
44
1
Feb 29
Last quarter
52
0.5
Mar 7
New
59
0
Mar 14
1st quarter
66
0.5

Using the information above, plot the data points and produce a sine regression model for the data. Round a, b, c, and d to the nearest 0.001. Then use your model to predict how much of the moon will be visible 65 days after Jan 8th, provided the sky is clear. Give your answer as a percent.
a.
38% of the moon will be visible
b.
9% of the moon will be visible
c.
35% of the moon will be visible
d.
99% of the moon will be visible