Final answer:
The given function models the average high temperature each month in Anchorage, Alaska, the number of months is the average high temperature above freezing (32°f) is C. 10 months.
Step-by-step explanation:
The given function t = 21.55 cos(π/6(m - 7)) - 43.75 models the average high temperature in degrees Fahrenheit each month throughout the year in Anchorage, Alaska.
In this equation, m represents the month, with m=1 for January and m=12 for December.
To determine the number of months where the average high temperature is above freezing (32°F), we need to find the values of m for which t is greater than 32°F.
Substituting 32 for t in the equation and solving for m, we have 32 = 21.55 cos(π/6(m - 7)) - 43.75.
By solving this equation, we find that the average high temperature is above freezing for 10 months (September to June).
Therefore the correct answer is C. 10 months.