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To find the time of useful consciousness at an altitude of 37,000 ft, we need to substitute a = 15 into the equation T = 10 * 2^(-0.274a).
T = 10 * 2^(-0.274(15))
T = 10 * 2^(-4.11)
Now, we can calculate the value of T.
T = 10 * 0.0366
T = 0.366 minutes
Converting minutes to seconds:
T = 0.366 * 60
T ≈ 22 seconds
Therefore, the pilot and passengers have approximately 22 seconds to deploy oxygen masks before they become incapacitated.