Answer:
g(x) = sinh^-1 ( ln(7x^6 +3) / sqrt( 8+cot( x^( 3+x))))
Step-by-step explanation:
Using the fundamental theorem of calculus
Taking the derivative of the integral gives back the function
Since the lower limit is a constant when we take the derivative it is zero
d/dx
g(t) = sinh^-1 ( ln(7t^6 +3) / sqrt( 8+cot( t^( 3+t))))
Replacing t with x
g(x) = sinh^-1 ( ln(7x^6 +3) / sqrt( 8+cot( x^( 3+x))))
Using the Poisson distribution, it is found that there is a 0.507 = 50.7% probability that the bird feeder will be visited by at most 5 birds in a 45 minute period during daylight hours.
<h3>What is the Poisson distribution?</h3>In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:
The parameters are:
Considering the average of 15 birds every 2 hours during daylight hours, the mean for a 45-minute period is given by:
The probability that the bird feeder will be visited by at most 5 birds in a 45 minute period during daylight hours is given by:
In which:
Then:
0.507 = 50.7% probability that the bird feeder will be visited by at most 5 birds in a 45 minute period during daylight hours.
More can be learned about the Poisson distribution at brainly.com/question/13971530
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