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A student commutes daily from his house to school. On average, the trip one way takes 24 minutes
with a standard deviation of 3 minutes. Assume that the data is normally distributed. What is the
probability that the trip will take more than half an hour?
Experiments in an electrical engineering laboratory appear to be related by the following hyperbolic and trognometric relationship.

3sinh x + 2cosh x = Tan(81.87°)

a) Using your knowledge of exponential represntation of hyperbolic function, find all values of a which satisfy the equation.

b) Verify your solutions using the standard hyperbolic and trigonometric functions.
Q. Which of the following sets are countable or uncountable.
(i) set of real numbers
(ii) set of complex numbers
Q. Which of the following sets are countable or uncountable.
(i)set of negative integers
(ii) set of rational numbers
Q. Which of the following sets are countable or uncountable.
(i) set of natural numbers
(ii) set of whole numbers
(iii) set of positive integers
Q. Show that the real line is a metric space.
Q. Is d(x, y) =√(│x-y│) a metric space?(solve it)
Solve the partial differential equation p cos(x+y) + q sin( x+y)=z, where the partial derivatives of z with respect to x,y are denoted by p and q respectively.
Prove that lim x-->oo ((11x+7)/(8-5x)) = -11/5 using the delta - epsilon definition of limits?
The average number of patients admitted per day to the emergency room of a small hospital is 2.5. If, on any given day, there is/are only 9 bed(s) available for new patients,
what is the probability that the hospital will not have enough beds to accommodate its newly admitted patients?