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The function f(x)= [x]- x is not integrable in [ 0,3] , where [ x] denote greatest integer function.


True or false with full explanation

A basket contains 10 ripe and 4 unripe bananas. If three bananas are taken from the basket one after the other, determine the values of the random R representing the number of ripe bananas

ind the smallest relation containing the relation {(1, 2), (1, 4), (3


, 3), (4, 1)} that is




a)


reflexive and transitive.





b)


symmetric and transitive.





c)


reflexive, symmetric, and transitive.







In general, a statement involving n variables x1 , x 2 ,…, x n can be denoted by P( x1 , x 2 ,…, x n ) and is the value of the predicate P at the n-tuple (x1 , x2 ,…, x n ) . (a) Suppose Q(x , y) denotes the statement “ x=y+3 .” What are the truth values of the propositions Q(1,2) and Q(3,0)? (b) Let R(x , y ,


Marites walks 3.0 m due East and 4.0 m due North. Find the displacement of marites using graphical method.


Assume that 99.7% of grade 11 students have weights between 45 kg and 60 kg and the data are normally distributed.




a)find the mean




b) compute the standard deviation




c) construct the normal curve of the normal distribution

Thatobaked 25 muffins. He gave 3/25 of the muffins to his friend and 9/25 of the muffins to his sister.what fraction of the muffins is left?


Neon lights in an industrial park are replaced at the rate of 100 units per day. The physical planet orders the neon lights periodically. It costs Rs.500 to initiate a purchase order. A neon light kept in storage is estimated to cost about Rs.20 per day. The lead time between placing and receiving an order is 12 days. Determine the optimum inventory policy for ordering the neon lights.


How do you write the residue at z=∞ where f(z) = 1/z^3+z^5?


A)-2


B)-1


C)1


D)0


Find the inverse Laplace of {2s+5/s^2+25}?

A) 2Sin5t+Cos5t

B) Cos5t-2Sin5t

C) 2Cos5t+Sin5t D) 2Cos5t-Sin5t

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