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If X has the distribution N(10, 9) and if Y = 5X − 3, then Y has distribution
N(53,84) .
What value assigned to f (x) at x = 2 will make the function f defined by
4
6
( ) 2
2

+ −
=
x
x x
f x continuous?
Solve the following LPP by two Phase simplex method.

Max: 3x1 + 2x2 + 3x3

Subject to:
2x1 - x2 + 3x3 ≥ 5
3x1 + 3x2 + x3 ≥ 8
x1, x2, x3 ≥ 0
In queueing theory, if the arrivals are according to a Poisson distribution with parameter λ , the inter-arrival time is according to an exponential distribution with parameter eλ. State whether the statement is true or false. Justify your answer briefly.
Find all the basic solutions of the following system of equations:

x1 + 2x2 + x3 = 14

3x1 + x2 + x3 = 12

Which of these solutions are basic feasible solutions?
Ryan walks -935 m at 85 m/min. (the negative signs represents west.) For how long has Ryan been walking?
What is the effective annual rate of interest if ​$900.00900.00 grows to ​$1400.001400.00 in years compounded quarterly​? round 4 decimal places as needed.
Find the nominal annual rate of interest compounded semi-annually that is equivalent to 4.2 %4.2% compounded quarterly. round 4 decimals
A bank pays 11.7​% compounded monthly on certain types of deposits. If interest is compounded semi-annually, what nominal rate of interest will maintain the same effective rate of​ interest?
The construction of a building may be delayed by a strike. Suppose that the
probability that there will be a strike is 0.70, the probability that the construction
will be completed on time if there is no strike is 0.90 and the probability that the
building will be completed on time if there is a strike is 0.40, what is the
probability that the construction will be completed on time.
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