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Fantom [35]
3 years ago
14

Find the absolute maximum of m(t)=t^3-12t^2-144t and justify your answer​

Mathematics
1 answer:
ruslelena [56]3 years ago
3 0

Answer:

Step-by-step explanation:

m(t)=t³-12t²-144t

Take the derivative of t:

t'=3t²-24t-144

Set it to 0:

3t²-24t-144=0

Solve for t:

t²-8t-48=0

(t-12)(t+4)=0

t=12 or -4

On a graph, you'll find that the maximum value occurs at t=-4 ..............

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Answer:

a) E(X) = 6.45

b) E(X^{2} )= 57.25

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Step-by-step explanation:

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b)

E(X^{2} ) = (1^{2} *0.05) + (2^{2} *0.10) + (4^{2} *0.35) + (8^{2} *0.40) + (16^{2} *0.10)\\  E(X^{2} )= 57.25

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V(X) = E(X^{2} ) - (E(X))^{2} \\V(X) = 57.25 - 6.45^{2} \\V(X) = 15.648

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E(3X^{2} +2) = 3E(X^{2} ) + 2\\E(3X^{2} +2) = (3*57.25) + 2 \\E(3X^{2} +2) = 173.75

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E(X+1) = E(X) + 1\\E(X+1) = 6.45 + 1\\E(X+1) =7.45

h)

V(X+1) = 1^{2} V(X)\\V(X+1) = 15.648

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