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Alona [7]
3 years ago
6

True or False: If we have an integer primal solution with cost C and a fractional dual solution with cost at least C/2, the size

of the vertex cover corresponding to the primal solution is at most twice the size of the smallest vertex cover. Briefly justify your answer
Mathematics
1 answer:
maria [59]3 years ago
3 0

Answer:

True

Step-by-step explanation:

The size of the vertex cover is atleast twice the size of the maximum edge. Vertex must contain atleast one vertex from the matched edge. Vertex are never the strong dual solutions of each other.

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From a standard deck of cards, a 5-card hand is dealt. Calculate the number of hands that contain 4 diamonds and 1 black king
rjkz [21]

Answer:

1430

Step-by-step explanation:

Given that a standard deck of cards is 52 cards, we have 13 Diamonds and we need 4 diamonds.

Hence, we have 13C4.

Also, we have 4 kings in a standard deck of cards, and in which we have 2 black kings but we need 1 king.

Hence we have a 2C1

Therefore:

13C4 * 2C1

=> 13! ÷ [4! (13 - 4)!] * 2! ÷ [1! (2-1)!]

=> 13! ÷ [4! (9)!]

=> (1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 x 11 x 12 x 13) ÷ [(1 x 2 x 3 x 4) (1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9)]

=> (10 x 11 x 12 x 13) ÷ 24

=> (17160 ÷ 24) * (24 ÷ 6)

=> 715

2! ÷ [1! (2-1)!]

=> 2

Hence, we have 715 * 2

=> 1430

Hence, in this case, the correct answer to the question is 1430

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Step-by-step explanation:

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