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3 years ago

Let G be a connnectde graph with n vertices and m edges. supposed also that m = n. prove that G contains exactly one cycle

Mathematics

1 answer:

ElenaW [278]3 years ago

7 0

Answer:

Contradiction

Step-by-step explanation:

Suppose that G has more than one cycle and let C be one of the cycles of G, if we remove one of the edges of C from G, then by our supposition the new graph G' would have a cycle. However, the number of edges of G' is equal to m-1=n-1 and G' has the same vertices of G, which means that n is the number of vertices of G. Therefore, the number of edges of G' is equal to the number of vertices of G' minus 1, which tells us that G' is a tree (it has no cycles), and so we get a contradiction.

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mojhsa [17]

She has 1 quarter, 1 dime and 13 nickels. So the probability that one coin at random is a nickel is 13/15.

My work:

1$= 100

1 quarter=25

1 dime=10

1+1+13= 15

25×1= 25

10×1= 10

5×13= 65

65+25+10= 100

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Answer:

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PIT_PIT [208]

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At a local restaurant, the amount of time that customers have to wait for their food is normally distributed with a mean of 18 m

Colt1911 [192]

Answer:

99.7% of customers have to wait between 8 minutes to 30 minutes for their food.

Step-by-step explanation:

We are given the following in the question:

Mean, μ = 18 minutes

Standard Deviation, σ = 4 minutes

We are given that the distribution of amount of time is a bell shaped distribution that is a normal distribution.

Empirical Formula:

Almost all the data lies within three standard deviation from the mean for a normally distributed data.
About 68% of data lies within one standard deviation from the mean.
About 95% of data lies within two standard deviations of the mean.
About 99.7% of data lies within three standard deviation of the mean.

Thus, 99.7% of the customers have to wait:

$\mu -3\sigma = 18-3(4) = 6\\\mu +3\sigma = 18+3(4) = 30$

Thus, 99.7% of customers have to wait between 8 minutes to 30 minutes for their food.

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3 years ago