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olya-2409 [2.1K]

2 years ago

12

1. Among all simple graphs with 20 vertices, determine (with justification) the minimum possible and the maximum possible number

of edges such a graph could have.

1 answer:

Inessa [10]2 years ago

8 0

Answer:

Minimum possible edges is 19,

Maximum possible edges is 190.

Step-by-step explanation:

∵ When n vertices is joined by edges,

The minimum number of edges = n - 1 ( i.e. they are making a unique path in which first and last vertex are joined with only one vertex while the other vertices are joined with two vertices only )

Also, if the number of edges < n - 1 then the graph would be disconnected ,

While, the maximum number of edges = $\frac{n(n-1)}{2}$ ( i.e. every vertex is joined with every vertex )

Here, n = 20,

So, the minimum possible edges = 20 - 1 = 19,

And, maximum possible edges = $\frac{20(20-1)}{2}$

= $\frac{20\times 19}{2}$

= 10 × 19

= 190

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From generation to generation, the mean age when smokers first start to smoke varies. However, the standard deviation of that ag

Jlenok [28]

Answer:

If we compare the p value and the significance level given for example $\alpha=0.05$ we see that $p_v$ so we can conclude that we to reject the null hypothesis, and the the actual mean starting age of smokers is significantly lower than 19.

Step-by-step explanation:

1) Data given and notation

$\bar X=18.1$ represent the mean age when smokers first start to smoke varies

$s=1.3$ represent the standard deviation for the sample

$\sigma=2.1$ represent the population standard deviation

$n=37$ sample size

$\mu_o =5.7$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to determine if the mean starting age is at least 19, the system of hypothesis would be:

Null hypothesis: $\mu\geq 19$

Alternative hypothesis: $\mu < 19$

We know the population deviation, so for this case is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{18.1-19}{\frac{2.1}{\sqrt{37}}}=-2.607$

Calculate the P-value

Since is a one-side lower test the p value would be:

$p_v =P(z$

Conclusion

If we compare the p value and the significance level given for example $\alpha=0.05$ we see that $p_v$ so we can conclude that we to reject the null hypothesis, and the the actual mean starting age of smokers is significantly lower than 19.

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