MRS.Bonnette's recipe for banana bread calls for 3 and one fourths cups of sugar. She wants to make 6.5 batches so that she has
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The number of edges can be calculated from the number of vertices.
- <em>There are 14 vertices for 105 edges</em>
- <em>There are 200 vertices for 19900 edges</em>
The variable N is used to always represent the number of vertices.
So, we represent the edges as:
<u />
<u>(a) The value of N for 105 edges</u>
The relationship between N and E is:
Substitute 105 for E
Multiply through by 2
Rewrite as:
Expand
Factorize
Factor out N + 14
Solve for N
or
The number of vertices (N) cannot be negative. So:
<u>(b) The value of N for 19900 edges</u>
We have:
Substitute 19900 for E
Multiply through by 2
Rewrite as:
Expand
Factorize
Factor out N + 199
Solve for N
or
The number of vertices (N) cannot be negative. So:
<em>Hence, there are 200 vertices for 19900 edges</em>
Read more about vertices and edges at:
Answer:
1. There is not enough evidence to support the claim that men who were distance runners lived, on average, five years longer than those who were not distance runners.
2. The test statistic is t.
Step-by-step explanation:
<em>The question is incomplete:</em>
- <em>Test the claim that men who were distance runners lived, on average, five years longer than those who were not distance runners.</em>
- <em>Which of the following is the test statistic for the appropriate test to determine if men who are distance runners live significantly longer, on average, than men who are not distance runners?</em>
The test statistic is t, as this is a t-test for the difference of means.
The claim is that men who were distance runners lived, on average, five years longer than those who were not distance runners.
Then, the null and alternative hypothesis are:
H_0: \mu_1-\mu_2=5\\\\H_a:\mu_1-\mu_2> 5
The significance level is 0.05.
The sample 1, of size n1=50 has a mean of 84.2 and a standard deviation of 10.2.
The sample 1, of size n1=30 has a mean of 79.2 and a standard deviation of 6.8.
The difference between sample means is Md=5.
The estimated standard error of the difference between means is computed using the formula:
Then, we can calculate the t-statistic as:
The degrees of freedom for this test are:
This test is a right-tailed test, with 78 degrees of freedom and t=0, so the P-value for this test is calculated as (using a t-table):
As the P-value (0.5) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that men who were distance runners lived, on average, five years longer than those who were not distance runners.