One-eighth π times the cube of the diameter (d).
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Answer:
We conclude that the mean duration of 15-sided union rugby games has decreased after the meeting.
Step-by-step explanation:
We are given that Before the meeting, the mean duration of the 15-sided rugby game time was 3 hours, 5 minutes, that is, 185 minutes.
A random sample of 36 of the 15-sided rugby games after the meeting showed a mean of 179 minutes with a standard deviation of 12 minutes.
Let = <em><u>mean duration of 15-sided union rugby games after the meeting.</u></em>
So, Null Hypothesis, :
185 minutes {means that the mean duration of 15-sided union rugby games has increased or remained same after the meeting}
Alternate Hypothesis, :
< 185 minutes {means that the mean duration of 15-sided union rugby games has decreased after the meeting}
The test statistics that would be used here <u>One-sample t test statistics</u> as we don't know about the population standard deviation;
T.S. = ~
where, = sample mean duration of 15-sided union rugby games = 179 min
s = sample standard deviation = 12 minutes
n = sample of 15-sided rugby games = 36
So, <u><em>the test statistics</em></u> = ~
= -3
The value of t test statistics is -3.
<u>Now, at 1% significance level the t table gives critical value of -2.437 at 35 degree of freedom for left-tailed test.</u>
Since our test statistic is less than the critical value of t as -3 < -2.437, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which <u>we reject our null hypothesis</u>.
Therefore, we conclude that the mean duration of 15-sided union rugby games has decreased after the meeting.
The inscribed angle theorem says that
Triangle AOC is isosceles because both AO and CO are radii of the circle and have the same length. This means angles CAO and ACO have the same measure and are congruent.
Angles ACO and COD are congruent because they form an alternating interior pair between the parallel lines AC and OD.
Taking all these facts together, we have
and since angle COB is made up of angles COD and DOB, these angles must be congruent, and so the arcs they subtend (CD and DB, respectively) must also congruent.