In 2000, the average duration of long-distance telephone calls originating in one town was 9.4 minutes. Five years later, in 2005, a long-distance telephone company performs a hypothesis test to determine whether the average duration of long dash distance phone calls has changed from the 2000 mean of 9.4 minutes. The hypotheses are: Upper H 0 : mu equals 9.4 minutes Upper H Subscript a Baseline : mu not equals 9.4 minutes where mu is the mean duration, in 2005, of long-distance telephone calls originating in the town. Suppose that the results of the sampling lead to nonrejection of the null hypothesis. Classify that conclusion as a Type I error, a Type II error, or a correct decision, if in fact the mean duration of long-distance phone calls has changed from the 2000 mean of 9.4 minutes.

The central angle measure when one hand points at 2 and the other points at 4 is 60°; With one hand at 5 and the other at 10, the minor arc formed by the hands is about 15.7 in; The length of the minor arc between 11 and 2 is the same as the length of the minor arc between 7 and 10.

Step-by-step explanation:

Since the clock is divided into 12 equal parts, each part has an angle measure of

360/12 = 30°.

When one hand points at 2 and the other points at 4, this is 2 sections (from 2 to 3 an from 3 to 4); this is 2(30) = 60°.

The circumference of the clock is given by the formula

C = 2πr, where r is the radius and π = 3.14.  Since the radius of the clock is 6, the circumference would be

C = 2(3.14)(6) = 37.68 in.  This is not 19 in.

with one hand at 5 and the other at 10, this is 5 sections (from 5 to 6, from 6 to 7, from 7 to 8, from 8 to 9, and from 9 to 10).  Each section is 30°; this makes the total angle measure 30(5) = 150°.  The arc length is found by multiplying the portion of the circle represented by the arc (150/360) by the circumference (37.68);

150/360(37.68) = 15.7 in.

When one hand points at 1 and the other points at 9, the minor arc would be 4 sections (from 9 to 10, from 10 to 11, from 11 to 12 and from 12 to 1).  Each section is 30°; this makes the total arc length

30(4) = 120°.  This is not 150°.

The length of the minor arc from 11 to 2 would be 3(30) = 90° (three sections) and the minor arc from 7 to 10 is 3(30) = 90° (three sections).  These are the same.