At the 5% significance level, there is sufficient evidence to conclude that the die is not fair.
Step-by-step explanation:
Null hypothesis is a statement that is to be tested against the alternative hypothesis and then decision is taken whether to accept or reject the null hypothesis. The critical value is 15.091 and test statistic is 11.070. The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value Test statistics is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. In the given case p-value is less than critical value then we should reject the null hypothesis.
Let denote the speed of the ship, and let denote the duration of the trip. The magnitude of the displacement of this ship would be .
Refer to the diagram attached. The direction means west of south. Thus, start with the south direction and turn towards west (clockwise) by to find the direction of the displacement of the ship.
The hypothenuse of the right triangle in this diagram represents the displacement of the ship, with a length of . The dashed horizontal line segment represents the distance that the ship has travelled to the west (which this question is asking for.) The angle opposite to that line segment is exactly .
Since the hypotenuse is of length , the dashed line segment opposite to the vertex would have a length of: