Hence, option D is correct (i.e. Distance is not preserved under dilation).
Step-by-step explanation:
<em>" A dilation is a transformation that produces an image that is the same shape as the original, but is a different size ".</em>
A) Angle measure:
Angle measures remains same as there is only a difference in their size the shape does not changes.
Hence angle measure is preserved.
B) Betweenness:
It is also preserved. since if any point in before dilation is between two points than after dilation it remain between them only.
C) Collinearity:
Points remain on the same line.
Hence, it is preserved.
D) Distance:
The distance is not preserved. since the length of the segment increase or decrease in dilation hence distance between two point also increase or decrease.
E) Proportionality:
In a dilation, the sides of the pre-image and the corresponding sides of the image are proportional. Hence it is also preserved.
Since the p value is lower than the significance level given of 0.05 we have enough evidence to reject the null hypothesis on this case. And the best conclusion for this case is:
We (reject) the null hypothesis. That means that we (found) evidence to support the alternative.
Step-by-step explanation:
We have the following info given:
represent the sampel mean for the age of customers
represent the population standard deviation
represent the sample size selected
We want to test if the mean age of her customers is over 35 so then the system of hypothesis for this case are:
Null hypothesis:
Alternative hypothesis
The statistic for this case is given by:
And replacing the data given we got:
We can calculate the p value since we are conducting a right tailed test like this:
Since the p value is lower than the significance level given of 0.05 we have enough evidence to reject the null hypothesis on this case. And the best conclusion for this case is:
We (reject) the null hypothesis. That means that we (found) evidence to support the alternative.