A figure is located entirely in the third quadrant. If you reflect it over y = 0. Which quadrant will the resulting figure lie i
n?
1 answer:
Answer: Quadrant 2
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Explanation:
Check out the diagram below. An example point in the third quadrant is (-2,-5). This quadrant is the southwest quadrant. Reflect the example point over the x axis (aka the line y = 0) and we get (-2,5). This is shown when we go from point A to point B in the diagram.
The reflection rule is showing that only the y coordinate changes from y to -y. If y is negative, then flip to positive, or vice versa. The x coordinate stays the same.
The point started in quadrant 3 and it moves to quadrant 2 after the reflection over the line y = 0.
Side note: all points on the line y = 0 have a y coordinate of 0
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Answer:
The degrees of freedom are:
And the p value would be:
Since we have a p value lower than the significance level given of 0.05 we can reject the null hypothesis and we can conclude that the true mean for car rental rates in Boston are significantly higher than those in Dallas
Step-by-step explanation:
Data given
represent the sample size for group Boston
represent the sample size for group Dallas
represent the sample mean for the group Boston
represent the sample mean for the group Dallas
represent the sample standard deviation for group Boston
represent the sample standard deviation for group Dallas
We can assume that we have independent samples from two normal distributions with equal variances and that is:
Let the subindex 1 for Boston and 2 for Dallas we want to check the following hypothesis:
Null hypothesis:
Alternative hypothesis:
The statistic is given by this formula:
Where t follows a t student distribution with degrees of freedom and the pooled variance
is given by this formula:
Replacing we got:
And the deviation would be just the square root of the variance:
The statitsic would be:
The degrees of freedom are:
And the p value would be:
Since we have a p value lower than the significance level given of 0.05 we can reject the null hypothesis and we can conclude that the true mean for car rental rates in Boston are significantly higher than those in Dallas
Answer
Find out the how many shorter pieces can a seamstress cut.
To prove
Let us assume that the number of shorter pieces cut be x.
As given
A seamstress has a piece of cloth that is 3 yards long.
she cuts it into shorter lengths of 16 inches each.
As
1 yards = 36 inches
Now convert 3 yards into inches.
= 3 × 36
= 108 yards
Than the equation becomes
16x = 108
x = 6.75
Therefore the number of shorter pieces be 6 .