Which ordered pair is a solution of the inequality? 3y-6<12x
1 answer:
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Answer:
So with the p value obtained and using the significance level given we have
so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the mean of the group A is significantly lower than the mean for the group B.
Step-by-step explanation:
The statistic to test the hypothesis is given by this formula:
Where t follows a t distribution with degrees of freedom
The system of hypothesis on this case are:
Null hypothesis:
Alternative hypothesis:
Or equivalently:
Null hypothesis:
Alternative hypothesis:
Our notation on this case :
represent the sample size for group A
represent the sample size for group B
represent the sample mean for the group A
represent the sample mean for the group B
represent the sample standard deviation for group A
represent the sample standard deviation for group B
And now we can calculate the statistic:
Now we can calculate the degrees of freedom given by:
And now we can calculate the p value using the alternative hypothesis:
So with the p value obtained and using the significance level given we have
so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the mean of the group A is significantly lower than the mean for the group B.
Answer:
Step-by-step explanation:
The diagonal of any square with side length is equal to
. Since the side length of the square is 10, the diagonal must be
.
To support and prove this:
The diagonal creates two 45-45-90 triangles, with the diagonal being the hypotenuse of both of these triangles. The Pythagorean Theorem states that in any triangle, the sum of the squares of both legs is equal to the square of the hypotenuse ().
Call the diagonal . In these two triangles, both legs are equal to 10 (the side lengths of the square), and the hypotenuse is the diagonal. Thus, we have: