In ΔVWX, the measure of ∠X=90°, VX = 35, XW = 12, and WV = 37. What is the value of the cosine of ∠W to the nearest hundredth?
2 answers:
<u>Given</u>:
Given that VWX is a right triangle.
The measure of ∠X is 90°
The length of VX = 35, XW = 12, and WV = 37.
We need to determine the value of cosine of ∠W.
<u>Value of cosine of ∠W:</u>
The value of cosine of ∠W can be determined using the trigonometric ratio.
Thus, we have;
Substituting , the side adjacent to W is XW and hypotenuse is WV
Thus, we get;
Substituting XW = 12 and WV = 37, we have;
Thus, the value of cosine of ∠W is 71.09°
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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.