It has multiple functions but it should be close to the middle
Answer:
The proportions differ from those reported in the survey.
Step-by-step explanation:
The Chi-square goodness of fit test would be used to determine whether the proportions differ from those reported in the survey.
The hypothesis for the test can be defined as follows:
<em>H</em>₀: The proportions does not differ from those reported in the survey.
<em>Hₐ</em>: The proportions differ from those reported in the survey.
Assume that the significance level of the test is, α = 0.01.
The Chi-square test statistic is given by:

Consider the Excel sheet provided.
The Chi-square test statistic value is 191.32.
The <em>p</em>-value of the test is:

The <em>p</em>-value of the test is very small. The null hypothesis will be rejected at 1% level of significance.
Thus, concluding that the proportions differ from those reported in the survey.
De Moivre's theorem uses this general formula z = r(cos α + i<span> sin α) that is where we can have the form a + bi. If the given is raised to a certain number, then the r is raised to the same number while the angles are being multiplied by that number.
For 1) </span>[3cos(27))+isin(27)]^5 we first apply the concept I mentioned above where it becomes
[3^5cos(27*5))+isin(27*5)] and then after simplifying we get, [243 (cos (135) + isin (135))]
it is then further simplified to 243 (-1/ √2) + 243i (1/√2) = -243/√2 + 243/<span>√2 i
and that is the answer.
For 2) </span>[2(cos(40))+isin(40)]^6, we apply the same steps in 1)
[2^6(cos(40*6))+isin(40*6)],
[64(cos(240))+isin(240)] = 64 (-1/2) + 64i (-√3 /2)
And the answer is -32 -32 √3 i
Summary:
1) -243/√2 + 243/√2 i
2)-32 -32 √3 i
Answer:
A
Step-by-step explanation: If you count a the answer will be 48
Answer:
5) arccos A = 28°
6) arcsin A = 53°
Step-by-step explanation:
5) cos A = 30/34
6) sin A = 32/40