Answer:
<em>H₀</em>: The voting preference of men and women are not different.
<em>Hₐ</em>: The voting preference of men and women are not different.
Step-by-step explanation:
A hypothesis test for two proportions can be used to determine whether the preference of men differ from women in case of voting.
A Chi-square test contingency table can be used to perform the test.
The hypothesis can be defined as:
<em>H₀</em>: The voting preference of men and women are not different.
<em>Hₐ</em>: The voting preference of men and women are not different.
The test statistic is:
Decision rule:
If the <em>p</em>-value of the Chi-square test statistic is less than the significance level <em>α</em> = 0.05 then the null hypothesis will be rejected. And if the <em>p</em>-value is more than the significance level then the null hypothesis will not be rejected.
Problem 1
Draw a straight line and plot P anywhere on it. Use the compass to trace out a faint circle of radius 8 cm with center P. This circle crosses the previous line at point Q.
Repeat these steps to set up another circle centered at Q and keep the radius the same. The two circles cross at two locations. Let's mark one of those locations point X. From here, we could connect points X, P, Q to form an equilateral triangle. However, we only want the 60 degree angle from it.
With P as the center, draw another circle with radius 7.5 cm. This circle will cross the ray PX at location R.
Refer to the diagram below.
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Problem 2
I'm not sure why your teacher wants you to use a compass and straightedge to construct an 80 degree angle. Such a task is not possible. The proof is lengthy but look up the term "constructible angles" and you'll find that only angles of the form 3n are possible to make with compass/straight edge.
In other words, you can only do multiples of 3. Unfortunately 80 is not a multiple of 3. I used GeoGebra to create the image below, as well as problem 1.
Answer:
18
Step-by-step explanation:
1/4 is close to 0 so 18 rounded to the nearest ones place is just 18
