If Angle 6 is congruent to angle 10 and Angle 5 is congruent to angle 7, which describes all the lines that must be parallel? Li
nes r and s are crossed by lines t and u to form 16 angles. Clockwise from top left, at the intersection of r and t, the angles are 1, 2, 3, 4; at the intersection of s and t, 5, 6, 7, 8; at the intersection of u and s, 9, 10, 11, 12; at the intersection of u and r, 13, 14, 15, 16. Only lines r and s must be parallel. Only lines t and u must be parallel. Lines r and s and lines t and u must be parallel. Neither lines r and s nor lines t and u must be parallel.
2 answers:
Answer:
Third option: Lines "r" and "s" and lines "t" and "u" must be parallel.
Step-by-step explanation:
The missing figure is attached.
You need to remember that:
1- A Transversal is defined as a line that intersects two or more lines.
2- When a transversal cut two parallel lines, several angles are formed, which are grouped in pairs. Some of them are:
a. Vertical angles: are those pairs of angles that share the same vertex and are opposite to each other. These angles are congruent.
b. Corresponding angles: are those pairs of non-adjacent angles located on the same side of the transversal and outside the parallel lines. They are congruent.
In this case, you can identify in the figure that:
and
are Corresponding angles.
and
are Vertical angles.
Therefore, based on the explained before, you can conclude that lines "r" and "s" and lines "t" and "u", must be parallel.
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Answer:
Null hypothesis:
Alternative hypothesis:
So the p value is a very low value and using any significance level for example always
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say the two proportions NOT differs significantly.
Step-by-step explanation:
Data given and notation
represent the number of homeowners who would buy the security system
represent the number of renters who would buy the security system
sample 1
sample 2
represent the proportion of homeowners who would buy the security system
represent the proportion of renters who would buy the security system
z would represent the statistic (variable of interest)
represent the value for the test (variable of interest)
Concepts and formulas to use
We need to conduct a hypothesis in order to check if the two proportions differs , the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
We need to apply a z test to compare proportions, and the statistic is given by:
(1)
Where
Calculate the statistic
Replacing in formula (1) the values obtained we got this:
Statistical decision
For this case we don't have a significance level provided , but we can calculate the p value for this test.
Since is a two sided test the p value would be:
So the p value is a very low value and using any significance level for example always
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say the two proportions NOT differs significantly.