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Salsk061 [2.6K]
2 years ago
5

SELECT THE CORRECT ANSWER. GIVEN: LINE L AND LINE M INTERSECT PROVE: ∠⁢1≅ ∠⁢3 . ∠⁢1IS SUPPLEMENTARY TO ∠⁢4 3. LINEAR PAIR THEORE

M M∠⁢1+M∠⁢2=180∘ 3. DEFINITION OF SUPPLEMENTARY ANGLES .M∠1+M∠3=180∘ 3. DEFINITION OF SUPPLEMENTARY ANGLES ∠3IS SUPPLEMENTARY TO ∠2 3. LINEAR PAIR THEOREM
Mathematics
1 answer:
olga55 [171]2 years ago
6 0

The missing reasons are;

Definition of linear pair.

Definition of supplementary angles.

Substitution.

Subtraction property of equality.

Definition of congruence.

<h3>What is the Angle proof?</h3>

The angles are supplementary because the angles 1 and 2, 2 and 3 form a linear pair and thus because of the definition of linear pair, they are supplementary angles.

The sum of angles of 1 and 2, 2 and 3 is equal to 180 because these pair of angles are supplementary angles. Supplementary angles are those angles whose sum is 180 degrees.

Reason 5:

m∠1 + m∠2 = 180°

m∠2 + m∠3 = 180°

Substitute m∠2 + m∠3 in place of 180 for the first sum.

So, m∠1 + m∠2 = m∠2 + m∠3

Using subtraction property of equality and thus we get:

m∠1 = m∠3

As angle 1 is equal to angle 3, therefore by definition of congruence, these angles are congruent.

So, m∠1 ≅ m∠3

Read more about Angle Proof at; brainly.com/question/24839702

#SPJ1

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z=\frac{0.554 -0.5}{\sqrt{\frac{0.5(1-0.5)}{377}}}=2.097  

p_v =P(Z>2.097)=0.018  

If we compare the p value obtained and the significance level given \alpha=0.05 we have p_v so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of  students reported experiencing excessive daytime sleepiness (EDS) is significantly higher than 0.5 or the half.

Step-by-step explanation:

1) Data given and notation

n=377 represent the random sample taken

X=209 represent the students reported experiencing excessive daytime sleepiness (EDS)

\hat p=\frac{209}{377}=0.554 estimated proportion of students reported experiencing excessive daytime sleepiness (EDS)

p_o=0.5 is the value that we want to test

\alpha=0.05 represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)  

2) Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportion is higher than 0.5:  

Null hypothesis:p\leq 0.5  

Alternative hypothesis:p > 0.5  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

The One-Sample Proportion Test is used to assess whether a population proportion \hat p is significantly different from a hypothesized value p_o.

3) Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

z=\frac{0.554 -0.5}{\sqrt{\frac{0.5(1-0.5)}{377}}}=2.097  

4) Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level provided \alpha=0.05. The next step would be calculate the p value for this test.  

Since is a right tailed test the p value would be:  

p_v =P(Z>2.097)=0.018  

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