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Contact [7]
1 year ago
7

What is a requirement of adjacent angles? adjacent angles must be vertical. adjacent angles must be supplementary. adjacent angl

es must share a vertex. adjacent angles must share interior points.
Mathematics
1 answer:
WITCHER [35]1 year ago
3 0

<u>Adjacent angles</u><u> must share a vertex , is a requirement of adjacent angles.</u>

  • Two angles are Adjacent when they have a common side and a common vertex.

<u>Adjacent angles -</u>

  • The two angles are said to be adjacent angles when they share the common vertex and side.
  • The endpoint of the rays, forming the sides of an angle, is called the vertex of an angle.
  • Adjacent angles can be a complementary angle or supplementary angle when they share the common vertex and side.
  • Supplementary adjacent angles always add up to 180. This is because the two angles sit next to each other on a straight line and all angles on a straight line add up to 180.
  • However, if the adjacent angles are not linear pairs and another angle is in the mix, the two adjacent angles will not add up to 180.

Therefore, Adjacent angles must share a vertex.

Learn more about Adjacent angles

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Answer:

Case n =5

z=\frac{4.8-5}{\frac{0.5}{\sqrt{5}}}=-0.894  

Case n =15

z=\frac{4.8-5}{\frac{0.5}{\sqrt{15}}}=-1.549  

Case n = 40

z=\frac{4.8-5}{\frac{0.5}{\sqrt{40}}}=-2.530  

P value

Case n =5

p_v =P(z  

Case n =15

p_v =P(z  

Case n =40

p_v =P(z  

Step-by-step explanation:

Data given and notation  

\bar X=4.8 represent the sample mean

\sigma=0.5 represent the population standard deviation

n sample size  

\mu_o =5 represent the value that we want to test  

\alpha represent the significance level for the hypothesis test.  

z would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean is lower than 5, the system of hypothesis would be:  

Null hypothesis:\mu \geq 5  

Alternative hypothesis:\mu < 5  

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:  

z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}} (1)  

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic  

We can replace in formula (1) the info given like this:  

Case n =5

z=\frac{4.8-5}{\frac{0.5}{\sqrt{5}}}=-0.894  

Case n =15

z=\frac{4.8-5}{\frac{0.5}{\sqrt{15}}}=-1.549  

Case n = 40

z=\frac{4.8-5}{\frac{0.5}{\sqrt{40}}}=-2.530  

P-value  

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

Case n =5

p_v =P(z  

Case n =15

p_v =P(z  

Case n =40

p_v =P(z  

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