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NeX [460]
3 years ago
5

In the given figure, C is the midpoint of AB and M is the midpoint of AC . Find the length of NB if MC = 4 and AN = 14.

Mathematics
1 answer:
Elina [12.6K]3 years ago
8 0

Answer:

Given MC = 4

AN = 14

To Find, the length of NB

Step-by-step explanation:

AB is a line which has midpoint “C”. Now the line is divided into two equal portion AC and CB.

The AC has midpoint “M” and MC is 4, so AM will also be 4.

N is the midpoint of CB. So, CB = CN + NB

Now we know AC = AM + MC = 4  + 4 =8

Given, AN = 14

AN = AC + CN

14 = 8 + CN

CN = 6

Since N is the midpoint of CB then, CN = NB

Therefore, the NB is 6

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Use the normal distribution and the given sample results to complete the test of the given hypotheses. Assume the results come f
AlladinOne [14]

Answer:

z=\frac{0.64 -0.5}{\sqrt{\frac{0.5(1-0.5)}{75}}}=2.43  

Now we can calculate the p value with the following probability:

p_v =P(z>2.43)=0.0075 \approx 0.008  

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true proportion for this case is higher than 0.5

Step-by-step explanation:

Data given and notation

n=75 represent the random sample taken

\hat p=0.64 estimated proportion of interest

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

p_v represent the p value

System of hypothesis

We want to verify if the true proportion is higher than 0.5:  

Null hypothesis:p =0.5  

Alternative hypothesis:p > 0.5  

The statistic is given by:

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

Replacing the info given we got:

z=\frac{0.64 -0.5}{\sqrt{\frac{0.5(1-0.5)}{75}}}=2.43  

Now we can calculate the p value with the following probability:

p_v =P(z>2.43)=0.0075 \approx 0.008  

Since the p value is lower than the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true proportion for this case is higher than 0.5

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3 years ago
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