Answer:
Step-by-step explanation:
Since MNP is equilateral, so <PNM=60, and since OP//NM, and <PON is 90, so <MNO=90=<PNM+PNO,so 90=60+<PNO,so <PNO=30
Answer:
p-value = 0.1277
Step-by-step explanation:
p-value is the probability value tell us how likely it is to get a result like this if the Null Hypothesis is true.
Firstly we find the mean and standard deviation of the given data set.
⇒ Mean = ![\frac{4.41 +4.37+ 4.33+ 4.35 +4.30 +4.39 +4.36+ 4.38+ 4.40+ 4.39}{10}](https://tex.z-dn.net/?f=%5Cfrac%7B4.41%20%2B4.37%2B%204.33%2B%204.35%20%2B4.30%20%2B4.39%20%2B4.36%2B%204.38%2B%204.40%2B%204.39%7D%7B10%7D)
⇒ Mean = 4.368
![Standard deviation(\sigma) = \sqrt{\frac{1}{n}\sum_{i=1}^{n}{(x_{i}-\bar{x})^{2}} }](https://tex.z-dn.net/?f=Standard%20deviation%28%5Csigma%29%20%3D%20%5Csqrt%7B%5Cfrac%7B1%7D%7Bn%7D%5Csum_%7Bi%3D1%7D%5E%7Bn%7D%7B%28x_%7Bi%7D-%5Cbar%7Bx%7D%29%5E%7B2%7D%7D%20%7D)
where,
is mean of the distribution.
⇒ Standard Deviation = 0.034
Applying t- test:
Let out hypothesis is:
H₀: μ = 4.35
H₁: μ ≠ 4.35
Now,
Here, μ = Population Mean = 4.35
= Sample Mean = 4.368
σ = Standard Deviation = 0.034
n = 10
![t=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}} }](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B%5Cbar%7Bx%7D-%5Cmu%7D%7B%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%20%7D)
Putting all values we get, t = 1.6777 with (10 -1) = 9 degree of freedom.
Then the p-value at 99% level of significance.
⇒ p-value = 0.1277
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![6z + 7 = 8z - 9](https://tex.z-dn.net/?f=6z%20%2B%207%20%20%3D%208z%20-%209)
![8z - 9 = 6z + 7](https://tex.z-dn.net/?f=8z%20-%209%20%3D%206z%20%2B%207)
Add sides 9
![8z - 9 + 9 = 6z + 7 + 9](https://tex.z-dn.net/?f=8z%20-%209%20%2B%209%20%3D%206z%20%2B%207%20%2B%209)
![8z = 6z + 16](https://tex.z-dn.net/?f=8z%20%3D%206z%20%2B%2016)
Subtract sides 6z
![- 6z + 8z = - 6z + 6z + 16](https://tex.z-dn.net/?f=%20-%206z%20%2B%208z%20%3D%20%20-%206z%20%2B%206z%20%2B%2016)
![2z = 16](https://tex.z-dn.net/?f=2z%20%3D%2016)
Divide sides by 2
![\frac{2z}{2} = \frac{16}{2} \\](https://tex.z-dn.net/?f=%20%5Cfrac%7B2z%7D%7B2%7D%20%20%3D%20%20%5Cfrac%7B16%7D%7B2%7D%20%20%5C%5C%20)
![z = 8](https://tex.z-dn.net/?f=z%20%3D%208)
Thus ;
![NP = 8z - 9](https://tex.z-dn.net/?f=NP%20%3D%208z%20-%209)
![NP = 8(8) - 9](https://tex.z-dn.net/?f=NP%20%3D%208%288%29%20-%209)
![NP = 64 - 9](https://tex.z-dn.net/?f=NP%20%3D%2064%20-%209)
![NP = 64 - 4 - 5](https://tex.z-dn.net/?f=NP%20%3D%2064%20-%204%20-%205)
![NP = 60 - 5](https://tex.z-dn.net/?f=NP%20%3D%2060%20-%205)
![NP = 55](https://tex.z-dn.net/?f=NP%20%3D%2055)
Done...
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Answer
It’s x= -4 for sure