Answer:
Step-by-step explanation:
Data given
20 13 21 18 19 22 19 15 12 12 18 21
We can calculate the sample mean and deviation with the following formulas:
![\bar X =\frac{\sum_{i=1}^n X_i}{n}](https://tex.z-dn.net/?f=%5Cbar%20X%20%3D%5Cfrac%7B%5Csum_%7Bi%3D1%7D%5En%20X_i%7D%7Bn%7D)
![s= \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}](https://tex.z-dn.net/?f=s%3D%20%5Csqrt%7B%5Cfrac%7B%5Csum_%7Bi%3D1%7D%5En%20%28X_i%20-%5Cbar%20X%29%5E2%7D%7Bn-1%7D%7D)
And we got:
represent the sample mean
population mean (variable of interest)
s=3.61 represent the sample standard deviation
n=12 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
(1)
The degrees of freedom are given by:
Since the Confidence is 0.90 or 90%, the significance is
and
, the critical value would be given by
Now we have everything in order to replace into formula (1):
For any inscribed quadrilateral, the opposite angles add to 180
(angle PMN) + (angle NOP) = 180
(8x-24) + (4x) = 180
12x-24 = 180
12x-24+24 = 180+24 ..... add 24 to both sides
12x = 204
12x/12 = 204/12 ..... divide both sides by 12
x = 17
angle NOP = 4x
angle NOP = 4*17
<h3>
angle NOP = 68 degrees</h3>
Answer:
<2 and <8
and
<3 and <5
Step-by-step explanation:
alternate interior angles are a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal.
I hope this helps :) (if so, brainliest, please?!)
About 6 minutes, if you need to be more specific then 5.75
Answers:
Reason 3: Definition of Parallelogram
Reason 4: Alternate Interior Angles Theorem
Reason 5: Reflexive Property of Congruence
Reason 6: ASA Congruence Property
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Explanations:
Explanation for Reason 3: A parallelogram, by definition, has opposite sides that are parallel. It's built into the name more or less. Sides AB and CD are opposite one another in the parallelogram so they are parallel segments
Explanation for Reason 4: Angle ABD is congruent to angle CDB because they are alternate interior angles. They are on the inside of the "train tracks" that are formed by AB and CD. They lay on opposite sides of the transversal BD
Explanation for Reason 5: Any segment is congruent to itself; ie, the same length
Explanation for Reason 6: Using reasons 2,5 and 4, we can use ASA (angle side angle) to prove the two triangles ABD and CDB congruent. Reason 2 is the first "A" in ASA. Reason 5 is the S in ASA. Reason 4 is the other A in ASA. The side is between the two pairs of angles. See the attache image for a visual summary of how ASA is being used.