12ad to the third power and which term are like terms?
1 answer:
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To prove the QRST is a parallelogram.
Step 1: Given and
Step 2: are alternate interior angles.
Definition of alternate interior angles
Step 3: Alternate interior angle theorem:
If two parallel lines cut by a transversal then the alternate interior angles are congruence.
QR and TS are parallel lines cut by QS.
Therefore,
Step 4: Reflexive property of congruence:
Any geometric figure is congruence to itself.
Therefore,
Step 5: By the above steps
(Angle),
(Angle) and
(Side)
Hence (by ASA congruence theorem)
Step 6: Corresponding parts of congruence triangles are congruent.
Step 7: Property of parallelogram:
If one pair of opposite sides are both parallel and congruent, then the quadrilateral is a parallelogram.
Hence Quadrilateral QRST is a parallelogram.
Answer:
So the p value obtained was a very low value and using the significance level given we have
so we can conclude that we have enough evidence to reject the null hypothesis, and we can say that at 2% of significance the proportion of voters that favored construction is higher than 0.63 or 63%.
Step-by-step explanation:
Data given and notation
n=1700 represent the random sample taken
estimated proportion of voters that favored construction
is the value that we want to test
represent the significance level
Confidence=98% or 0.98
z would represent the statistic (variable of interest)
represent the p value (variable of interest)
Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that percentage of residents who favor construction is more than 63%.:
Null hypothesis:
Alternative hypothesis:
When we conduct a proportion test we need to use the z statisitc, and the is given by:
(1)
The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value
.
Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
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 . The next step would be calculate the p value for this test.
Since is a right tailed test the p value would be:
So the p value obtained was a very low value and using the significance level given we have
so we can conclude that we have enough evidence to reject the null hypothesis, and we can say that at 2% of significance the proportion of voters that favored construction is higher than 0.63 or 63%.