Triangle Q R S is shown with exterior angles. Line R Q extends through point D. Line Q R extends through point E. Line Q S exten
ds through point C.
Which angle has a measure equal to the sum of m∠SQR and m∠QRS?
∠RSC
∠SRE
∠DQS
∠QSR
Which angle has a measure equal to the sum of m∠SQR and m∠QRS?
∠RSC
∠SRE
∠DQS
∠QSR
2 answers:
Answer:
Option A.
Step-by-step explanation:
In triangle QRS, Line R Q extends through point D. Line Q R extends through point E. Line Q S extends through point C as shown below.
We need to find an angle that has a measure equal to the sum of m∠SQR and m∠QRS.
According to the exterior angle theorem, the measure of an exterior angle of a triangle is equal to the sum of measures of two opposite interior angles.
Since ∠SQR and ∠QRS are two interior angles of a triangle QRS, so ∠RSC is the exterior angle of opposite to ∠SQR and ∠QRS.
By using exterior angle theorem we conclude that
m∠RSC = m∠SQR + m∠QRS
∠RSC has a measure equal to the sum of m∠SQR and m∠QRS.
Therefore, the correct option is A.
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Step-by-step explanation:
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a)
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The p value for this case would be given by:
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Step-by-step explanation:
Information given
represent the sample mean for the cubic feets of households
represent the population standard deviation
sample size
represent the value to verify
represent the significance level
t would represent the statistic
represent the p value
Part a
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Null hypothesis:
Alternative hypothesis:
Since we don't know the deviation the statistic is given by:
(1)
The statistic is given by:
The degrees of freedom are given by:
The p value for this case would be given by:
Since the p value is significantly lower than he significance level given we have enough evidence to reject the null hypothesis and we can conclude that the true mean is lower than 1425
Part b
For this case we need to find a critical value in the t distribution with 99 degrees of freedom who accumulates 0.025 of the area in the right tail and we got:
Since the calculated value is higher than the critical value we can reject the null hypothesis at the significance level provided and we can say that the true mean is higher than 1425