Answer:
Step-by-step explanation:
Given the rational expression: , to express this in simplified form, we would need to apply the concept of partial fraction.
Step 1: factorise the denominator
Thus, we now have:
Step 2: Apply the concept of Partial Fraction
Let,
=
Multiply both sides by (x - 1)(x - 4)
=
Step 3:
Substituting x = 4 in
Substituting x = 1 in
Step 4: Plug in the values of A and B into the original equation in step 2
Let be the average weight of chocolate chips in each bag.
As per given , we have
Since is left-tailed , so we perform a left-tailed test.
Also, the population standard deviation is known .
So we use z-test.
Test statistic :
Substitute given value ,
Significance level = 0.05
Decision rule : Reject when p-value < 0.05.
By z-table , P- value for left-tailed test = P(z<-1.96)= 1- P(z<1.96)
[∵ P(Z<-z)=1-P(Z<z)]
= 1- 0.9750
=0.025
Since , P-value(0.025) < 0.05 , so we reject the null hypothesis.
We support the claim that the machine is underfilling the bags at 0.05 significance level .
Linear pair angles, which are angles that together form a straight line are
supplementary angles.
The one that completed the proof incorrectly is <u>Becky</u>.
Reasons:
The two column proof is presented as follows;
Statement Reason
1. Segment GH intersects segment AB at K 1. Given
2. m∠AKG + m∠HKB = 180° 2.Definition of Supplementary Angles
m∠GKB + m∠HKB = 180°
3. m∠AKG + m∠HKB = m∠GKB + m∠HKB 3. Substitution property
4. m∠AKG = m∠HKB 4. Subtraction Property
The difference between Angie's Proof and Becky's Proof is in Statement 2.
Becky's proof is incorrect because the measure of angles m∠AKG and
m∠HKB and m∠GKB and m∠HKB are not given, therefore, the use of the
reason of Angle Addition Postulate in statement 2. is incorrect.
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