Given:
A.)Consider
Also,
Since,
Therefore, both functions are inverses of each other.
B.
For the Composition function
Since, the function is not defined for
.
Therefore, the domain is
For the Composition function
Since, the function is not defined for
.
Therefore, the domain is
Answer:
p value = 0.0174
Conclusion : we reject the null hypothesis
Step-by-step explanation:
Thinking step:
We need to perform a test to determine if the proportion of the good parts is the same for all three shifts at a significance level of
Assumption : all the population for each or the three shifts is not equal.
Calculation:
Let p₁ be the sample of the first shift
p₂ be the sample of the second shift
p₃ be the sample of the third shift
According to the null hypothesis
H₀ = p₁ = p₂ = p₃
In other words, all the population sample proportions are equal.
Alternatively, we can assume that the three shift are not equal p₁ ≠ p₂ ≠ p₃
Tabulating and performing the ² test gives 8.10
degrees of freedom:
df = k - 1
= 3 - 1 = 2
Thus the degree of freedom is 2
Solving using the MINITAB software gives: p = 0.174
The solution shows that the p value < level of significance, then p-value lies in the range 0.0174≤≤0.05
Therefore, we reject the null hypothesis based on the fact that the three shifts are not equal.
Answer:
x 19/6
Step-by-step explanation:
1. Multiply both sides by 6 (the LCM of 6,3)
5/2 + 3-x <= 2(x-2)
2. Simplify 5/2+3-x to 11/2-x
11/2 - x<=2 (x-2)
3. Expand.
11/2-x<= 2x-4
4. Add x to both sides.
11/2<= 2x-4+x
5. Simplify 2x-4+x to 3x-4.
11/2<=3x-4
6. Add 4 to both sides.
11/2+4<=3x
7. Simplify 11/2+4 to 19/2
19/2<=3x
8. Divide both sides by 3
19/2 /3 <=x
9. Simplify 19/2 /3 to 19/2*3
19/2*3<=x
10. Simplify 2*3 to 6
19/6<=x
11. Switch sides.
x>= 19/6
Hope this helps!