6(x^2-1)(6x-1/6(x+1))
On factoring (x^2-1)=(x+1)(x-1)
= 6(x-1)(x+1)(6x-1/6(x+1))
Cancelling (x+1) from numerator and denominator we get,
= 6(x-1)(6x-1)/6
Cancelling 6 we get,
= (x-1)(6x-1)
A number that can be rounded to 4 can be anywhere from 3.5 to 3.9
Answer:
96
Step-by-step explanation:
3*6=18*2=36
6*10=60*2=120
10*3=30*2=60
36+60+120=
216
Answer:
Cpk = Cpu = Cpl = 0.4785
Step-by-step explanation:
Solution:-
- The capability of a process is determined using the capability index ( Cpk ). The index helps in determining the output of the process lies within the specification limits.
- The key dimension on a product measure is:
105 ± 12 units
- Process is producing this product at a 6-sigma quality standards i.e ( process is producing this product has a standard deviation (σ) of three units.)
Where, Standard Error in measured value = 12 units.
- The process capability (Cpu) is defined based on the Upper Specification Limit of the process (USL):
Cpu = (USL - u) / 3σ
- The process capability (Cpl) is defined based on the Lower Specification Limit of the process (LSL):
Cpl = ( u - LSL) / 3σ
- Assume that the process is centered with respect to specifications, then the given absolute value of u = 105 units.
Where the specification limits are defined as:
LSL = u - SE = 105 - 12
LSL = 93 units
USL = u + SE = 105 + 12
USL = 117 units
- Now evaluate the Process capability on each of the two limits specification limits:
Cpu = (USL - u) / 3σ
Cpu = (117 - 105) / 3σ
Cpu = 4 / σ
Cpl = ( u - LSL) / 3σ
Cpl = ( 105 - 99 ) / 3σ
Cpl = 4 / σ
- The minimum of Cpu and Cpl is denoted as the Cpk value:
Cpk = min ( Cpu , Cpl )
Cpk = Cpu = Cpl = 4 / 8.36
Cpk = Cpu = Cpl = 4 / 8.36 = 0.4785
