What is the constant of variation, k, of the direct variation, y = kx, through (5, 8)? k = – k equals negative StartFraction 8 O
2 answers:
The value of constant of variation "k" is
<em><u>Solution:</u></em>
Given that the direct variation is:
y = kx ----- eqn 1
Where "k" is the constant of variation
Given that the point is (5, 8)
<em><u>To find the value of "k" , substitute (x, y) = (5, 8) in eqn 1</u></em>
Thus the value of constant of variation "k" is
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Answer:
a) Upper Control Limit = 0.10
Lower Control Limit = 0.01
b) The tech assistance process is stable and in control.
Step-by-step explanation:
Given - After a number of complaints about its tech assistance, a
computer manufacturer examined samples of calls to determine
the frequency of wrong advice given to callers. Each sample
consisted of 100 calls.
SAMPLE 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Number of errors 5 3 5 7 4 6 8 4 5 9 3 4 5 6 6 7
To find - a. Determine 95 percent limits.
b. Is the tech assistance process stable (i.e., in control)
Proof -
z = 95% confidence interval
= 1.96
⇒z = 1.96
Proportion of defects,P = total defectives/total observations
= 0.0544
⇒P = 0.0544
Now,
Q = 1-P
= 0.9456
⇒Q = 0.9456
Now,
Average sample size, N = 100
Standard deviation =
= 0.0227
Now,
Upper Control Limit = P + z(Standard deviation)
= 0.0988
⇒Upper Control Limit = 0.0988 ≈ 0.10
And
Lower Control Limit = P - z(Standard deviation )
= 0.0099
⇒Lower Control Limit = 0.0099 ≈ 0.01
∴ we get
Upper Control Limit = 0.10
Lower Control Limit = 0.01
b.)
Now,
it is clear that the fraction defective values are wit in upper an lower control limits.
So, The tech assistance process is stable and in control.
Answer:
- See the graph attached
- x₁ ≈ - 2.1
- x₂ ≈ 0.2
Explanation:
To solve log (−5.6x + 1.3) = −1 − x graphycally, you must graph this system of equations on the same coordinate plane:
- Equation 1: y = log (5.6x + 1.3)
- Equatin2: y = - 1 - x
1) To graph the equation 1 you can use these features of logarithmfunctions:
- Domain: positive values ⇒ -5.6x + 1.3 > 0 ⇒ x < 13/56 (≈ 0.23)
- Range: all real numbers (- ∞ , ∞)
- x-intercept:
log ( -5.6x + 1.3) = 0 ⇒ -5.6x + 1.3 = 1 ⇒x = 0.3/5.6 ≈ 0.054
- y-intercept:
x = 0 ⇒ log (0 + 1.3) = log (1.3) ≈ 0.11
- Pick some other values and build a table:
x log (-5.6x + 1.3)
-1 0.8
-2 1.1
-3 1.3
- You can see such graph on the picture attached: it is the red curve.
2) Graphing the equation 2 is easier because it is a line: y = - 1 - x
- slope, m = - 1 (the coeficient of x)
- y - intercept, b = - 1 (the constant term)
- x - intercept: y = 0 = - 1 - x ⇒ x = - 1
- The graph is the blue line on the picture.
3) The solution or solutions of the equations are the intersection points of the two graphs. So, now the graph method just requires that you read the x coordinates of the intersection points. From the least to the greatest, rounded to the nearest tenth, they are:
- <u><em>x₁ ≈ - 2.1</em></u>
- <u><em>x₂ ≈ 0.2</em></u>
