Answer:
values of x and y is (4, -2), (0, 0) and (2, 10)
Step-by-step explanation:
Answer: 7,308
Step-by-step explanation: 28 X 9 = 252
252 X 29 = 7,308
Applying the law of sines, the approximate length of side YZ is: A. 15.7 units.
<h3>How to Apply the Law of Sines?</h3>
Law of sines is expressed as follows: x/sin X = y/sin Y = c/sin Z.
Given the following:
- x (YZ) = ?
- X = 32°
- z = 24
- Z = 180 - 32 - 94 = 54°
Plug in the values
x/sin 32 = 24/54
x = (sin 32 × 24)/sin 54
x ≈ 15.7 units.
Learn more about the law of sines on:
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Answer:
286.97
Step-by-step explanation:
find the area of the rectangle first
14*15=210
Next
Find the area of a circle
πr^2=a
the radius of the circle is half the height of the rectangle
π*(7*7)=a
a=153.94
Now
Divide the area by two
153.94/2=76.97
Now add the two areas
76.97+210
Complete Question
A milling process has an upper specification of 1.68 millimeters and a lower specification of 1.52 millimeters. A sample of parts had a mean of 1.6 millimeters with a standard deviation of 0.03 millimeters. what standard deviation will be needed to achieve a process capability index f 2.0?
Answer:
The value required is
Step-by-step explanation:
From the question we are told that
The upper specification is 
The lower specification is
The sample mean is
The standard deviation is 
Generally the capability index in mathematically represented as
![Cpk = min[ \frac{USL - \mu }{ 3 * \sigma } , \frac{\mu - LSL }{ 3 * \sigma } ]](https://tex.z-dn.net/?f=Cpk%20%20%3D%20%20min%5B%20%5Cfrac%7BUSL%20-%20%20%5Cmu%20%7D%7B%203%20%2A%20%20%5Csigma%20%7D%20%20%2C%20%20%5Cfrac%7B%5Cmu%20-%20LSL%20%7D%7B%203%20%2A%20%20%5Csigma%20%7D%20%5D)
Now what min means is that the value of CPk is the minimum between the value is the bracket
substituting value given in the question
![Cpk = min[ \frac{1.68 - 1.6 }{ 3 * 0.03 } , \frac{1.60 - 1.52 }{ 3 * 0.03} ]](https://tex.z-dn.net/?f=Cpk%20%20%3D%20%20min%5B%20%5Cfrac%7B1.68%20-%20%201.6%20%7D%7B%203%20%2A%20%200.03%20%7D%20%20%2C%20%20%5Cfrac%7B1.60%20-%20%201.52%20%7D%7B%203%20%2A%20%200.03%7D%20%5D)
=> ![Cpk = min[ 0.88 , 0.88 ]](https://tex.z-dn.net/?f=Cpk%20%20%3D%20%20min%5B%200.88%20%2C%200.88%20%20%5D)
So

Now from the question we are asked to evaluated the value of standard deviation that will produce a capability index of 2
Now let assuming that

So

=> 
=> 
So

=> 
Hence
![Cpk = min[ 2, 2 ]](https://tex.z-dn.net/?f=Cpk%20%20%3D%20%20min%5B%202%2C%202%20%5D)
So

So
is the value of standard deviation required