Answer:
- the given dimension was used as the radius
- 5.57 m³
Step-by-step explanation:
The volume of a sphere can be found using the formula ...
V = 4/3πr³ . . . . . where r is the radius
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The figure points to a diameter line and indicates 2.2 m. The arrowhead is in the middle of a radius line, making it easy to interpret the dimension as the radius of the sphere.
If 2.2 m is used as the radius, the volume is computed to be ...
V = 4/3π(2.2 m)³ ≈ 44.58 m³
This agrees with your friend's volume, suggesting the diameter was used in place of the radius in the computation.
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The correct volume, using 2.2 m as the diameter, is ...
V = 4/3π(1.1 m)³ ≈ 5.57 m³
5.6 is the correct answer because 1.3 +4.3 would be 5.6 so the next one in the sequence is 9.9
Adding 1/9 to both sides, we get 2/3+y=8/9. Next, 2/3 can be multiplied by 3/3 to get 6/9 due to that 3*3=9 and using the identity property. We then subtract 6/9 from both sides to get y=2/9
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
Answer:
see explanation
Step-by-step explanation:
The product of 3 and x is 3x
Four more than this product is 3x + 4, thus
3x + 4 = 19 ← is the equation