<span>120 degs --> 1/3 of the circumference :) hope i helped!</span>
Answer:
2 raisins.
Step-by-step explanation:
Let x represent total number of required ingredient.
We have been given that Ren finds 6 peanuts, 4 raisins, 3 cranberries, and 5 chocolate chips in a handful of trail mix. We are asked to find of which ingredient Ren will have 2 pieces for a total of 9 pieces.
First of all, we will find total number of ingredients by adding each ingredient as:


Now, we will use ratio to solve for our given problem as:





Since there are 4 raisins, therefore, for every 9 pieces in Ren's handful of trail mix there are 2 raisins.
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
A histogram is a graphical representation of discrete or continuous data. To put it another way, it gives a visual representation of numerical data by displaying the amount of data points that fall within a given range of values.
Find ing the common denominator would make it 10.
for 1/2 to get to 10 you have to multiply by 5
1/2x5= 5/10
then you have to convert 2/5 to get the denominator to be 10
so you multiply 2/5 by 2
2/5x2= 4/10
5/10 is greater than 4/10