<span>Cylinder Volume = </span><span>π <span>• r² • height
height = </span></span><span>Cylinder Volume / (PI * radius^2)
</span><span>height = 500 cubic inches / 3.14159 * 16
</span><span><span><span>height = 9.9471839432
</span>
</span>
</span>
<span>height = 9.95 (rounded)
</span>
Answer:
a

b

Step-by-step explanation:
From the question we are told that
The mean value is 
The standard deviation is 
Considering question a
The sample size is n = 9
Generally the standard error of the mean is mathematically represented as

=>
=> 
Generally the probability that the sample mean hardness for a random sample of 9 pins is at least 51 is mathematically represented as



=> 
From the z table the area under the normal curve to the left corresponding to 2.5 is

=> 
=> 
Considering question b
The sample size is n = 40
Generally the standard error of the mean is mathematically represented as

=>
=> 
Generally the (approximate) probability that the sample mean hardness for a random sample of 40 pins is at least 51 is mathematically represented as

=> 
=> 
From the z table the area under the normal curve to the left corresponding to 5.2715 and
=> 
So

=> 
Answer:
r = ( -14.4 , 6.47 )
Step-by-step explanation:
in the photo you will find all the steps
The percentage of more juices that will be in the new package is 35.71%
<h3>What are word problems?</h3>
Word problems in mathematics are things happening in our daily life and we can use mathematical concepts and arithmetic operations to put a solution to those things.
From the given information, it was stated that:
- Almarai usually have 9 ounces of juice in each package, while
- Their new package will contain 14 ounces.
Our objective is to find the percentage of more juice that will be in the new package.
The percentage of more juice in the new package will be:


= 35.71%
Learn more about word problems here:
brainly.com/question/21405634