The answer is: The diameter is 4 centimeters.
The explanation is shown below:
1. The volume of the cylinder is:
Where is the radius (
) and
is the height (
).
Then:
2. The total volume of the 12 spheres is:
3. The volume of the cylinder and the total volume of all the 12 spheres, are equal, therefore:
4. Now, you must solve for the radius:
5. The diameter is:
Answer:
See explanation below.
Step-by-step explanation:
For this case we define first some notation:
A= A new training program will increase customer satisfaction ratings
B= The training program can be kept within the original budget allocation
And for these two events we have defined the following probabilities
We are assuming that the two events are independent so then we have the following propert:
And we want to find the probability that the cost of the training program is not kept within budget or the training program will not increase the customer ratings so then if we use symbols we want to find:
And using the De Morgan laws we know that:
So then we can write the probability like this:
And using the complement rule we can do this:
Since A and B are independent we have:
And then our final answer would be: