Plz show work and explain
1 answer:
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Answer:
The number of ways are 40320.
Step-by-step explanation:
Consider the provided information.
Ms. Smith keeps eight different cookbooks on a shelf in one of her kitchen cabinets.
We need to determine the number of different ways to put eight cookbooks on the shelf.
We need to select 8 cookbooks taking 8 at a time.
So use the permutation formula:
Substitute n=8 and simplify.
Hence, the number of ways are 40320.
First, we are going to find the scaling factor of the volume, and then, we are going to multiply that scaling factor by the volume of the smaller prism.
We know that our hexagonal prism <span>has dimensions that are triple the dimensions of a similar smaller hexagonal prism. The scaling factor for each dimension is 3, but since we have 3 dimension (a prism is a 3 dimensional figure), we need to rise that scaling factor to the power 3 (that represent the three dimensions of our prism):
</span>
<span>
Now we just need to multiply our volume scaling factor by the volume of our smaller prism:
</span>
<span>
We can conclude that the correct answer is the fourth choice: </span><span>128.25 cm3</span>
We know that our hexagonal prism <span>has dimensions that are triple the dimensions of a similar smaller hexagonal prism. The scaling factor for each dimension is 3, but since we have 3 dimension (a prism is a 3 dimensional figure), we need to rise that scaling factor to the power 3 (that represent the three dimensions of our prism):
</span>
<span>
Now we just need to multiply our volume scaling factor by the volume of our smaller prism:
</span>
<span>
We can conclude that the correct answer is the fourth choice: </span><span>128.25 cm3</span>