Answer: D) cube root of 16
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Explanation:
The rule we use is
![x^{m/n} = \sqrt[n]{x^m}](https://tex.z-dn.net/?f=x%5E%7Bm%2Fn%7D%20%3D%20%5Csqrt%5Bn%5D%7Bx%5Em%7D)
In this case, x = 4, m = 2 and n = 3.
So,
![x^{m/n} = \sqrt[n]{x^m}\\\\\\4^{2/3} = \sqrt[3]{4^2}\\\\\\4^{2/3} = \sqrt[3]{16}\\\\\\](https://tex.z-dn.net/?f=x%5E%7Bm%2Fn%7D%20%3D%20%5Csqrt%5Bn%5D%7Bx%5Em%7D%5C%5C%5C%5C%5C%5C4%5E%7B2%2F3%7D%20%3D%20%5Csqrt%5B3%5D%7B4%5E2%7D%5C%5C%5C%5C%5C%5C4%5E%7B2%2F3%7D%20%3D%20%5Csqrt%5B3%5D%7B16%7D%5C%5C%5C%5C%5C%5C)
Showing that the original expression turns into the cube root of 16.
Using the fundamental counting theorem, we have that:
- 648 different area codes are possible with this rule.
- There are 6,480,000,000 possible 10-digit phone numbers.
- The amount of possible phone numbers is greater than 400,000,000, thus, there are enough possible phone numbers.
The fundamental counting principle states that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are ways to do both things.
For the area code:
- 8 options for the first digit.
- 9 options for the second and third.
Thus:

648 different area codes are possible with this rule.
For the number of 10-digit phone numbers:
- 7 digits, each with 10 options.
- 648 different area codes.
Then

There are 6,480,000,000 possible 10-digit phone numbers.
The amount of possible phone numbers is greater than 400,000,000, thus, there are enough possible phone numbers.
A similar problem is given at brainly.com/question/24067651
32 models need to make model of 3200.
Given that a 1 model contain 100.
Two series of numbers, usually empirical data, that are proportional or proportional if their respective elements are in constant proportion, called the scaling factor or the rate constant.
One model has 100 elements.
Now, we have to find how many model contains 3200 elements.
So, 1 model=100 elements
n model =3200 elements
We will write this in proportion as
1/n=100/3200
Applying the cross multiply, we get
3200×1=n×100
Divide both sides with 100, we get
3200/100=100n/100
3200/100=n
32=n
Hence, the 32 models contain 3200 elements when one contain 100 elements.
Learn more about proportional from here brainly.com/question/23536327
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Answer:
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