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Softa [21]
3 years ago
6

We’ve seen that natural numbers are closed under addition. Determine the closure of natural numbers under the other three operat

ions, and give examples to support your answers.
Mathematics
1 answer:
Butoxors [25]3 years ago
6 0
The natural numbers are the counting numbers.
The set of natural numbers consists of 1, 2, 3, 4, 5, ...
Zero is not part of the natural numbers.

You need to know what it means for natural numbers to be closed under addition. That means that if you add any two natural numbers, you get a natural number. Natural numbers are closed under addition since the sum of any two natural numbers is a natural number. You cannot find any pair of natural numbers whose sum is not a natural number. 5 + 6 = 11; 10 + 12 = 22; 40 + 50 = 90. Al the numbers above are natural numbers.

Now think of multiplication. If you multiply any two natural numbers, will the answer always be a natural number? The answer is yes. That means that natural numbers are closed under multiplication. For example, 4 * 2 = 8; 10 * 20 = 200; 15 * 3 = 45. All numbers above are natural numbers.

What about subtraction? If you subtract a natural number from another natural number, will the difference always be a natural number?
Look at 8 - 18 = -10. The difference, -10, is not a natural number, so the natural numbers are not closed under subtraction.

Finally, think of division. If you divide a natural number by another natural number, the quotient may or may not be a natural number.
For example, 24/6 = 4. Here the quotient is a natural number,
but 4/24 = 1/4. 1/4 is not a natural number,
so with division, you may not get a natural number, so the natural numbers are not closed under division.
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liraira [26]

Answer:

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Step-by-step explanation:

5 0
2 years ago
Express 52 thousandths in scientific notation
Alexus [3.1K]

Answer:

5.2 x 10^-2

Step-by-step explanation:

Scientific notation is used to simplify very large or very small numbers.

The formula for scientific notation is (a x 10^ n)

(a) is a number that is both greater than 1 and less than 10

(n) is the number of places the decimal place moves. This number can be positive or negative depending on the number you are converting. If the original number is greater than 1 (n) will be positive, and if the number is less than 1 (n) will be negative.

First you should write out the number.

0.052

Then, you should determine the number places the decimal point must move, and create a number greater than 1 and less than 10. (You should also pay attention to the direction the decimal point moves)

For this problem you will move the decimal place 2 places to the right to create the number 5.2.

Last, substitute the values into the formula. For this problem (a)= 5.2 and (n)= -2. This gives us the expression 5.2 x 10^-2.

8 0
3 years ago
To rent a bike there is a set fee, plus an hourly rate. Renting a bike for 4 hours costs $24. Renting it for 7 hours costs $37.5
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I believe it's 13.05
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3 years ago
A circle is never a square?
Nookie1986 [14]

Answer:

never

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2 years ago
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Assume that y varies directly as x. If y= -15 when x=5, what is the constant of variation?
torisob [31]

Answer:

k = -3

Step-by-step explanation:

Given

Variation: Direct

y = -15 when x = 5

Required

Find the constant of variation

A direct variation is represented as:

y = kx

Where

k = constant of variation

Substitute values for x and y

-15 = k * 5

Multiply both sides by ⅕

⅕ * -15 = k * ⅕ * 5

-3 = k * 1

-3 = k

k = -3

Hence, the constant of variation is -3

4 0
3 years ago
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