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True or False? Natural Numbers are closed under division.

Answers

Answer 1

Answer: False

Natural numbers are not closed under division

Some natural numbers divide to get another natural number. For example, divide 10 over 2 to get 10/2 = 5.

However, there are infinitely many natural numbers that divide to get something that isn't a natural number. Example: 10/7 = 1.43 approximately. All we need is one counterexample to contradict the original statement.

A set is considered closed under division if dividing any two values in that set leads to another value in the set. More formally, if a & b are in some set then a/b must also be in the same set for that set to be closed under division.

If we changed "natural numbers" to "rational numbers", then that set is closed under division. If p, q are rational numbers then p/q is also rational. Basically, dividing any two fraction leads to some other fraction. The value of q cannot be zero.


Related Questions


What is the empirical formula of an oxide of chromium that is 48 percent oxygen by mass?

Answers

Answer:

CrO₃.

Step-by-step explanation:

We'll begin by calculating the percentage of chromium in the oxide. This can be obtained as follow:

Oxygen (O) = 48%

Chromium (Cr) =?

Oxide of chromium contains only chromium and oxygen. Therefore, the percentage of chromium in the oxide is given by:

Cr = 100 – percentage of oxygen

Cr = 100 – 48

Cr = 52%

Finally, we shall determine the empirical formula of the oxide as follow:

Chromium (Cr) = 52%

Oxygen (O) = 48%

Divide by their molar mass

Cr = 52/52 = 1

O = 48/16 = 3

Divide by the smallest

Cr = 1/1 = 1

O = 3/1 = 3

Therefore, the empirical formula of the oxide is CrO₃.

How many solutions exist for -2|3x − 1| = 0?

Answers

Answer:

one solution

Step-by-step explanation:

-2|3x − 1| = 0?

Divide each side by -2

|3x − 1| = 0

3x-1 = ±0

Since +0 = -0 =0

3x-1 =0

There will be only one solution

Please help with geometry ASAP

Answers

Answer:

≈ 0.39

Step-by-step explanation:

Area of circle:

S = πr² = π4² ≈ 50.27 cm²

Area of triangle:

S = 1/2bh = 1/2*2*3 *(4+2.5) = 19.5 cm²

Probability of the point within red shaded area:

P = 19.5/50.27 ≈ 0.39

how to write 2.31818 as a mixed fraction

Answers

Answer:

[tex]2\frac{15909}{5000}[/tex]

Step-by-step explanation:

To make [tex]2.31818[/tex] into a fraction, you must first move it to the numerator and make 1 the denominator.

[tex]\frac{2.31818}{1}[/tex]

And then you multiply it by [tex]10,000[/tex] or you can say [tex]10^5[/tex]

[tex]\frac{2.31818}{1}*\frac{100000}{100000}[/tex]

After you multiply you divide the numerator and denominator by 2.

[tex]\frac{231818/2}{100000/2}[/tex]

And now this equals:

[tex]2\frac{15909}{5000}[/tex]

Hope this helps!

The number before the decimals always represents the whole number of a mixed number and the number after the decimals represents the fraction part of the mixed number.

2.31818 = 2.0 + 0.31818

In  2.31818

2 represents the whole number  and

0.31818 represents the fraction  31818/100000

Dividing the  fraction  31818/100000 by 2 gives

15909/50000 which cannot be further reduced.

2.31818 = 2 [tex]\frac{15909}{50000}[/tex]

https://brainly.com/question/1369626

The selling price of an article becomes 27/25 times the listed price due to the inclusion of sales tax. find the rate sales tax.​

Answers

Answer:

  8%

Step-by-step explanation:

If you subtract 1 times the original cost, the result is the tax rate:

  27/25 - 1 = tax rate = (27 -25)/25 = 2/25 = 8/100 = 8%

The tax rate is 8%.

Need as much help as I can get before 7 minutes are over

Answers

Answer:

think the answer is E but not 100%. been a while. let me know either way

125 feet in 25 seconds what’s the unit rate?

Answers

Answer: 5 feet per second.

Work: This is a fraction equal to
125 Feet ÷ 25 Seconds

We want a unit rate where
1 is in the denominator,
so we divide top and bottom by 25

This makes 5 feet/1 second which makes the answer 5 feet!

Answer:

The unit rate is 5 ft/1 second

Step-by-step explanation:

Unit rates must always be a fraction with a denominator of 1

Our unit rate is 125/25

To get to a denominator of 1 divide 25 by 25

25 ÷ 25 = 1 second

What we do to one side we have to do to the other so also divide 125 by 25

125 ÷ 25 = 5 ft

frank liked to buy packs of baseball cards. on 3 different days, he bought 3 packs. on 3 other days, he bought 4 packs each day. After that he splits his packs with his 2 brothers. How many packs will they each have. Choose the expression that best matches this situation.

Answers

Answer:

First, frank buys 3 packs on 3 different days, so in those first 3 days he buys:

3*3 = 9 packs.

Then on other 3 days he buys 4 packs each day, so he has:

3*4 = 12 packs.

In total he haves:

9 + 12 = 21 packs.

Now he divides the packs with his 2 brothers (So we divide 21 packs between 3 people)

Then each brother gets:

N = 21/3 = 7 packs each.

the quotient of 13÷24 is a decimal number. which digit in the quotient is overlined?

Answers

Answer:

6 would be the overlined number

Step-by-step explanation:

Answer:

6 will be the overlined number.

Step-by-step explanation:

how do you decipher between the graphs of cubic and cube root parent functions

Answers

Answer:

Step-by-step explanation:

.....

Evaluate A² for A = -3

Answers

Answer:

9

Step-by-step explanation:

If A = - 3, than A^2 is equal to (-3)^2

If a number is squared (to power of 2), it is multiplied by itself (there are two of that number being multiplied together) so it is - 3x-3

-3 x - 3 = 9,

Because 3x3 =9 and a negative multiplied by a negative makes a positive.

Hope this helped!

Answer:

9

Step-by-step explanation:

(A)^2 is a better way to write it. That way the answer is unambiguous (-3)^2 = -3 * - 3 = 9

That is the answer.

If two angles form a linear pair, they are

Answers

Answer:

If two angles form a linear pair, they are supplementary.

Step-by-step explanation:

A linear pair is two angles that are adjacent and the non-common sides form a straight line.

Answer:

They are supplementary

Step-by-step explanation:

A linear pair is two angles ajacent. The non - common side forms a straight line. So the angles added together are equal to 180 degrees.

Find the equation of a line in parallel to y=2x + 8 that passes through the point (4, 4).

Answers

the answer is sksksksksk

The sum of any two consecutive prime numbers is also prime true or false

Answers

Answer:

True

Step-by-step explanation:

The answer to this question is: true

Mr. Lowe is setting up his room for art class. He has 6 boxes of crayons with 24 crayons each, 3 packages of pencils with 20 pencils each, and 9 packages of paint brushes with 15 brushes each. What is the difference between the total number of crayons and the total number of paint brushes?

Answers

so first we need to find the total number of crayons

to do that we're going to multiply 6 by 24 cause each box has 24 crayons

24 × 6 = 144

so the answer of total number of crayons is 144 crayons

next we're going to find the total number of paint brushes

to do that we're going to multiply 9 by 15 cause each package has 15 paint brushes

9 × 15 = 135

so the answer of total number of paint brushes is 135 crayons

finally we're going to calculate the difference

so its 144 crayons subtracted by 135 paint brushes

144 - 135 = 9

so the difference of total number of crayons and total number of paint brushes is 9

hope that helped :))

The difference between the crayons and the paintbrush the total. I just see which one is greater

18. Identify the inverse function of

Answers

Answer:

[tex]\huge\boxed{D) \ f^{-1}(x) = (x-3)^2+2}[/tex]

Step-by-step explanation:

[tex]f(x) = \sqrt{x-2} + 3[/tex]

Replace f(x) by y

[tex]y = \sqrt{x-2} + 3[/tex]

Interchange x and y

[tex]x = \sqrt{y-2} + 3[/tex]

Solve for y

[tex]x = \sqrt{y-2} + 3[/tex]

Subtracting 3 to both sides

[tex]x - 3 = \sqrt{y-2}[/tex]

Taking square on both sides

[tex](x-3)^2 = y-2[/tex]

Adding 2 to both sides

[tex]y = (x-3)^2 + 2[/tex]

Replace [tex]y = f^{-1}(x)[/tex]

[tex]f^{-1}(x) = (x-3)^2+2[/tex]

evaluate the function for f(2)

f(t) =-t - 5; find f(2)

Answers

Answer:

[tex]f(2)=-7[/tex]

Step-by-step explanation:

So we have the function:

[tex]f(t)=-t-5[/tex]

To find f(2), substitute 2 for t. Thus:

[tex]f(2)=-2-5[/tex]

Subtract:

[tex]f(2)=-7[/tex]

And, we're done!

In June 2011, CBS News and the New York Times reported the results of a poll about problems and priorities for the U.S. In the poll, 979 U.S. adults answered the question, “What do you think is the most important problem facing this country today?” From a list of options, 53% of those polled said “economy/jobs.” This is an observational study designed to answer a question about a population. Who is the population?

Answers

Answer:  All adults of United States.

Step-by-step explanation:

A population is a large community of individuals that share some same characteristic or root.

Here, the study is all about the problem have been facing by the population of U.S.

Since adults of a society are likely voters.

So, population = All adults of United States., as only they can address the current situation or problems because they live there.

There are 12 pencils and eight pens in a cup holder select all of the simplified ratios that could be written (MULTIPLE CHOICE) A: 6 to 4 B: 5 to 3 C:4:10 D: 5:2 E: 3/2 F:5/2 I WILL GIVE BRAINLIEST TO FIRST ANSWER

Answers

A and E are the correct answers:

Square root of 45 to the nearest five hundredths

Answers

Answer:

√45 =6.71

Step-by-step explanation:

[tex]\sqrt{45} = 6.708203932\\\\= 6.71[/tex]

What is the solution the equation 1/4x +2= -5/8x-5

Answers

Answer:

-8

Step-by-step explanation:

I've taken a picture of the way I solved the equation.

#7: Twenty-three more than 10 times a number is the same as 5 more than 1 point
the number. *
Your answer
26 more than twice the

Answers

Answer:

23+10r= 5+r

Step-by-step explanation:

let r be the number

Which division problem does the number line below best illustrate? A number line going from 0 to 13. An arrow jumps from 0 to 3, from 3 to 6, from 6 to 9, and from 9 to 12. please help ;(

Answers

Without the screenshot, it's fairly difficult to know what your teacher wants exactly. I found this similar problem

https://brainly.com/question/13583475

which might help. It sounds like you have 4 semicircles which can be thought of as a division problem 12/3 = 4. Note how I'm dividing by 3 which is the width of each section (eg: from 6 to 9 is 9-6 = 3 units)

Answer:

Which division problem does the number line below best illustrate?

A number line going from 0 to 2. Arrows go from 0 to 2, from 2 to 4, from 4 to 6, from 6 to 8, and from 8 to 10.

10 divided by 2 = 5

15 divided by 3 = 5

50 divided by 5 = 10

20 divided by 10 = 2

Step-by-step explanation:

which means its a

Kenya wants to buy a car. Dealer A said she could pay $2000 upfront and $150 per month after. When will she have paid $3500

Answers

Answer:

10 months

Step-by-step explanation:

3500 - 2000 = 1500

1500/150 = 10

Answer:

On the 23rd month

Step-by-step explanation:

z-ak=y+c solve for a

Answers

isolate the variable by dividing each side by factors that don’t contain the variable.
a=y/k-c/k+z/k

Three roommates split the utilities each month for their apartment. If the utilities for this month add up to $162.54, how much do they each owe?

Answers

164.54 divided by 3(the number of roommates) your answer is 54.18 good luck

Answer:

54.18

Step-by-step explanation:

Which of the following represents “ 10 times the sum of a number and 14 is equal 9 times the number”?

Answers

Answer:

The expressión is:

10(a+14) = 9a

and the number is:

-140

Step-by-step explanation:

The expression is:

10(a+14) = 9a

then:

10*a + 10*14 = 9a

10a + 140 = 9a

10a - 9a = -140

a = -140

Check:

10(-140+14) = 9*140

10*-126 = 1260

Need help with the question attached ASAP. Will give 5 stars & brainliest!

Answers

if sum of any two angles 90 then they are called complementary

A +B =90 let the complement of A is B

4x+2 +B =90

B= 90-4x-2

B = 88-4x

complementary angle = B = 88-4x

Hope it helps

Write the following set using roster notation. Do not include repeats.
C is the set of colors in a U.S. flag.

Answers

Answer:

Step-by-step explanation:C

How do you do this question?

Answers

Answer:

-30√(t/a) cos(√(at)) + 30/a sin(√(at)) + C

Step-by-step explanation:

∫ 15 sin(√(at)) dt

Use substitution:

If x = √(at), then:

dx = ½ (at)^-½ (a dt)

dx = a / (2√(at)) dt

dx = a/(2x) dt

dt = (2/a) x dx

Plugging in:

∫ 15 sin x (2/a) x dx

30/a ∫ x sin x dx

Integrate by parts:

If u = x, then du = dx.

If dv = sin x dx, then v = -cos x.

∫ u dv = uv − ∫ v du

= 30/a (-x cos x − ∫ -cos x dx)

= 30/a (-x cos x + ∫ cos x dx)

= 30/a (-x cos x + sin x + C)

Substitute back:

30/a (-√(at) cos(√(at)) + sin(√(at)) + C)

-30√(t/a) cos(√(at)) + 30/a sin(√(at)) + C

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