What is the 7.2222222222..... as a rational number?

Answers

Answer 1

Final answer:

The repeating decimal 7.2222222222... as a rational number is 7 2/9. The conversion involves setting the repeating decimal equal to x, scaling it by a power of 10, subtracting the original number, and then solving for x to find the equivalent fraction.

Explanation:

The number 7.2222222222..., when expressed as a rational number, is the fraction 7 2/9. To convert a repeating decimal to a fraction, you can use the following steps:

Let x equal the repeating decimal, so x = 7.2222222222...Multiply x by a power of 10 that moves the decimal point to the right just before the repeating digits start. In this case, we use 10x to get 10x = 72.222222222...Subtract the original number (x) from this new number (10x). Doing this will get 10x - x = 72.222222222... - 7.222222222... = 65.Since 10x - x = 9x, we now have 9x = 65. Therefore, x = 65/9, which simplifies to 7 2/9.

This process shows how to express the repeating decimal as a fraction and thereby convert it into a rational number.

Related Questions

You put $550 in an account that earns 4.4% simple interest per year. How much interest do you earn in 6 month

$1.21

$12.10

$121.00

$145.20

Answers

(550*4.4)/100=24.2
24.2/12=2.016 $ in month
2.016*6=12.10 $

12.10 would be the interest for only 6 months.

ShopRite has jeans on sale for 3/10 off .Save more has jeans on sale for 33% off for has a better sale on jeans?explain.

Answers

3/10 is 30%
Save more jeans are 33% off

Find the value of x (5x) (3x+12

Answers

The value that shows the expansion of the given algebraic expression is 6.

What is the solution to the algebraic expression.

An algebraic expression is a mathematical expression that has the variables, coefficients, and its arithmetic operators

In the complete question attached below, we are to find the value of x.

We can see that the angles are alternate angles.

So, 5x = (3x + 12).Combine like terms, we have:

5x - 3x = 12

2x = 12

x = 12/2

x = 6

Therefore, the value of x is = 6.

4. Grace works from 10 to 20 hours per week while attending college. She earns $9.00 per hour. Her roommate Frances also has a job. Her pay for t hours each week is given by the function f(t)= 10t, where 5

Answers

Given that Grace works from 10 to 20 hours per week while attending college. She earns $9.00 per hour. Her roommate Frances also has a job. Her pay for t hours each week is given by the function f(t)= 10t, where 5 ≤ t ≤ 15.

Part A:

Given that Grace's time is rounded to the nearest quarter of an hour. The domain for Grace is given by {10, 10.25, 10.50, 10.75, - - -, 19.75, 20}.

The range for grace is given by {9(10), 9(10.25), 9(10.50), 9(10.75), - - -, 9(19.75), 9(20)} = {90, 92.25, 94.5, 96.75, - - -, 177.75, 180}

The domain for Frances is given by: 5 ≤ t ≤ 15.

The range for Frances is given by: 10(5) ≤ f(t) ≤ 10(15) = 50 ≤ f(t) ≤ 150.

Part B:

Grace earns $9 per hour and $80 to $180 per week while Frances earns $10 per hour and $50 to $150 per week.

write the answer as a decimal fraction 14/100=? /10+? /100=?

Answers

14.100 or you can do something like that try it in see if it’s right

Final answer:

To write the fraction 14/100 as a decimal fraction, divide the numerator by the denominator. The result is 0.14. Additionally, dividing any number by 100 will result in moving the decimal two places to the left.

Explanation:

To write the fraction 14/100 as a decimal fraction, divide the numerator (14) by the denominator (100). 14 divided by 100 is equal to 0.14.

To find an expression as a decimal fraction, you can first convert the fractions to a decimal by dividing the numerator by the denominator.

For example, 10/100 is equal to 0.10 (10 divided by 100) and ?/100 is equal to ? (dividing any number by 100 will result in moving the decimal two places to the left).

Learn more about Converting fractions to decimal fractions here:

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The figure shows the letter T and four of its transformed images—A, B, C, and D. (See image.)

Which of the four images was formed by a reflection of the letter T?

A) A
B) B
C) C
D) D

Answers

its C
I believe it is

A pet store has 9 puppies and 48 kittens.

What is the ratio of kittens to puppies?

Enter your answer in simplest fractional form in the box.

Answers

ratio of kittens to puppies = 48/9 = 16/3

answer
ratio of kittens to puppies = 16/3

hope it helps

The ratio of kittens to puppies is [tex]\dfrac{16}{3}[/tex].

Given:

The number of puppies is 9.

The number of kittens is 48.

To find:

The ratio of kittens to puppies.

Explanation:

The ratio of kittens to puppies is the fraction of the number of kittens and the number of puppies. So,

[tex]\text{Ratio}=\dfrac{\text{Number of kittens}}{\text{Number of puppies}}[/tex]

[tex]\text{Ratio}=\dfrac{48}{9}[/tex]

[tex]\text{Ratio}=\dfrac{16}{3}[/tex]

Therefore, the ratio of kittens to puppies is [tex]\dfrac{16}{3}[/tex].

Learn more:

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What is the sum of the geometric sequence −4, 24, −144, … if there are 7 terms?-159,964

−26,661

26,661

159,963

Answers

The common difference is multiply f(n-1) by -6 and (f)1=-4

mutiply -144 by -6, then 864 by -6, then -5184 by -6. then 31104 by -6 to get -186624

so we have -4, 24, -144, 864, -5184, 31104, -186624 as the seven terms in the geometric sequence, now we just need to add these together and getting the final answer of -159,964

Answ

-159,964

Step-by-step explan

I got it right on the test

Noah currently has an account balance of $2,976.45. He opened the account 11 years ago with a deposit of $1,963.45. If the interest compounds quarterly, what is the interest rate on the account?

Answers

What we know:
Acct. balance A (11)= $2,976.45
Pricipal=$1,963.45
Compounded (n)=quarterly (4)
rate=r
Compound interest formula: A (t)=p (1+r/n)^nt

What we need toi find:
If the interest compounds quarterly, what is the interest rate on the account? Find r.
A (t)=p (1+r/n)^nt
2976.45=1963.45 (1+r/4)^(4×11)
2976.45=1963.45 (1+r/4)^44
2976.45/1963.45=1963.45/1963.45 (1+r/4)^44
1.5159=(1+r/4)^44
(1.5159)^(1/44)=((1+r/4)^44)^(1/44)

1.0095=1+r/4
1.0095-1=1-1+r/4
.0095=r/4
.0095(4)=r/4 (4)
.038=r

Rate = 3.8%

Answer:

The interest rate is 3.79% or 3.8%

Step-by-step explanation:

The formula to find how much money A we have at the end of t years if we start with a principal or amount of money P today and the interest is compounded n times in the years is:

A=P(1+ r/n)^(nt) (1)

Here A = $2,976.45 the final amount

t = 11 years

P = $1,963.45.

and n = 4 because the interest is compounded quarterly or 4 times in the year.

We the need to simplify the interest rate r in (1) so:

A=P(1+ r/n)^(nt) (1)

A/P = (1+ r/n)^(nt)

(A/P)^(1/nt) = (1+ r/n)

(A/P)^(1/nt) - 1 = r/n

((A/P)^(1/nt) - 1 ) * n = r

r = ((A/P)^(1/nt) - 1 ) * n

We replace values and solve doing parenthesis exponents first

r = ((2,976.45/1,963.45.)^(1/(4*11)) - 1 ) * 4

r= ((1.51^(1/44)) -1)*4

((1.51^(1/44)) -1)*4

r= (1.009499443 - 1)*4

r= 0.009499443 *4 = 0.037997773

That expressed in percentage multiplying by 100 is 3.79% or 3.8% interest

I need help Simplifying!!!!!!!!!!
2x−(x+6)

Answers

To simplify this, we first need to distribute the negative sign to the (x+6). It's easier to see if we rewrite the negative as -1:
[tex]2x+(-1)(x+6)=2x+(-1)*x+(-1)*6=2x-x-6[/tex]

Now combine like terms:
[tex]2x-x-6=x-6[/tex]

2x - (x + 6)

The first step is to multiply every term inside the parentheses by -1.

2x - x - 6

Now combine like terms.

x - 6

Done.

Find the outlier in the data: 38, 38, 18, 28, 36, 30, 39, 32. How does the outlier affect the mean? If necessary, round to the nearest tenth. 43; raises it by 1.5. 18; lowers it by 2. 43; lowers it by 1.5. 18; raises it by 2.

Answers

the outlier is 18. This outlier will lower the average mean. The answer is B

The outlier is 18.
and it lowers the mean by about 2

do any of the points below fall on the linear equation shown. Please show work

Answers

You are given three points. Each point consists of an abscissa (x-value) and an ordinate (y-value). One by one, take the abscissas and insert them into the given formula to produce a y value. Then, compare this calculated y-value to the ordinate given.

Example: Determine whether (2,0) lies on the graph of the given line.

Subst. 2 for x: y = (9/5)(2-273) + 32 = -455.8. This is not equal to the given ordinate (0), so NO, (2,0) does NOT lie on the graph of the given function.

is 5 factor of the number 38 yes or no

Answers

no it is not. 5 can go into 35 and 40, but not 38

The factors of the number 38 are 1, 2, 19 and 38. For any positive number, the number 1 and the number itself are factors, so 1 and 38 are inherent factors. Additional numbers that divide 38 evenly are 2 and 19.

A baker used 4 cups of flour to make 5 batches of brownies. He used_of a cup of flour to make 1 batch of brownies

Answers

(I dont know if this is the way your teacher told you how solve the problem but I'm gonna try it anyway)

First of all, Let x = the mystery amount of flour

To create my equation, I put cups of flour over the amount batches in a formation, kind of like a fraction.

cups
-----------
batches

Next, I fill in the values.

cups 4
----------- = ---------
batches 5

The 4/5 represents the first ratio of flour/batches.

cups   4 x
----------- = ---------   = ---------
batches 5 1

Since we do not know that amount of flour it took to make one batch, we put x in it's place.

Now it's time to cross multiply. It's exactly like it sounds! Multiply diagonally.

Multiply 5 and 'x'. Multiply 4 and 1.

You end up with a eqaution that looks like:

5x = 4

As you would for any solve-by-x equation, divide the five on both sides.

5x= 4
- -
5   5

4/5 = Four-Fifths

5/5 cancels itself out and poofs into thin air.

You end with x = 4/5

This is the answer.

The baker used 4/5 cups of flour to make 1 batch of brownies :)

Please help me!! This is due by 11.59pm. Please show how you got the answer. I got $270.

Answers

It is $150 because you want 125% of 120. You can put 125% as a fraction so the equation now is 125/100*120. So simplifying, you get 12.5*12. So the actual answer is $150.

you can use similar triangles to find the height of a tree. Triangle ABC is similar to triangle DEC. what is the height of the tree?

please explain it too ^_^

Answers

So if triangle ABC is similiar to triangle DEC then we know that when two figures are similar, the ratios of the lengths of their corresponding sides are equal.So we can write:

AC/DC = BC/EC =AB/DE = k

BC= 9ft + 6ft = 15

BC/EC= k
15/6=k

Now that we know the k we can find the height of the tree that's equal to AB:

AB/DE= k
AB/4=15/6
6AB= 15 x 4
AB= 60/6 = 10

The height of the tree is 10ft

The height of the tree is 10 feet.

What is a triangle?

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know the ratios of the lengths of the corresponding sides are equal when two figures are similar, if triangle ABC and triangle DEC are similar, then we may write,

AC/DC = BC/EC = AB/DE = k

BC= 9ft + 6ft = 15

BC/EC= k

15/6=k

Now from this value of 'K' we can determine the height of the tree which is,

AB/DE = k

AB/4 = 15/6

6AB = 15 x 4

AB = 60/6 = 10

The height of the tree is 10ft.

learn more about triangles here :

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What is the smallest power of 10 that would exceed 987,654,321,098,765,432?

Answers

it is 10^18:1000000000000000000

Giving who ever answers correctly over 30 points.

1: Solve for x.

x - 3/8 = - 5/8

a: x=1/4
b: x= -1/4
c: x= -1

2: Solve for x.

2x = 15 + x

a: x= -15
b: x= 15
c: x= 15/2

3: Solve for x.

x + 5 = 2x

a: x=3
b: x= -5
c: x= 5

Answers

The first one would be b,

second is b

third is c.

Hope this helps!

Number 1 is b
Number 2 is b
Number 3 is c

How do you write 1/10 in percent

Answers

1/10 = 10/100

10/100 = 0.10

0.10 = 10%

10% is your answer

hope this helps

10% cause it's just like counting by 10's

What number goes on top and how do you solve it.

Answers

So basically, each number is equal to the two numbers below it added together.

See, 7 = 3+4, 8 = 5 +3, etc.

So, the top would be 16 + 17.

16 + 17 = 33

So 33 goes on top.

A soccer field has an area of 7/8 square miles. The length of the field is 2/5 miles. What is the width of the soccer field?

Answers

Answer: The answer is 35/16 miles

Step-by-step explanation: I have my ways ;>

Dr. McDonald thinks that his group of earth science students is particularly special (in a good way), and he is interested in knowing if their class average falls within the boundaries of the average score for the larger group of students who have taken earth science over the past 20 years. Because he has kept good records, he knows the means and standard deviations for both his group of 36 students and the larger group of 1,000 past enrollees. Here are the data he has, and the values for which you will need to compute the z-test

Answers

I don't know what witch is this

4(x+8)-4=34-2x steps

Answers

Step 1: Simplify both sides of the equation.4(x+8)−4=34−2x(4)(x)+(4)(8)+−4=34+−2x(Distribute)4x+32+−4=34+−2x(4x)+(32+−4)=−2x+34(Combine Like Terms)4x+28=−2x+344x+28=−2x+34Step 2: Add 2x to both sides.4x+28+2x=−2x+34+2x6x+28=34Step 3: Subtract 28 from both sides.6x+28−28=34−286x=6Step 4: Divide both sides by 6.6x6=66x=1

Set up an equation that can be used to solve the problem. Solve the equation and determine the desired value.
At a boating and sports store, the cost of renting a personal watercraft is $53 per half hour, which includes a 6% sales tax. Determine the cost of a half hour rental before tax.

The equation is ?. The cost of a half hour rental is $? Per half hour.

Type an equation using x as the variable.

Answers

[tex]y = 53x[/tex]
y= 53(1)
[tex]y = 53[/tex]

Simplify this algebrtic expression
Z-4/4+8

Answers

it equals to z/16

brainliest answer plz:)

1/12z + -1/3 is the answer.

A farmer had 1,000 horses and cows. After selling some of them, he had 550 horses and 350 cows left. How many horses and cows did he sell altogether?

Answers

the farmer had sold 100 horses and cows

A recipe requires 1/4 lb of onions to make 3 servingsof soup. Mark has 1 1/2 lb of onions. How many servings can mark make?

Answers

16 servings of soup. 1/4 times 4 equals 1 pound and 1/4 times 2 equals 1/2 a pound so it equals 1 1/2.

Hello,

We know that if you have 1/4 Ib of onions, that will make 3 servings. If we make a unit rate table, you'll end up with 18 servings when you have 1 1/2 Ibs of onions.

He would be able to make 18 servings. Hope this helps.

May.

If d = 20 and C = 20π
If d = 26 and C = 26π
If r = 12 and C = π
If r = 18 and C = 14π
If r = 6 and C = 12π
If r = 50 and C = 100π

^Matches w
then d = 1
then d = 100
then d = 12
then d = 14
then r = 10
then r = 13

What goes w what!

Answers

If d = 20 and C = 20π, then r = 10.
If d = 26 and C = 26π, then r = 13.
If r = 1/2 and C = π, then d = 1.
If r = 7 and C = 14π, then d = 14.
If r = 6 and C = 12π, then d = 12.
If r = 50 and C = 100π, then d = 100.
*Note, r= 1/2×d or d=2×r

Benjamin solved the equation 3+/2=10 and justified each step as shown. Identify Benjamin’s error and fix his mistake.
3+x/2=10 GIVEN
x/2=7 MULTIPLICATION PROPERTY OF EQUALITY
x=14 SUBTRACTION PROPERTY OF EQUALITY

Answers

How to solve the equation properly:

3 + x / 2 = 10

Multiply 2 on both sides.

3 + x = 20

Subtract 3 from both sides.

x = 17.

What he did wrong:

He subtracted the three on both sides before he multiplied the two. This will make him get the incorrect answer because he did it in the wrong order.

Hope this helps!

What is 23/35 simplified?

Answers

There is no least common enominator for this answer due to the fact that these numbers don't share a common factor (23 is odd number with only two factors: 1, 23; while 35 is odd number with 4 factors: 1, 5, 7, 35) other than 1.

*But if you do 1/1, it will be 1; so this won't work properly.

So the answer is 23/35.

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