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The repeating decimal [tex]\(0.1 \overline{23}\)[/tex] is equivalent to the fraction [tex]\(\frac{611}{5000}\)[/tex].
To convert the repeating decimal [tex]\(0.1 \overline{23}\)[/tex] to a fraction, let's denote it as x:
[tex]\[ x = 0.1 \overline{23} \][/tex]
Now, we can manipulate the decimal to eliminate the repeating part. Multiply both sides of the equation by an appropriate power of 10 to shift the decimal:
[tex]\[ 100x = 12.323232\ldots \][/tex]
Now, subtract the original equation from the manipulated equation to eliminate the repeating part:
[tex]\[ 100x - x = 12.323232\ldots - 0.1 \overline{23} \][/tex]
Simplify:
[tex]\[ 99x = 12.22 \][/tex]
Now, solve for x:
[tex]\[ x = \frac{12.22}{99} \][/tex]
To simplify the fraction, find the greatest common divisor (GCD) of 12.22 and 99, which is 1. Divide both the numerator and denominator by the GCD:
[tex]\[ x = \frac{12.22}{99} = \frac{611}{5000} \][/tex]
So, [tex]\(0.1 \overline{23}\)[/tex] as a fraction is [tex]\(\frac{611}{5000}\)[/tex].
Related Questions
Find the future value of $1800 deposited at 8% for 5 years if the account pays simple interest, and the account pays interest compounded annually.
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0.08(1800) + 1800
But because it is 5 years:
5(0.08(1800)) + 1800
0.4(1800) + 1800
We can make it simpler:
1.4(1800)
Multiply:
2520
YOU NOW HAVE $2520
Answer:
The answer is 2,644.79.
You would have to calculate the three variables to get and complete your answer.
Step-by-step explanation:
Originally priced at $15.99 was marked down 15% and then it was moved to a clearance rack marked take an additional 50% off the lowest marked price what is the final price of the PlayStation game
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Enter the value of 5 times (13.5-4.5)
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Expansion is a means by which complex function are simplified. The value of the expression 5 times (13.5-4.5) is 45
Factorization and expansionExpansion is a means by which complex function are simplified by multiplying the expression with one another.
Given the expression:
5(13. 5 - 4.5)
According to the distributive property:
= 5(13. 5 - 4.5)
= 5(13.5) - 5(4.5)
= 67.5 - 22.5
= 45.0
Hence the value of the expression 5 times (13.5-4.5) is 45
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Add the two expressions. 4.6x−3 and −5.3x+9 Enter your answer, in simplified form, in the box. PLEASE ANSWER FAST THIS IS A BIG DEAL!!!
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[tex]4.6x - 3 + - 5.3x + 9\\ = (4.6x - 5.3x) + (-3 + 9)\\ = -0.7x + 6[/tex]
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Answer: -0.7x + 6
An expression is defined as a set of numbers, variables, and mathematical operations. The addition of the two given expressions (4.6x-3) and (-5.3x+9) is (-0.7x+6).
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The addition of the two given expressions (4.6x-3) and (-5.3x+9) is,
(4.6x-3) + (-5.3x+9)
= 4.6x - 3 - 5.3x + 9
= -0.7x + 6
Hence, The addition of the two given expressions (4.6x-3) and (-5.3x+9) is (-0.7x+6).
Learn more about Expression:
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Robin’s scores: 99, 108, 102, 107, 119 Evelyn’s scores: 125, 137, 138, 145, 145 Find and compare the medians of the data sets. Do the medians support your conclusion that Robin is winning the game?
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Robin's scores: 99, 102, 107, 108, 119. Median is 107.
Evelyn's scores: 125, 137, 138, 145, 145. Median is 138.
The median from Evelyn's scores is greater than the median from Robin's. Therefore, the medians do NOT support the conclusion that Robin is winning the game.
Answer:
The median score for Robin is 107. The Median Score of Evelyn is 138. The medians are the same as the means, so the same conclusion that Robin is winning will be drawn.
Step-by-step explanation:
370x1/10 = please help
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It is thirty seven, use a calculator
This is because 370 times 1/10 is the same as 370 times 0.1 which would be equal to 37
Please help me answer this question. Explain if possible.
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"The functions have the same rate of change" is wrong because as we can see, the table goes up by 10, however, the graph goes up by 15
"Both functions are the same" is also wrong, we already proved they have a different slope, how could they possibly be the same?
"The rate of change for Tour 1 is greater" is also wrong because tour 2 goes by 15, which is greater than 10.
"The functions have the same initial value is correct because as we can see on the graph(tour 2), the y-intercept is 35, using the slope on the tab;e(tour 1) we can calculate that when x is 0, the y-value is 35, which means both of the tours has a y-intercept of 35, therefore, this is the correct choice
Explanation: Alright let's do answer of elimination. It cannot be "Both functions are the same" Due to the fact that for one person in Tour 1 is 45 dollars while for Tour 2 is 50. It cannot be "The functions have the same initial value. Since for initial value it's kind of like a constant. For example for 1 person it would be 20 dollars for 2 it would be 40 and so on. It cannot be the last one since rate of change is obviously different. I don't think I have to go into that.
Also I see your doing an IReady Lesson
The equation below shows The area of a trapezoid, a, with a height of 9 cm, and one base 35 cm. A=9/2(b+35)
Which formula correctly solves for the other base, b?
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A = 9/2 (b + 35)
We must clear b from the equation, to obtain the value of the other base.
Clearing b we have:
(b + 35) = (2/9) A
b = (2/9) A - 35
Answer:
A formula that correctly solves for the other base, b is:
b = (2/9) A - 35
Find the area of the trapezoid to the nearest tenth.
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The area of the trapezoid would be 153. What I’d did was 1.3 added to 1.5 added to 0.6, multiplied by 45, and I got the answer of 153.
What is the answer to part d. Thanks so much.
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What is the formula for the perimeter of a rectangle?
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Find the area of a parallelogram....
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A = bh
Substituting the given values, you have
A = (3x +5)(7x -1)
We presume you want the product multiplied out. Use the distributive property for that.
A = 3x(7x -1) +5(7x -1)
A = 21x² -3x +35x -5
A = 21x² +32x -5
The area of the parallelogram is 21x² +32x -5.
What is the range of the following graph?
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what does a highter and lower standard deviation tell you!!!!?
what does a higher and lower z-score tell you ?
what does the varience tell you?
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V = s^2
where V = variance and s = standard deviation
So the variance can also be used to determine how grouped or spread out the data values are
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The z score tells us where this score is located in terms of the group. If the z score is positive, then it is above the mean. If the z score is negative, then it is below the mean. The further the z score is from zero, the further the raw score is from the mean. A score of z = 0 is right at the mean.
Triangle BCD is similar to triangle ACE. If the triangles are isosceles, what is the length of AB?
F.) 16cm
G.) 11cm
H.) 40cm
J.) 35cm
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[tex] \frac{2.75}{22} = \frac{5}{ac} \\ ac = 5 \div ( \frac{2.75}{22} ) = 40 \\ ab = 40 - 5 = 35[/tex]
Correspondind sides, similar triangles
Cheryl used 40% of her money to buy a dress and 1/5 of the remainder to buy a pair of shoes. She then donated $60 to charity and had $132 left How much money did Cheryl have at first?
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Amount used for dress= 40% of a
amount left =60% of a
amount used for shoe= 1/5*60a/100=3a/25
left=60a/100-12a/100=48a/100
=>48a/100-60=132
=>a=192*100/49=400
She had $400 at first.
Hope I helped, good luck.
Dress = 40% x = 0.4x
Amount left = x - 0.4x = 0.6x
Shoes = 1/5 x 0.6x = 0.12x
Amount left = 0.6x - 0.12x = 0.48x
Donated $60 and had $132 left:
⇒ 0.48x - 60 = 132
Solve x:
0.48x - 60 = 132
0.48x = 192
x = $400
Answer: $400
Which of the following shows of the slope of the line and one point on the line?
A. 6/5 and (-3, 1)
B. 5/6 and (1, -3)
C. 5/6 and (-3, 1)
D. -6/5 and (1, -3)
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This is the only answer choice with a negative slope, so we don't even need to look at the point really. Though if you wanted, you can confirm that the point (1,-3) is on the diagonal line. This point is shown in red in the attached image.
To find that the slope is -6/5, you pick two points on the diagonal line and use the slope formula. Two points you can use are (1,-3) and (-4,3).
The slope formula is m = (y2-y1)/(x2-x1)
Note: The negative slope is because we move downhill as we move from left to right along the diagonal line.
A crane is rented at $1000 per day plus a charge per hour of use. The crane was used for 7 hours on a day, and the total charge was $3450. Which equation can be used to find the charge x, in dollars, per hour of use?
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The big bend national park covers 800,000 acres. Brazos Bend state park covers about 5,000 acres. About how many more acres does Big Bend National Park cover then Brazos Bend state park?
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this but okay....
Big Bend National Park is larger by approximately 795,000 acres than Brazos Bend State Park. This figure was obtained by subtracting the area of the Brazos Bend State Park from the area of the Big Bend National Park.
Explanation:The Big Bend National Park and the Brazos Bend State Park have a substantial difference in size. You can calculate this size difference by performing a simple subtraction operation. In this case, the size of the Big Bend National Park is 800,000 acres, whereas Brazos Bend State Park covers about 5,000 acres. By subtracting the size of Brazos Bend State Park from the size of the Big Bend National Park, we will get about 795,000 acres, which represents the size difference.
So, the formula would appear as follows:
800,000 acres (Big Bend National Park) - 5,000 acres (Brazos Bend State Park) = 795,000 acres difference.
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Sudhanshu is solving a system representing a race between two remote control cars. The variable x is defined as time in seconds, and y is the distance in meters from the starting line. How many solutions should Sudhanshu find?
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However, if the speeds are changing, then there could be multiple solutions.
Answer:
The lines would only cross ONCE. So the answer is ONE.
Step-by-step explanation:
If using a graphing calculator you will see that the lines are at different slopes and will soon cross at (5,20) on a graph. Which means that the second cars is also faster even though the first car had a head start.
Can someone please help me with number 25
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Answer:
x² + 10x + 24 = (x + 4)(x + 6)
b = 4 or 6
A rectangular prism has a length of 5 meters, a width of 6 3/4 meters, and a height of 3 1/2 meters. What is the volume of the prism?
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5 x 6.75 = 33.75 33.75 x 3.5 = 118.125
Your answer is: V = 118.125 m³
Answer:
118.13
Step-by-step explanation:
6 3/4= 6.75
3 1/2 = 3.5
Find f(x) if it is known that f(3k)=3k+7.
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Since f(3k) = 3k+7 (Equation 1)
We have to determine the value of f(x).
That is we have to replace 3k by x,
3k = x
Substituting the value of 3k in equation 1.
So, f(x) = x + 7
Therefore, f(x)=x+7 is the required function.
Kristen invests $5,745 in a bank. The bank pays 6.5% interest compounded monthly. How long must she leave the money in the bank for it to double? Round to nearest tenth of a year.
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where
[tex]A[/tex] is the final amount
[tex]P[/tex] is the initial investment
[tex]r[/tex] is the interest rate in decimal form
[tex]t[/tex] is the time in years
We know that initial investment is $5,745, so [tex]P=5745[/tex]. We also know that Kristen wants his investment to double, so [tex]A=2*5745=11490[/tex]. Now, to convert the interest rate to decimal form, we are going to divide the rate by 100%: [tex]r= \frac{6.5}{100}=0.065 [/tex]. Since the interest is compounded monthly, it is compounded 12 times per year: therefore, [tex]n=12[/tex]. Now that we have all the information we need, lets replace the values in our formula and solve for [tex]t[/tex]:
[tex]A=P(1+ \frac{r}{n})^{nt} [/tex]
[tex]11490=5745(1+ \frac{0.065}{12})^{12t} [/tex]
[tex] \frac{11490}{5745} =(1+ \frac{0.065}{12})^{12t}[/tex]
[tex]2=( \frac{2413}{2400} )^{12t}[/tex]
[tex]ln(2)=ln(\frac{2413}{2400} )^{12t}[/tex]
[tex]ln(2)=12tln(\frac{2413}{2400} )[/tex]
[tex] \frac{ln(2)}{12ln(\frac{2413}{2400} )} =t[/tex]
[tex]t=\frac{ln(2)}{12ln(\frac{2413}{2400} )}[/tex]
[tex]t=10.7[/tex]
We can conclude that she must leave the money for 10.7 years in the bank for it to double.
vector works the same number of hours every week he worked a total of 532.5 and hours in the last 15 weeks. how many hrs did he work in one week
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this will give you the hours in one week
= 35.5
532.5/15 = 35.5
Vector worked 35.5 hours in one week.
what does x equal
5x+2y=3
1x+2y=6
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Solve the equation (x-5)1/2+5=2
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((x-5) ^ (1/2)) + 5 = 2
Clearing x we have:
(x-5) ^ (1/2) = 2-5
(x-5) ^ (1/2) = -3
x-5 = root (-3)
x-5 = i * root (3)
x = 5 + i * root (3)
Answer:
The value of x is given by:
x = 5 + i * root (3)
(x - 5)1/2 + 5 - 5 = 2 - 5
(x - 5)1/2 = -3
1/2x - 2.5 = -3
1/2x - 2.5 + 2.5 = -3 + 2.5
1/2x = -1/2
(1/2x)/(1/2) = (-1/2)/(1/2)
x = -1 <-------------answer :)
mary draws the number line below to repersent the solution set of the inequality 50-8t<90
what mistake did Mary make?
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50-90<8t
-40<8t
8t>-40
t>-5
Solutions should go to the right.
Mary probably was solving it as following
50-8t<90
-8t<90-50
-8t<40 (here, when she divided both sides by -8, she had to change sign < to the sign >)
But she did not change the sign, and got
t<-5
Can I have some help with this question?
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-10+90x+6x-60
96x-70
so d is the answer
-10(1-9x)=90x-10
6(x-10)=6x-60
(90x-10)+(6x-60)=96x-70 (same thing as -70+96x)
So, the answer is D. -70+96x
Have a nice day! ♪
A patrolman spends 25% every day completing paperwork. The patrolman’s shift each day is 8 hours. How much of his time does he spend doing paperwork each day?
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[tex]8 \times 25\% \\ = 8 \times \dfrac{25}{100} \\ = 2[/tex]
Answer : He spends 2 hours doing paperwork each day.
Hope this helps. - M