Answers
Converting each of the question mentioned decimal into fractions in their simplest form, we get,
(i) 0.6 with 6 recurring = (2/3)
(ii) 3.405 with (405) recurring = (378/37)
(iii) 0.75 with (75) recurring = (25/33)
(iv) 0.3 with 3 recurring = (1/3)
As per the question statement and the attached reference along with the question, we are provided with four recurring decimal values.
We are required to convert each of the decimal values into fractions in their simplest form.
Starting with (i), 0.6 with 6 recurring = 0.66666...
Now, let [x = 0.6666...]
Or, [10x = 6.6666...]
Or, [(10x - x) = (6.6666...) - (0.6666...)]
Or, (9x = 6)
Or, [x = (6/9)]
Or, [x = (2/3)]
Or, [0.6666... = (2/3)]
Similarly for (ii), 3.405 with (405) recurring = 3.405405405405...
Now, let [x = 3.405405405...]
Or, [1000x = 3405.405405405...]
Or, [(1000x - x) = (3405.405405405...) - (3.405405405...)]
Or, (999x = 3402)
Or, [x = (3402/999)]
Or, [x = (378/37)]
Or, [3.40540405... = (378/37)]
Coming to (iii), 0.75 with (75) recurring = 0.757575...
Now, let [x = 0.757575...]
Or, [100x = 75.757575...]
Or, [(100x - x) = (75.757575...) - (0.757575...)]
Or, (99x = 75)
Or, [x = (75/99)]
Or, [x = (25/33)]
Or, [0.757575... = (25/33)]
Finally coming to (iv), 0.3 with (3) recurring = 0.333...
Now, let [x = 0.333...]
Or, [10x = 3.333...]
Or, [(10x - x) = (3.333...) - (0.333...)]
Or, (9x = 3)
Or, [x = (3/9)]
Or, [x = (1/3)]
Or, [0.333... = (1/3)]
Recurring Decimal: A recurring decimal is a decimal in which, a particular digit or sequence of digits repeat(s) itself indefinitely after a certain point.Fractions: Any mathematical quantity which is not a whole number, and is expressed as a quotient of two numbers, one at the numerator (top) and the other at the denominator (bottom), separate by a (/) in between, is known as a fraction.To learn more about Recurring Decimals & Fractions, click on the link below.
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Related Questions
What is -8.64 / -0.024?
Answers
Let's first write both numbers in their fraction form:
[tex]\begin{gathered} -8.64=-\frac{864}{100} \\ -0.024=-\frac{24}{1000} \end{gathered}[/tex]then, we can write the division like this:
[tex]-8.64\frac{\cdot}{\cdot}-0.024=-\frac{864}{100}\frac{\cdot}{\cdot}(-\frac{24}{1000})[/tex]Now, given the general rule for the division of fractions, we have:
[tex]\begin{gathered} \frac{a}{b}\frac{\cdot}{\cdot}\frac{c}{d}=\frac{a\cdot d}{b\cdot c} \\ b,d\ne0 \end{gathered}[/tex]also notice that we are dividing two negative numbers, then our final result will be positive according to the law of signs. Then, we have in this case:
[tex]-\frac{864}{100}\frac{\cdot}{\cdot}(-\frac{24}{1000})=\frac{864\cdot1000}{24\cdot100}=\frac{864\cdot10}{24}=\frac{8640}{24}=360[/tex]therefore the final result is 360
solve for t
275,000 = 300 1-(1 + .038/12 ) ^(-12t)/(.038/12)
Answers
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.
The value of t exists [tex]$t=-\frac{\ln \left(\frac{12781}{6}\right)}{12 \ln \left(\frac{12.038}{12}\right)}$$[/tex].
What is meant by an expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Expressions have the following structure: (Number/variable, Math Operator, Number/variable).
Given: [tex]$275000=\frac{3001-\left(1+\frac{0.038}{12}\right)^{(-12 t)}}{\left(\frac{0.038}{12}\right)}$$[/tex]
Multiply both sides by 0.038 / 12, we get
[tex]$275000 \cdot \frac{0.038}{12}=\frac{3001-\left(1+\frac{0.038}{12}\right)^{-12 t}}{\frac{0.038}{12}} \cdot \frac{0.038}{12}$$[/tex]
Simplifying the above equation, we get
[tex]$\frac{5225}{6}=3001-\left(1+\frac{0.038}{12}\right)^{-12 t}$$[/tex]
Add [tex]$\left(1+\frac{0.038}{12}\right)^{-12 t}$[/tex] to both sides
[tex]$\frac{5225}{6}+\left(1+\frac{0.038}{12}\right)^{-12 t}=3001-\left(1+\frac{0.038}{12}\right)^{-12 t}+\left(1+\frac{0.038}{12}\right)^{-12 t}$$[/tex]
Simplifying the above equation, we get
[tex]$\frac{5225}{6}+\left(1+\frac{0.038}{12}\right)^{-12 t}=3001$$[/tex]
Subtract 5225 / 6 from both sides
[tex]$\frac{5225}{6}+\left(1+\frac{0.038}{12}\right)^{-12 t}-\frac{5225}{6}=3001-\frac{5225}{6}$$[/tex]
Simplify
[tex]$\left(1+\frac{0.038}{12}\right)^{-12 t}=\frac{12781}{6}$$[/tex]
By using exponent rules, we get
[tex]$-12 t \ln \left(1+\frac{0.038}{12}\right)=\ln \left(\frac{12781}{6}\right)$$[/tex]
Solve [tex]$-12 t \ln \left(1+\frac{0.038}{12}\right)=\ln \left(\frac{12781}{6}\right): \quad t=-\frac{\ln \left(\frac{12781}{6}\right)}{12 \ln \left(\frac{12.038}{12}\right)}$[/tex]
[tex]$t=-\frac{\ln \left(\frac{12781}{6}\right)}{12 \ln \left(\frac{12.038}{12}\right)}$$[/tex]
Therefore, the value of t exists [tex]$t=-\frac{\ln \left(\frac{12781}{6}\right)}{12 \ln \left(\frac{12.038}{12}\right)}$$[/tex].
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When 6 times a number is increased by 11 the result is 16 less than 9 times the number. Find the number
Answers
Answer:
The number is 9
Step-by-step explanation:
6n + 11 = 9n -16 Subtract 6n from both sides of the equation
11 = 3x -16 Add 16 to both sides of the equation
27 = 3n Divide both sides of the equation by 3
9 = n
a computer password is required to be 8 characters long. how many passwords are possible if the password requires 1 letter(s) followed by 7 digits (numbers 0-9), where no repetition of any letter or digit is allowed?
Answers
There will be 15724800 computer passwords possible with 1 letter followed by 7 digits without any repetition of letters or digits.
It is given to us that -
A computer password is required to be 8 characters long
The computer password requires 1 letter(s) followed by 7 digits
The 7 digits are from numbers 0-9.
It is also mentioned that there will be no repetition of any letter or digit
We know that,
The total number of English alphabets = 26 (from a-z)
The total number of digits = 10 (from 0-9)
Since it is given that the computer password has
1 letter followed by 7 digits without any repetition of any letters or digits
So, the number of computer passwords that are possible can be -
[tex]26*10*9*8*7*6*5*4\\= 15724800[/tex] (1 letter and 7 digits with no repetition)
Thus, 15724800 computer passwords are possible that contains 1 letter followed by 7 digits where no repetition of any letter or digit is allowed.
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a package container 72 plastic cups 17.99
Answers
Approximately, the unit cost of the plastic cups is $0.25
Here, we want to get the unit rate of the plastic cups
By unit rate, we mean the price of 1
From the question, the total 72 costs $17.99
The cost of one is thus;
[tex]\frac{17.99}{72}\text{ = 0.25}[/tex]The answer is 0.25
is -1/3-4/5 positive,negative,or zero
Answers
The fraction expression given as -1/3-4/5 is a negative number
How to categorize the number?The fraction expression is given as
-1/3 - 4/5
From the above expression, we observe that:
The numbers are fractionsThe numbers are negative numbersThe sum of two negative numbers will result in another negative number
This means that the value of -1/3 - 4/5 is a negative expression
Solving further, we have:
-1/3 - 4/5
Evaluate the expression
-1/3 - 4/5 = -17/15
See that 17/15 is negative
Hence, -1/3 - 4/5 is negative
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Levi is 5 feet, 9 inches tall. How many centimeters tall is Levi? (1 inch = 2.5 centimeters)
Answers
Answer:
175.259 cm
Step-by-step explanation:
Solve the equation 3 sinx+3 = 1 for 0°
Answers
The value of x after solving the equation 3sinx+3 = 1 for 0° is -46.455.
First, take the equation 3sinx+3 = 1. This is a first order linear equation with a single variable, x. To solve this equation find the value of x.
First subtract three from both LHS and RHS part. The equation becomes
3sinx+3-3 = 1-3,
which is equal to,
3sinx = -2. now divide both LHS and RHS by 3 and the equation becomes, (3sinx)÷3 = -2÷3 solving this we get the equation as sinx = -2÷3.
now take the sine to the LHS we get the equation as,
x = [tex]sin^{-1}[/tex](-2÷3)
so by solving this, the final answer for x is,
x = -46.455
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It rained all week, and it created a leak in the roof! The roof repair was $100.00 for the repairman to come and fix it.
What is the balance after the roof repair$
Answers
Answer:
100.00
Step-by-step explanation:
it's 100.00 because the roof is being repaired and the person will have to pay after
HELPPPP ME PLEASE!!!!
Always True
Sometimes True
Never True
Answers
Answer:
always
never
always
always (not 100% sure)
sometimes
sometimes (not 100% sure)
Step-by-step explanation:
this is what I got, hope it helps
Characterize the slope of the line in the graph
A. Positive
B. Negative
C. Zero
D. Undefined
Answers
The slope of the line in the graph is undefined.
The line in the graph is a straight vertical line whose slope can be found.
The characteristics of a vertical line can be used to find the slope of the vertical line given.
A vertical line has same x-co-ordinate but will have different y-co-ordinates.
Slope of a line is the change in y-co-ordinates divided by change in x-co-ordinates.
That is, slope = change in y-co-ordinates/ change in y-co-ordinates
But here, change in x-co-ordinates is zero since the x-co-ordinates are same for the vertical line given in the graph.
So slope = change in y-co-ordinates/ 0
This is undefined.
So the slope of the line in the graph is undefined.
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help !
Select the correct answer.
What is the measure of an angle that is the complement of angle R? R 80
Answers
Answer: B: 10
Step-by-step explanation:
complementary angles are two angles that add up to 90 degrees
How many pounds of walnuts that cost $.80 per pound must be mixed with 8 pounds of cashews that cost $1.25 per pound to make a mixture of nuts that cost $1.00 per pound?
Answers
How many pounds of walnuts that cost $.80 per pound must be mixed with 8 pounds of cashews that cost $1.25 per pound to make a mixture of nuts that cost $1.00 per pound?
Let
x ------> pounds of walnuts
we have that
0.80x+
what are the coordinates of r, the image of r(-4,3) after s reflection in the line y=x
Answers
Answer:
(3, - 4 )
Step-by-step explanation:
under a reflection in the line y = x
a point (x, y ) → (y, x ) , then
(- 4, 3 ) → (3, - 4 )
Question 7 (2 points) Solve for x.
Round to the nearest hundredth.
cos x = 11.3/16.6
Blank 1:
Blank 2:
Answers
Answer:+0.82 and -0.8
Step-by-step explanation:
HELP ME PLEASE!!! due tonight
Answers
Answer:
y=1x-5
Step-by-step explanation:
Use rise/run
Answer:
[tex]y=x-5[/tex]
Step-by-step explanation:
Just look at the slope and the y-intercept.
The y-intercept is b, and it's -5. The slope is 1, so it is x.
Pls help Me its Due tonight I really struggle and have no time to do this pls help me .
Answers
The factorized polynomial 6x² + 15xy -14x -35y is given as (2x + 5y) (3x - 7)
Factorization of PolynomialsA polynomial is an expression consisting of a sum of a finite number of terms, each term being the product of a constant coefficient and one or more variables raised to a non-negative integer power.
To solve this problem, we simply need to factorize the polynomial given.
[tex]6x^2 + 15xy - 14x - 35y[/tex]
Let's look for a common factor and factorize similar or like terms.[tex]6x^2 + 15xy - 14x - 35y\\(2x + 5y) (3x - 7)[/tex]
This is the the reduced or factorized form of the given polynomial.
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Rigid transformations are used to map the triangle formed by A(0,0),B(3,0),C(3,4) to triangle A ′ B ′ C ′ . If the coordinates of A ′ , B ′ And C′ are A ′ (−2,1) and B ′ (−2,−2) , what are the two possible answer for C’
Answers
The possible coordinates of the point C are : (-6,-2) and (2,-2).
A stiff transition called a rotation involves turning the item around a center point. The direction is changed, but the shape is still oriented in the same way. You can spin a form in any direction. A 180 degree rotation of the triangle is made around point C. A rigorous transition like this one may be seen here.
Rotation and translation are the only two elements of a rigid transformation. It does not alter the size or shape of an input object, nor does it involve reflection.
Hence as the graph shows, the coordinates of C' could be:
(-6,-2) and (2,-2)
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A map ratio is 1:50 000. Two villages
are 8km apart. How far apart are they
on the map?
Answers
Answer: they should be 2cm apart
Step-by-step explanation: This means that 1 cm on the map represents an actual distance of 50 000 cm (or 500 m or 0.5 km). We saw above that if a map has a scale of 1 : 50000, then 1 cm on the map is 50000 cm in real life.
A toy company that makes bubbles fills its 8-ounce bottles using a machine. To check that the machine fills the bottles with the proper amount, the company randomly checks bottles off the assembly line. A bottle passes inspection if the percent error of the amount is 2% or less. What is the range of values that a bottle could contain to pass inspection? Round to the nearest hundredth.
oz to
oz???
Answers
The range of values that a bottle could contain to pass inspection will be 7.840 - 8.160 ounces.
How to calculate the value?It was stated that the toy company that makes bubbles fills its 8-ounce bottles using a machine.
The bottle passes inspection if the percent error of the amount is 2% or less. The minimum range will be:
= 8 ounces - (2% × 8 ounces)
= 8 ounces - 0.16 ounces
= 7.84 ounces
The maximum range will be:.
= 8 ounces + (2% × 8 ounces)
= 8 ounces + 0.16 ounces
= 8.16 ounces.
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The allowable range for the toy company is [7.84, 8.16].
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, the allowable percentage error is 2% or less.
Now, 2% of 8 ounces is,
= (2/100)×8.
= 0.16 ounces.
So, the allowable range is from (8 - 0.16) = 7.84 ounces to
(8 + 0.16) = 8.16 ounces.
As it is being given that it is 2% or less we'll use include the least value too.
So, the allowable range of the bottles is [7.84, 8.16].
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8. Find the value of x if xsin45º. cos45°. tan60° = tan² 45° - cos²60⁰
Answers
The study of the correlations between triangles' side lengths and angles is known as trigonometry. x= 0.11
What is trigonometry?The study of the correlations between triangles' side lengths and angles is known as trigonometry. The field was created in Hellenistic era in the third century BC as a result of the use of geometry in astronomical research. While Indian mathematicians produced the earliest tables of values for trigonometric ratios (also known as trigonometric functions), such as sine, the Greeks concentrated on chord calculation.
Trigonometry has been used historically in the fields like geodesy, surveying, celestial mechanics, and navigation.
Trigonometry has a wide variety of identities. In order to simplify an expression, identify a more practical version of an expression, or solve an equation, trigonometric identities are frequently employed to rewrite trigonometrical expressions.
xsin45º. cos45°. tan60° = tan² 45° - cos²60⁰
x0.7*0.70*1.73 =1*1-0.5*0.5
x = [tex]\frac{0.7*0.70*1.73}{1*1 - 0.5*0.5}[/tex] = 0.11
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Simplify the equation. Show your work.[tex]-i^3^2[/tex]
Answers
[tex]{\Large \begin{array}{llll} i^4=1 \end{array}} \\\\[-0.35em] ~\dotfill\\\\ -i^{32}\implies -i^{4\cdot 8}\implies -(i^4)^8\implies -(1)^8\implies \text{\LARGE -1}[/tex]
Please help i’m begging due in a bit❗️❗️❗️❗️❗️❗️
Answers
3. 300
4. $180
5. $23.75
6. $102.6
Answer: 1 is 300 2 is 180 3 is 23.75 and the fourth one is 102.6
Step-by-step explanation: dont forget to add your $ signsss
A box is in the shape of a right rectangular prism made from cardboard has dimensions of 18 inches, by 12 inches, by 8 inches, as shown in the diagram below. find the volume of the box and show your calculations and use appropriate units
Answers
Volume of the rectangular prism = 1,728 in³
Explanation:Volume of the rectangular prism = width × height × length
width = 12 in
length = 18 in
height = 8 in
Volume of the rectangular prism = 12 in × 8 in × 18 in
Volume of the rectangular prism = 1,728 in³
Properties of equality can be used to justify steps in solving an equation.
Answers
ANSWER:
4x-1=27
or,4x=27+1
or, x=28/4
or, x=7
x = 8.27 rounded to the nearest tenth
Answers
Answer:
x = 8.3
Step-by-step explanation:
We look at the final place of the decimal to round, in this case the thousandths place (underlined)
8.27
If the final place of the decimal is greater than or equal to 5, we round up the decimal to the left, otherwise we round down.
Because 7 > 5, round 2 up to 3, therefore giving 8.3
Answer:
Your answer is 8.3!
Step-by-step explanation:
Step 1: Locate and underline the tenths place (2) then look at the digit to the right (7):
8.27
Step 2: In this case, the digit to the right (7) is 5 or above. So, we add 1 to the tenth place (2). The digit(s) after the (2) are replaced by zeros (or dropped). Thus, we get 8.3 as the answer.
In short: 8.27 rounded to the nearest tenth is 8.3.
PLEASE HELPPPPP
Which graph represents the same relation as the set
♦
5
4
3
2-
1
--5-4-3-2-1₁ 1 2 3 45
-2+
-3
4 9
st²
•
t{(-3,2).(5.5).(3.3).(3.-2)}?
X
Answers
Answer: I think it’s t{(-3,2).(5.5).(3.3).(3.-2)}
Step-by-step explanation:
Eyesight is key m’lady
The first graph represents the same relation as the set {(-3,2).(5.5).(3.3).(3.-2)}
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The given relation is {(-3,2).(5.5).(3.3).(3.-2)}
We have to find the graph which represents the relation of the set
A binary relation on a set may, or may not, hold between two given set members.
The first number in the ordered pair represents the x coordiantes
The second number in the ordered pair represents the y coordiantes
When we match the ordered pairs with the given graphs
The first graph matches with the given relation
Hence, the first graph represents the same relation as the set {(-3,2).(5.5).(3.3).(3.-2)}
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A b c or d in problem below
Answers
The value of the expression will be;
⇒ log₅ (1/25) = - 2
Option D is true.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ log₅ (1/25)
Now,
Solve the expression as;
⇒ log₅ (1/25)
Since, log (a/b) = log a - log b
Hence,
⇒ log₅ (1/25) = log₅ 1 - log₅ 25
Since, log 1 = 0
⇒ log₅ (1/25) = 0 - log₅ 25
⇒ log₅ (1/25) = - log₅ 5²
Since, log a² = 2 log a
⇒ log₅ (1/25) = - 2 log₅ 5
Since, log₅ 5 = 1
⇒ log₅ (1/25) = - 2 x 1
⇒ log₅ (1/25) = - 2
Thus, The value of the expression will be;
⇒ log₅ (1/25) = - 2
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Help me please I need help pleeeeeeeeeeaaaaaaaaaaase help I’ll give brainly
Answers
The Area of a Rectangle as a Sum and as a Product are as follows:
21. Area as sum = 12x + 60
Area as Product = 12(x + 5)
22. Area as sum = 5x + 20
Area as Product = 5(x + 4)
How to find the Area of a Rectangle as a Sum and as a Product?As a product, we can multiply the height and the base of the rectangle.
As a sum, we can estimate the area finding the sum of the areas of each piece of the rectangle.
The missing pieces that will fill into the circles exists shown in the diagram attached below. The Area of a Rectangle as a Sum and as a Product are as follows:
21. Area as sum = 12x + 60
Area as Product = 12(x + 5)
22. Area as sum = 5x + 20
Area as Product = 5(x + 4)
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seven distinct pieces of candy are to be distributed among three bags. the red bag and the blue bag must each receive at least one piece of candy; the white bag may remain empty. how many arrangements are possible?
Answers
Using combination, there are 1932 arrangments possible.
A combination is a mathematical approach that counts the number of potential configurations in a box containing objects, regardless of their order.
In combinations, we can select items in any order. In combinations, the order doesn’t matter.
The combination formula of given as: n! / r!(n-r)!
Each candy would be distributed in three different ways if there were no limits on how many candies might fit in a bag. 3⁷ different ways to distribute the sweets in this scenario. However, only empty blue and red bags count in this scenario.
There are 2⁷ methods to distribute candy if the red bag is left empty.
Similarly, for the blue bag.
Hence there are 2⁷ +2⁷ – 1 ways to distribute candy such that either blue or red bag is empty.
The total amount of circumstances and ways to deliver the sweets
= 3⁷ – (2⁷ + 2⁷ -1)
= 1932
Therefore, there are a total of 1932 arrangements possible.
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