The considered decimal number is expressed by the fraction given by: Option C: 4/33
How to convert from decimal to fraction?For conversion from decimal to fraction, we write it in the form a/b such that the result of the fraction comes as the given decimal. Usually, to get the decimal of the form a.bcd, we count how many digits are there after the decimal point (if its finite), then we write 10 raised to that many power as denominator, and the considered number without any decimal point as numerator.
For example:
[tex]0.99 = \dfrac{99}{10^2} = \dfrac{99}{100}[/tex]
(10 raised to power k = 1 followed by k zeroes)
What is the sum of an infinite geometric series?The sum of an infinite geometric series having the initial term "a" and the multiplication per term is done by "r" such that r < 1
is given by
[tex]S_{\infty} = \dfrac{a}{1-r}[/tex]
The series would look like [tex]a+ ar+ ar^2+\cdots[/tex]
For the considered case, the given decimal number is
[tex]0.\overline{12} = 0.121212\cdots[/tex]
We can check all the options available one by one, so as to know which one ends up giving this pattern, or we can use another technique as shown below.
[tex]0.12121... = (0.1 + 0.001 + 0.00001 + ... ) + (0.02 + 0.0002 + 0.000002 + ... )[/tex]
Each of the two series obtained are geometric series with the multiplication factor as 1/100
Using the sum formula for evaluation of an infinite geometric series, and the fact that initial term of first series is 0.1 and that of second series is 0.02, we get:
[tex]0.121212... = \dfrac{0.1}{1-1/100} + \dfrac{0.02}{1 - 1/100} = \dfrac{1}{99/100}(\dfrac{1}{10} + \dfrac{2}{100})\\0.121212... = \dfrac{100}{99}\times(\dfrac{10}{100} + \dfrac{2}{100})\\\\\\0.121212 ... = \dfrac{12}{99} = \dfrac{4}{33}[/tex]
Thus, the considered decimal number is expressed by the fraction given by: Option C: 4/33
Learn more about geometric series here:
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Answer:
4/33
Step-by-step explanation:
Option C
In the adjoining figure curved surface area and length of side of equilateral triangle are 1080cm ^ 2 and 12cm. Find the height of triangular prism.
no-one can do this! if you can ,,do it ,,
[tex]\\ \rm\rightarrowtail 36h=1080[/tex]
[tex]\\ \rm\rightarrowtail h=1080/36[/tex]
[tex]\\ \rm\rightarrowtail h=30cm[/tex]
we know that,
CSA of a Triangular prism
CSA⇢ perimeter of base x height1080cm²⇢12+12+12 x height
1080cm²⇢36cm x height
height⇢ 1080cm²/ 36cm
height ⇢ 30cm
Hence ,the height of the given triangular prism would be 30cm
If u get it right I guess brainliest and 100 points and 5 star
Answer:
Point C
Step-by-step explanation:
Hope it helps you in your learning process.
Answer:
The answer is Point C
Step-by-step explanation:
Where they first intersect is point C A intersection is a point or line common to lines or surfaces that intersect.
Hope this helps mark brainiest please :)
Solve the inequality and graph the solution on the line provided.
3 + 2x > 5
Answer:
x>1
Step-by-step explanation:
In order to do this, we can take the inequality:
3+2x>5
now there are constants on both sides meaning we can combine them like the following:
3+2x>5
-3 -3
------------
2x>2
Now we can simplify
2x/2>2/2
therefore, the answer is x>1
In order to graph this on a line you would need to put in a circle which is not filled in because x isn't equal to and greater than 1 so we put in a blank circle and since x is always going to be greater than 1, we would put a line that keeps going on.
You would put this line to the right of 1
o----------->
1 2 3 4 5 6
that is how the line would look like
What was the difference in profits between the two companies for the year 2000?
Profits
Dollars
70,000
60,000
50. 000
40,000
30,000
20,000
10. 000
Key
Company A
• Company B
0
2000
2001
2002
2003
2004
2005
2006
2007
Year
Pick one of these
$70,000
$10,000
$60,000
$80,000
Please please help me please please help me
Will give brainly
Answer:
10,000
Step-by-step explanation:
I think it is the right answer
Answer:
60,000
Step-by-step explanation:
A cylinder has a volume of 400 cubic feet. If the height of the cylinder is 25 feet, what is the radius of the cylinder? Use 3. 14 for π and round to the nearest hundredth.
The radius of the cylinder will be [tex]r=2.25ft[/tex]
What will be the radius of the cylinder?It is given that
[tex]Volume of the cylinder = 400 ft^{3}[/tex]
[tex]height of the cylinder= 25 ft^{3}[/tex]
Now we know that
[tex]Volume of the cylinder = \pi r^{2} h[/tex]
putting values in the formula
[tex]400= \pi \times r^{2} \times25[/tex]
[tex]r= \dfrac{4}{\sqrt{3.14} }[/tex]
[tex]r=2.25 ft[/tex]
Thus the radius of the cylinder will be [tex]r=2.25ft[/tex]
To learn more about the Volume of the cylinder follow
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HELP I NEED THIS BY 9:30
Angel is 3 years younger than seven times Nancyś age. If Angel is 25, how old is Nancy?
Answer: Look at description please
Step-by-step explanation:
Nancy would be 4 years old
Make the equation
7n-3=25
add 3 to both sides
7n=28
n = 4
Therefore making Nancy 4 years old.
*Let me know if I am worng*
Hope this helps :)
Angel is 3 years younger than seven times Nancyś age and if Angel is 25 then Nancy is 4 years old.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that Angel is 3 years younger than seven times Nancyś age.
Let N be Nancy's age.
We know that Angel's age is 7N - 3.
We also know that Angel is 25.
So we can set up the equation: 7N - 3 = 25.
7N-3=25
Add 3 on both sides to isolate N
7N=28
Divide both sides by 7
N=4
Hence, if Angel is 25 then Nancy is 4 years old.
To learn more on Equation:
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#SPJ2
Find the length of WY
Answer:
WY = 180
Step-by-step explanation:
the diagonals of an isosceles trapezoid are congruent , so
ZX = WY , that is
8y - 4 = 7y + 19 ( subtract 7y from both sides )
y - 4 = 19 ( add 4 to both sides )
y = 23
Then
WY = 7y + 19 = 7(23) + 19 = 161 + 19 = 180
Solve 3 x 4/5 pls help me
Answer:
2.5 OR 2 1/2
Step-by-step explanation:
PEMDAS
P: PARENTHESES
E: EXPONENT
M: MULTIPLICATION
D: DIVISION
A: ADD
S: SUBTRACT
3X4 15
12÷5= 2.5
ANSWER:2.5
When the polynomial p(x) = x^3+ ax^2+ bx+ 3 is divided by x+3, the remainder is 9.
a. Given that p(1) = 1. find a and b
b. Find the remainder when p(x) is divided by x-4
Answer:
a = 3, b = 8
Step-by-step explanation:
Since x+3 is a factor, x=-3 is a root. => f(−3)=2(−3)3+a(−3)2−b(−3)+3=0
=> 9a+3b=51 => 3a+b=17 — (1)
x-2 leaves a reminder of 15 => f(2)=2(2)3+a(2)2−b(2)+3=15
=>4a−2b=−4=>2a−b=−2 —- (2)
Adding (1) & (2), 5a=15=>a=3
Substituting the value of a in (1), b=8
what does y = x - 20 tell you about the relationship between x and y?
Answer:
LINEAR
Step-by-step explanation:
y depends on x. x is considered to be the independent variable.
the relationship is LINEAR
Josie is looking for a new part time job as a painter. She responds to a classified ad for a position that pays 38.2K. What would her weekly salary be to the nearest cent if she gets this job? Show work
Answer:
73461.53 Cents
Step-by-step explanation:
There are 52 weeks/yr
1k = 100,000 cents
Salary/week:
[tex] \frac{38.2}{52} \times 100000[/tex]
= 0.7346153 x 100000
Salary/Week = 73461.53 Cents
If the angle of elevation of the sun is 63° and the flagpole casts 27-foot shadow, how tall is the flagpole?
Answer:
Step-by-step explanation:
To help you solve
Use the fact that (height of flagpole)/(length of shadow) = tan(angle of elevation).
Solve. Use the strategy "work backward."
Larissa said, "If you multiply my age by 3, subtract 6 from the product, then divide the difference by 5, the result is 9." What is Larissa"s age?
Let that be x
ATQ
[tex]\\ \rm\Rrightarrow 3x-6/5=9[/tex]
Arrange accordingly to work backwards(Every thing is reversed)
[tex]\\ \rm\Rrightarrow 9(5)+6/3=x[/tex]
[tex]\\ \rm\Rrightarrow 45+6/3=x[/tex]
[tex]\\ \rm\Rrightarrow 51/3=x[/tex]
[tex]\\ \rm\Rrightarrow x=17[/tex]
.
Carrot is 5 in his but every minute gangs a inch how big would it be in 10 minutes
15 inches.
Step-by-step explanation:
solve the equation 3y/2 - 4 > 4/5 + 7y/10.
Answer:
y>6
Step-by-step explanation:
^^
Answer:
y > 6
Step-by-step explanation:
3 x [tex]\frac{y}{2}[/tex] - 4 > [tex]\frac{4}{5}[/tex] + 7 x [tex]\frac{y}{10}[/tex]
---
Subtract 7 [tex]\frac{y}{10}[/tex] from both sides
3 x [tex]\frac{y}{2}[/tex] - 4 - 7 x [tex]\frac{y}{10}[/tex] - 7 x [tex]\frac{y}{10}[/tex] (simplify) -> [tex]\frac{4y}{5}[/tex] - 4 > [tex]\frac{4}{5}[/tex]
Add 4 to both sides
[tex]\frac{4y}{5}[/tex] - 4 + 4 > [tex]\frac{4}{5}[/tex] + 4 (simplify) -> [tex]\frac{4y}{5}[/tex] > [tex]\frac{24}{5}[/tex]
Mulitply both sides by 5
[tex]\frac{5x4y}{5}[/tex] > [tex]\frac{24 x 5}{5}[/tex] (simplify) -> 4y >24
Divide both sides by 4
[tex]\frac{4y}{4}[/tex] > [tex]\frac{24}{4}[/tex] (simplify) -> y > 6
I need help with this question please.
Answer:
the second one
Step-by-step explanation:
Westside high’s 2015 senior-class science enrollment is summarized by the venn diagram. chemistry, biology, and physics class enrollments are denoted by the sets c, b, an p, respectively. how many students are in the 2015 senior class? how many students are taking chemistry and biology, but not physics? how many students are not taking science?
There are 63 students are in the 2015 senior class, 5 students who are taking chemistry and biology, but not physics, and 18 students who are not taking science.
What is the Venn diagram?A Venn diagram is a graphic that employs circles to depict connections between objects or finite groups of objects.
Circles that overlap share characteristics, but circles that do not overlap do not.
In the Venn diagram the following data is observed;
Chemistry - 9
Biology - 11
Physics - 7
Biology+Chemistry- 5
Biology+Physics - 4
Physics+Chemistry -6
Physics+Chemistry+Biology-3
None of the three - 18
Total -- 63
We can clearly see from the table that the grand total of the table of data is the total number of pupils in the senior class. In other words, the total number of people is 63.
In addition, there are 7 students who are taking chemistry and biology but not physics.
The number of students who do not take science is equal to the number of students who do not take biology, chemistry, or physics, i.e. the 18 students outside the circle.
There are 63 students are in the 2015 senior class
There are 5 students who are taking chemistry and biology, but not physics.
There are 18 students who are not taking science.
Hence there are 63 students are in the 2015 senior class, 5 students who are taking chemistry and biology, but not physics, and 18 students who are not taking science.
To learn more about the Venn diagram refer to the link;
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At Hippo Burger, Ava and Mia's meal cost $25.60. They left a 20% tip. how much tip did they leave? whats the total?
Answer:
5.12$
Step-by-step explanation:
I know this because when your dealing with 20% think of it like 1/5.
Know 1/5 of 25.60 is 5.12 how I can calculate this is by timesing 5.12 by 5.
Here is what is would look like.
5.12 x 1=5.12$
5.12 x 2=10.24$
5.12 x 3=15.36$
5.12 x 4=20.48$
5.12 x 5=25.60$
And there's your answer(the last one by the way:))
If you want another example based upon 1/5 and 20% then say they were
30 cows and 30 horses 1/5 of them or 20% of them are sitting how many are sitting.
And since it is 1/5 what times 5 would=60 ?
It would be 12 so 20% of 60 is 12, do you understand what I am saying.
Hope this helps have a great day:)
What is the value of the 24th term is the fourth term is 6 and the eighth term is 8
A. 24
B. 16
C. 8
D. 4.5
The value of the 24th term is 16.
Arithmetic progression:aₙ = a + (n - 1)dwhere
a = first term
d = common difference
n = number of terms
Therefore,
6 = a + 3d
8 = a + 7d
let's find a and d
2 = 4d
d = 2 / 4
d = 1 / 2
6 = a + 3 / 2
a = 6 - 3 /2
a = 4.5
Therefore, the 24th term can be found as follows;
24th term = 4.5 + 23(0.5)
24th term = 4.5 + 11.5
24th term = 16
learn more on arithmetic progression here; https://brainly.com/question/9882454
find the slope between (6,10) and (4,-2)
Answer:
6
Step-by-step explanation:
y2 - x1 / x2 - x1
10 - (-2) / 6 - 4
10 + 2 / 2
12 / 2
6
Determine the type of fee that will be charged in each situation. Lisa sold 50 shares of stock A on a given day. Her broker charged her $12 for this trade. Reggie’s broker charged him a front-end load of 2. 75% when he purchased a fund. John’s broker provided him with stock-trading software to manage his trading. Pete isn’t a regular investor. He hasn’t bought or sold any stock this year. His broker charged him an inactivity fee of $75 for the year. Joanne’s brokerage firm charged her for providing investment information
Answer:
Transaction Fee
- Lisa sold 50 shares of stock A on a given day. Her broker charged her $12 for this trade.
- Reggie’s broker charged him a front-end load of 2.75% when he purchased a fund.
Non-Transaction Fee
- Joanne’s brokerage firm charged her for providing investment information to help her make informed choices.
- Pete isn’t a regular investor. He hasn’t bought or sold any stock this year. His broker charged him an inactivity fee of $75 for the year.
- John’s broker provided him with stock-trading software to manage his trading.
Step-by-step explanation:
I am really bad at math so I need help
Answer:
What are we supposed to find
General Sherman led his army 425 miles in 50 days. Calculate the rate his army traveled in miles per day.
Answer:
8.5 miles per day
Step-by-step explanation:
divide 425 by 50 and boom u got the answer
1. An airplane moves at a constant speed of 120 miles per hour for 3 hours. How many miles does it go?
2. A train moves at a constant speed and travels 6 miles in 4 minutes. What is its speed in miles per minute?
3. A car moves at a constant speed of 50 miles per hour. How many hours does it take the care to go 200 miles?
Answer:
1. 360 miles
2. 1.5m/m
3. 4 hours
Step-by-step explanation:
1. d (distance) = v (speed) x t (time)
d = 120 x 3
d = 360
2. v = d/t
v = 6/4
v = 1.5
3. t = d/v
t = 200/50
t = 4
A farm lets you pick 3 pints of raspberries for $12.00.
A. what is the cost per pint?
B. How many pints do u get per dollar
C. At this rate how many pints can you afford for 20.00
D. At this rate how much will 8 pints raspberries cost
Can someone help me with this please???
Brainlyest if you help me lol
The mass of a freight train is 9.98 • 106 kilograms. The mass of an aircraft carrier is 7.3 • 107 kilograms. Approximately how many more kilograms is the mass of an aircraft carrier than the mass of a freight train? Show your work and write your answer in scientific notation. (10 points)
Expand the mass of each:
Freight train: 9.98 x 10^6 = 9,980,000 kg
Aircraft carrier: 7.3x10^7 = 73,000,000 kg
Now subtract:
73,000,000 - 9,980,000 = 63,020,000 kg
Convert to scientific notation: 6.302 x 10^7 kg
The pyramid below has a square base. Work out the volume of the pyramid
Answer:
17.2 x 17.2 =area of base. ( B x H) = 295.84
295.84 x 24.4 (perpendicular height) = 7218.496
7281.496 x 1/3 ( or divide by three) = 2406.1653
Not sure how many dp you need.
a rectangular parking lot that is 3 feet longer that is wide has an area of 550 square feet how many feet long is the parking lot?
Answer:
The parking lot is 25 feet long and 22 feet wide
Step-by-step explanation:
Let's say the rectangle is [tex]x[/tex] feet long. It means it has to be [tex]x+3[/tex] feet wide.
Knowing it's area we can write an equation for the unknown:
[tex]x(x+3) = 550\\x^2+3x-550 = 0\\x= \frac12(-3\pm\sqrt{2209})\\x_1=-25: x_2=22[/tex]
Since we're talking about measures of length, the negative answer is obviously not interesting, so we're left with [tex]x=22[/tex]
Each patron pays an annual fee of $36 to the library. If the library collects $20,304 from the annual fee, how many patrons are there?
Answer:
564 patrons.
Step-by-step explanation:
20,304/36 = 564
∠A and \angle B∠B are supplementary angles. If m\angle A=(8x-27)^{\circ}∠A=(8x−27)
∘
and m\angle B=(4x+3)^{\circ}∠B=(4x+3)
∘
, then find the measure of \angle A∠A.
i
Answer:I don know
Step-by-step explanation:
Yor welcome