write 0.216 as a rational number in lowest terms

Answers

Answer 1

Answer:

[tex]=\frac{27}{125}[/tex]

Step-by-step explanation:

[tex]0.216[/tex]

[tex]\mathrm{Multiply\:and\:divide\:by\:10\:for\:every\:number\:after\:the\:decimal\:point.}[/tex]

[tex]\mathrm{There\:are\:}3\mathrm{\:digits\:to\:the\:right\:of\:the\:decimal\:point,\:therefore\:multiply\:and\:divide\:by\:}1000[/tex]

[tex]=\frac{0.216\cdot \:1000}{1000}[/tex]

[tex]=\frac{216}{1000}[/tex]

[tex]216,\:1000[/tex]

[tex]\mathrm{The\:GCD\:of\:}a,\:b\mathrm{\:is\:the\:largest\:positive\:number\:that\:divides\:both\:}a\mathrm{\:and\:}b\mathrm{\:without\:a\:remainder}[/tex]

[tex]2,\:3\mathrm{\:are\:all\:prime\:numbers,\:therefore\:no\:further\:factorization\:is\:possible}[/tex]

[tex]=2\cdot \:2\cdot \:2\cdot \:3\cdot \:3\cdot \:3[/tex]

[tex]2,\:5\mathrm{\:are\:all\:prime\:numbers,\:therefore\:no\:further\:factorization\:is\:possible}[/tex]

[tex]=2\cdot \:2\cdot \:2\cdot \:5\cdot \:5\cdot \:5[/tex]

[tex]\mathrm{The\:prime\:factors\:common\:to\:}216,\:1000\mathrm{\:are\:}[/tex]

[tex]=2\cdot \:2\cdot \:2[/tex]

[tex]\mathrm{Multiply\:the\:numbers:}\:2\cdot \:2\cdot \:2=8[/tex]

[tex]=8[/tex]

[tex]=\frac{8\cdot \:27}{8\cdot \:125}[/tex]

[tex]\mathrm{Cancel\:the\:common\:factor:}\:8[/tex]

[tex]=\frac{27}{125}[/tex]

Hence, the correct answer is [tex]=\frac{27}{125}[/tex]


Related Questions

can i have some help please

Answers

Answer:

117

Step-by-step explanation:

38 + x + y = 180

x + y = 142

180 - 101 = 79

x + 79 = 142

x = 63

180 - 63 = 117

Have an amazing day!!

PLEASE RATE AND MARK BRAINLIEST!!!

One bottle of lemonade contains 8 ⅕ squeezes of lemon. How many squeezes of lemon would ¾ of a bottle of lemonade need?

Answers

Answer:

You need a 6 squeezes of lemon.

Step-by-step explanation:

If 1 bottle contains 1/4 , you need a 2 squeezes of lemon.

4 lemons if 1/2

6 lemons if 3/4.

8 squeezes if 1 bottle

#BrainliestBunch

Answer:

6 Lemons that you have to squeeze.

Step-by-step explanation:

#BrainliestBunch

Anyone know any of these

Answers

Answer:

I'm surprised to inform you that yes, yes I do.

Step-by-step explanation:

If you didn't know, all those lines stand for something. Stand for an equation.

For example, let's take the first line shown, question number 5.

The line moves down on the number line, going from 4 all the way down to -6.

Since the dot is filled in, that means that the line includes 4, which means our answer's greater than or lesser than sign should have a line under it, meaning "or equal to".

A is the only reasonable answer for question 5, because it reads "X (which you could substitute for any point in the blue line) is less than or equal to 4."

If we use what we learned from question 5 for the next 3 questions, we could rightly say that the answer to 6 is D, the answer to 7 is C, and the answer to 8 is B.

If I'm wrong on any of these, feel free to scream profanities. Wouldn't be the first time.


What is the midpoint of the segment with endpoints (5,2) and (4,1)?

Answers

The answer is provided in the image.

Please mark as Brainliest.

A vehicle purchased for $ 29800 depreciates at a constant rate of 6 %. Determine the approximate value of the vehicle 12 years after purchase.
how do i solve this

Answers

Answer:

$14,182.43

Step-by-step explanation:

we have the equation [tex]29800(.94)^12[/tex] that is supposed to be to the 12th power. but we have the .94, since the 6% is a negative. a good starting point is always 1.00, since 1=100, and if it was increasing in value, it would be 1+.06, and if it was negative like this, it would be 1-.06, which is the .94 that we have. and we put it to the 12th power because there are 12 years, and it only depreciates once per year. hope this helps, please mark as brainlest.

The function f(x) = 2(3.5)x is reflected across the x-axis to create g(x). what is the function definition of g(x)? g(x) = (3.5x) what is the initial value of g(x)? what are the outputs for inputs of –1 and 1 in g(x)? g(−1) = g(1) =

Answers

1) The reflected function [tex]g(x)=-2(3.5)^x[/tex] is defined everywhere.

2) Initial value of g(x) or g(0) is 1

3) Value of g(1) is -7

4) Value of g(-1) is -4/7

The given function is:

[tex]y=2(3.5)^x[/tex]

How reflection about the x-axis takes place?

We know that when a function is reflected about the x-axis,

y becomes -y while x is unchanged.

So, the reflection of [tex]y=2(3.5)^x[/tex] about x-axis is:

[tex]-y=2(3.5)^x[/tex]

[tex]y=-2(3.5)^x[/tex]

[tex]g(x)=-2(3.5)^x[/tex]

g(x) is an exponential function defined everywhere.

[tex]g(0) =-2[/tex]

[tex]g(1) =-7[/tex]

[tex]g(-1) =-\frac{4}{7}[/tex]

Therefore, 1) The reflected function [tex]g(x)=-2(3.5)^x[/tex] is defined everywhere.

2) Initial value of g(x) or g(0) is 1

3) Value of g(1) is -7

4) Value of g(-1) is -4/7

To get more about reflections visit:

https://brainly.com/question/1976264

Answer:

1. g(x) = -2 (3.5x)

2. -2

3. g(−1) = 0.57

4. g(1) = -7

Step-by-step explanation:

If someone were unable to pay cash right now, which financing option would be best for the laptop and for the refrigerator? rent-to-own; installment installment; rent-to-own rent-to-own; rent-to-own save up and pay cash

Answers

The lowest is the cash price for other options, you have to pay more for a laptop and refrigerator. Then the suitable method is to save up and pay cash.

What is decision-making?

The process of making choice is by identifying the correct decision, gathering information, and assessing alternative solutions.

If someone were unable to pay cash right now then the suitable method will be

For laptop:

Rent to own payments will be

$150 each month for 12 months, then the total becomes

⇒ 150 × 12 = $1800

The installment plan will be

$100.83 each month for 12 months, then the total becomes

⇒ 100.83 × 12 = $1209.96

The cash price is $1000. So, the lowest is the cash price for other options you have to pay more.

For refrigerator:

Rent to own payments will be

$140 each month for 12 months, then the total becomes

⇒ 140 × 12 = $1680

The installment plan will be

$80.67 each month for 12 months, then the total becomes

⇒ 80.67 × 12 = $968.04

The cash price is $800. So, the lowest is the cash price for other options you have to pay more.

More about the decision-making link is given below.

https://brainly.com/question/3369578

Work out the area of the triangle.
Give your answer correct to 1 decimal place.
105°
13 cm
10 cm

Answers

The area of the triangle is 62.8 Square cm

How to determine the area of the triangle

The figure represents the given parameter

From the figure, we have the following values

a = 10 cm

b = 13 cm

C = 105 degrees

The area of the triangle is calculated using the following area formula

Area = 1/2absin(C)

Substitute the known values in the above equation, so, we have the following representation

Area = 1/2 * 10 * 13 * sin(105 degrees)

Evaluate

Area = 62.8

Hence, the area is 62.8 Square cm

Read more about area at

https://brainly.com/question/25292087

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whats the medain range and mean for the numbers 36,4,40,11,9,12,8,4,16

Answers

Answer:

mean 15 5/9,  medain 11

Step-by-step explanation:

21(2 - x) + 12x = 44
I need y’all to check the steps for me pls I don’t need the answer just the check steps thxs


Answers

Answer:

Step-by-step explanation:

21(2 - x) + 12x = 44

42-21x+12x=44

42-9x=44

-42 -42

-9x=2

X=-2/9

Answer:

x = 2/33

Step-by-step explanation:

21 x 2 - 21 x x + 12 x x = 44

42 - 21x + 12x = 44

42 - 33x = 44

-33x = 44 +42

-33x = 86

x = -86/33

PS: I am not sure of the answer, but the steps should be reliable

What is the simplified form of this expression?

18 ÷ 6 + 8 × 7 – 12 + 8 × 2

A
62

B
63

C
81

D
146
help asap im being timed

Answers

Answer:

the answer is b

Step-by-step explanation:

first i did 18 divided by 6=3

then 8x7=56

3+56=59

59-12=47

8x2=16

47+16=63

Answer:

B.) 63

Step-by-step explanation:

18 divided by 6 = 3

8x7=56

3+56=59

59-12=47

8x2=16

47+16=63

The Goodyear blimp flies 153 miles with a tailwind (with the wind) in the same time it travels 57 miles with a headwind (against the wind). If the speed of the wind is 16 mph, what is the speed of the blimp in still air?

Answers

Using the relation between velocity, distance and time, it is found that the speed of the blimp in still air is of 35 mph.

What is the relation between velocity, distance and time?

Velocity is distance divided by time, that is:

[tex]v = \frac{d}{t}[/tex]

153 miles with a tailwind (with the wind), that is, with a velocity of v + 16, so:

[tex]v + 16 = \frac{153}{t}[/tex]

[tex](v + 16)t = 153[/tex]

[tex]t = \frac{153}{v + 16}[/tex]

57 miles with a headwind (against the wind), that is, with a velocity of v - 16, hence:

[tex]v - 16 = \frac{57}{t}[/tex]

[tex](v - 16)t = 57[/tex]

[tex]t = \frac{57}{v - 16}[/tex]

Since the times are equal, we have that:

[tex]\frac{153}{v + 16} = \frac{57}{v - 16}[/tex]

153(v - 16) = 57(v + 16)

96v = 3360

v = 3360/96

v = 35.

The speed of the blimp in still air is of 35 mph.

More can be learned about the relation between velocity, distance and time at https://brainly.com/question/24316569

Can someone please help me asap? I’ll mark brainlist!!!

Answers

Multiply the price by 40%

700 x 0.40 = 280

40% off would be $280, which is greater than $150

40% off is the better price.

Answer:

40% off is the better price

Step-by-step explanation:

Find out what 40% off $700 is, so you can compare the two offers:         40% × 700 = $280$280 is more than $150, so 40% is the better deal.

I hope this helps!

what is a simple definition for a function in math?

Answers

Answer:

Related order pairs that have one value from the second components of the order pain.

Hoped this worked :3

Answer:

A simple definition for a function in math is a relation between two quantities that has exactly one output value for each input value.

Step-by-step explanation:

Some other definitions you may need to know to understand the function definition is an input is a value that is put into a relation and an output is a value that results from putting an input into a relation. Lastly, a relation is a relationship between two sets of values, inputs, and outputs.  

I hope this helps you! :)

Jose invested $8,000 in an account paying an interest rate of 7 3 8 7 8 3 ​ % compounded daily. Adam invested $8,000 in an account paying an interest rate of 7 7 8 7 8 7 ​ % compounded annually. To the nearest dollar, how much money would Jose have in his account when Adam's money has tripled in value?

Answers

Answer:

Jose would have accumulated $23,325.21

Step-by-step explanation:

Giving the following information:

The interest rates are not clear. If they are not correct, replace them in the formulas.

Jose:

Initial investment= $8,000

Interest rate= 7.38 compounded daily.

Adam:

Initial investment= $8,000

Interest rate= 7.78% compounded annually.

Future value= 8,000*3= 24,000

First, we need to calculate the time required for Adam to triple its investment.

n= ln(FV/PV) / ln(1+i)

n= ln(24,000/8,000) / ln(1.0778)

n= 14.66 years

It will take Adam 14.66 years to triple the investment.

Now, the future value for Jose:

FV= PV*(1+i)^n

PV= 8,000

i= 0.0738/365= 0.0002

n= 14.66*365= 5,351 days

FV= 8,000*(1.0002^5,351)

FV= $23,325.21

Jose would have accumulated $23,325.21

Answer:

$23294

Step-by-step explanation:

im smart

deltamath gang

Jamal measured a house and its lot and made a scale drawing. The scale he used was 2 inches : 1 foot. In the drawing, the porch is 30 inches wide. What is the width of the actual porch? feet​

Answers

Answer:

15 feet

Step-by-step explanation:

since its 2 inches to 1 foot, just divide the 30 inches by 2 to get 15 feet

please help me to understand

Answers

Answer:

x = 57

Step-by-step explanation:

1. Look at the expression (x + 22). It's measurement the upper side of the lines. We know that if we add up all sides, we will get a full circle, or a value of 360. We know that if I extend the blue line to the left on the upper parallel line, it would equal 180 degrees.

We can express this as x + 22 = 180. Now lets look at the bottom equation, notice that the 2x - 13 is the missing side of x + 22. So we know:

x + 22 + 2x - 13 = 180

3x + 22 - 13 = 180

3x + 9 = 180

3x = 171

x = 57

2. We can check this by plugging it into our formula. x + 22 and 2x - 13. so 57 + 22 = 79 and 2(57) - 13 = 101. Add them together: 79 + 101 = 180.

3. We know this is true because both angles combined will be to form 180 degrees. For a better understanding, view the image I sent you. 1 = 3, and 4 = 2. Opposite angles are equal. In your equation, we have 3 and 8. we KNOW that 8 = 2. And we also know that adding up 2 + 3 MUST equal 180 degrees.

I hope this helps!

45 POINTS WILL BE MARKED BRAINLIEST IF ANSWERED CORRECTLY!!!!!
Rewrite the following as the square of a binomial if possible
x^2+x+y^2

Answers

Answer:

(x + y)^2 - 2xy

A new song has gone viral on the Internet. The website hosting the song uses the function f(t) = 2002t^2 to represent the number of daily hits over time, where t is time in days. Use the function to predict the day on which the number of daily hits reaches 1,000,000.

Answers

After 22 days and 8 hours (0.349×24 hours) and 22 minutes (0.376×60 minutes) and 34 seconds (0.56×60 ≈ 34), the number of daily hits reaches 1,000,000.

It is given that the website hosting the song uses the function:

[tex]\rm f(t) = 2002t^2[/tex]    to represent the number of daily hits over time, where t is time in days.

It is required to predict the day on which the number of daily hits reaches 1,000,000.

What is a function?

It is defined as a special type of relationship and they have a predefined domain and range according to the function.

We have a function:

[tex]\rm f(t) = 2002t^2[/tex]

When f(t) = 1,000,000 then what will be the value of 't'

Simply:

[tex]\rm 1,000,000 = 2002t^2\\\rm 499.500 = t^2\\\rm \sqrt{499.500} = t\\\rm t = 22.349\ Days[/tex]

t = 22 days and 8 hours (0.349×24 hours) and 22 minutes (0.376×60 minutes) and 34 seconds (0.56×60 ≈ 34).

Thus, after 22 days and 8 hours (0.349×24 hours) and 22 minutes (0.376×60 minutes), and 34 seconds (0.56×60 ≈ 34), the number of daily hits reaches 1,000,000.

Learn more about the function here:

https://brainly.com/question/5245372

The day on which the number of daily hits of the considered song for the specified website reaches 1,000,000 is 23rd day.

How to evaluate a given mathematical expression with variables if values of the variables are known?

You can simply replace those variables with the value you know of them and then operate on those values to get a final value. This is the result of that expression at those values of the considered variables.

So, suppose the day is t = d (dth day from the launch of the song) on which the daily hits reaches 1,000,000.

Then, evaluating the function [tex]f(t) = 2002(t^2)[/tex] at t = d should give us 1000000

Putting it, we get:

[tex]f(d) = 1000000\\2002(d^2) = 1000000\\\\\text{Dividing both the sides by 2002}\\\\d^2 = \dfrac{1000000}{2002}\\\\d = \sqrt{\dfrac{1000000}{2002}}\approx 22.35[/tex]

So after 22th day, ie on 23rd day (as 22.35 = 22 + 0.35 which shows 23rd day is still not completed) of the launch of the song, the number of daily hits reaches 1,000,000.

Thus, the day on which the number of daily hits of the considered song for the specified website reaches 1,000,000 is 23rd day.

Learn more about evaluating a function at a value  here:

https://brainly.com/question/2753269

Find the number that is between 0 and 120, is even, is a multiple of 5 and is the result of multiplying one of the counting numbers by itself

Answers

I think the answer is 2

.087 in scientific notation?​

Answers

Answer:

[tex] 8.7 \times {10}^{ - 2} [/tex]

Step-by-step explanation:

[tex].087 = 8.7 \times {10}^{ - 2} \\ [/tex]

The scientific notation is 8.7 x 10^-2.

angles.
4. Use the protractor to measure these
angles:
mAJK =
mBKJ =
mCLJ=

Answers

Answer:

m<AJK = 90 degrees

m<BKJ = 90 degrees

m<CLJ = 90 degrees

The line of the reflection has been returned to its original position.  Use the ruler to measure these two segments.

BK = 2.2 units

KB' = 2.2 units

Record the lengths of these segments.

AJ = 5.6 units

JA' = 5.6 units

Record the lengths of these segments.

CL = 3.8 units

LC' = 3.8 units

Which segments have equal lengths?

corresponding segments

Change the position of the line of reflection.  Does the line of reflection appear to be a perpendicular bisector of the segments that connect corresponding vertices?  

Yes

Answer:

they are all 90

Step-by-step explanation:

edg 2021

6
Answer:
How much
Jan borrowed $1,200 at 11.5% interest for three months.
does she have to repay under a single-payment plan?
a. $13
b. $1,238.50
c. $1,246
d. $1,234.50

Answers

Answer:

Step-by-step explanation:

First, convert percent to decimal:

11.5% = 0.115

Multiply by amount borrowed:

0.115*1200= 138

Multiply interest amount per month (138) by 3

138*3 =$414.00 interest

1242.

Name hypothesis and conclusion. Write converse.
1) When my clothes are dirty, then I have to do laundry

Answers

If my clothes are clean, then I do not have to do laundry.
The hypothesis is that if you wash your clothes then you do not have to do laundry.

Pls answer the question attached.
I WILL MARK U BRAINLIST

Answers

Answer:

First, we will find the coordinates of ABCD:

A: (1,1)

B: (1,4)

C: (4,6)

D: (5,3)

Now we will find the coordinates of PQRS:

P: (5,5)

Q: (8,6)

R: (7,4)

S: (7,2)

Have a great day!!

Pleas rate and mark brainliest!!

To find a coordinate of a vertice, we see the point that the x axis and the y axis intersect. And it's written in the form of (x;y - x axis first, y axis second)

Polygon 1 :
B vertice : (1;4)
A vertice : (1;1)
C vertice : (4;6)
D vertice : (5;3)

Polygon 2 :

P vertice : (5;5)
Q vertice : (8;6)
R vertice : (7;4)
S vertice : (7;2)

40x - 20x - 20(blank-blank)

Answers

Answer:

=20x-20

Step-by-step explanation:

40x-20x=20x

20x-20

=20x-20

NEED HELP ASAP!!!!!!

Answers

After 2 hours : 9 inches left

Why it take much longer time ghan the time calculated

Answers

Answer:

for what bro

Step-by-step explanation:

please mark me as brainlest

What do you mean? Attach a picture

Which of the following is the equation for the line perpendicular to the line y= -x + 20 that passes through the point (-4, 2)?

A. Y = x + 6
B. Y = -x - 2
C. Y = -x + 6
D. Y = x - 2

Answers

Answer:

Step-by-step explanation:

A 10= 4 plus 6

A construction company needs to remove 4 3/4 tons of dirt from a construction site. they can remove 5/6 tons of dirt each hour. What os the total number of hours will take to remove the dirt? ( write your answer as a mixed number in simplest form )

Answers

Answer:

5.7 hours

Step-by-step explanation:

Divide 4 3/4 by 5/6 hope this helps! :)

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The marketing manager at a local chain supermarket is testing the effectiveness of four advertising strategies (Factor A) on sales, and runs the advertising over a two-week period. It is suspected that sales also differs by store locations because of differing customer traffic; therefore, the stores were blocked on location (Factor B). The manager wants to understand how sales depends upon advertising strategy and location using a two-way ANOVA without interaction. The sales (in $1000s), along with column, row, and overall means, are displayed below. How many degrees of freedom are there for factors A and B, respectively Problem-focused coping strategies include:yoga.tai chi chuan.meditation.avoiding procrastination.Plz answer quick thanks guys!!! As the economy grew during the Gilded Age, many workers and their families did what? Condensed financial data are presented below for the Phoenix Corporation: 20X2 20X1 Accounts receivable $ 267,500 $ 230,000 Inventory 312,500 257,500 Total current assets 670,000 565,000 Intangible assets 50,000 60,000 Total assets 825,000 695,000 Current liabilities 252,500 200,000 Long-term liabilities 77,500 75,000 Sales 1,640,000 Cost of goods sold 982,500 Interest expense 10,000 Income tax expense 77,500 Net income 127,500 Cash flow from operations 71,000 Cash flow from investing activities (6,000 ) Cash flow from financing activities (62,500 ) Tax rate 30 % The profit margin used to calculate return on assets for 20X2 is (rounded): what are your feelings about war?is it necessary to wage war or there other better options? are there any benefits to war? what are some downsides to war? 8x8=8 to the power of ____ In what ways you can use your learnings about the things to do before, during and after an earthquake as a student Which pair of angles is not congruent? PLEASE ANSWER FAST!!!! Emperor Constantine established the city of __________ as the capital of the Roman Empire.A.RomeB.AntiochC.AnatoliaD.Constantinople A bullet leaves a rifle with a muzzle velocity of 521 m/s. While accelerating through the barrel of the rifle, the bullet moves a distend of 0.840 m. Determine the acceleration of the bullet (assume a uniform acceleration) leWhat is the simplified expression for the expression below?7(x - 4) 3(x + 5)0 4x - 43O4x + 10 4x - 13O 4X-9 A restaurant is making hamburgers. The cooks use 2/3 pounds of beef for each hamburger. If the cooks have 46 and 2/3 pounds of beef, how many hamburgers can they make? The force of gravity is also known as If you have 128 atoms of a radioactive substance, with a half-life of 31 seconds, how many atoms would remain after 62 seconds? Please show your work. What pathway uses fat reserves to produce ATP?aerobic respirationanaerobic respirationcreatine phosphate How would you say Zeus' and Hades' weapons if something belongs to both of them? Would I say it like that or would Hades only have the apostrophe after his name?? This is sorta urgent so please help. There is The Question and answers Express XCVI to Hindu Arabicnumerals. What is the unit rate of the better deal? (Number answers only.)LaTeX: \frac{160\:miles}{5\:gallons}\:or\:\frac{315\:miles}{9\:gallons}160 m i l e s 5 g a l l o n s o r 315 m i l e s 9 g a l l o n sThe better deal has a unit rate of [m] miles per gallon. dont get upset this is a real question Identify different groups that participated in the revolutionary war