Emma and her 3 friends did chores for Emma's dad on Saturday. They earned 55 and split evenly. How much money did each of the 4 children get?​

[tex] \large\underline{\sf{Solution-}}[/tex]

Given series is

[tex]\rm \longmapsto\:\displaystyle\sum_{k=1}^{\infty}\rm \displaystyle\sum_{n=1}^{\infty}\rm \frac{k}{ {2}^{n + k} } [/tex]

can be further rewritten as

[tex]\rm \:  =  \: \:\displaystyle\sum_{k=1}^{\infty}\rm \displaystyle\sum_{n=1}^{\infty}\rm \frac{k}{ {2}^{k} . {2}^{n} } [/tex]

can be further rewritten as

[tex]\rm \:  =  \: \displaystyle\sum_{k=1}^{\infty}\rm \bigg[\dfrac{k}{ {2}^{k}}\displaystyle\sum_{n=1}^{\infty}\rm \dfrac{1}{ {2}^{n} } \bigg][/tex]

[tex]\rm \:  =  \: \displaystyle\sum_{k=1}^{\infty}\rm \dfrac{k}{ {2}^{k} }\bigg(\dfrac{1}{2} + \dfrac{1}{ {2}^{2} } + \dfrac{1}{ {2}^{3} } - - - \infty \bigg) [/tex]

So, its an infinite GP series with

[tex] \purple{\rm \longmapsto\:a = \dfrac{1}{2}}[/tex]

[tex] \purple{\rm \longmapsto\:r = \dfrac{1}{2}}[/tex]

We know,

Sum of infinite GP series with common ratio r ( - 1 < r < 1 ) and first term a is given by

[tex]\boxed{\tt{ \: \: S_ \infty = \frac{a}{1 - r} , \: \: provided \: that \: |r| < 1}}[/tex]

So, 1using this, we get

[tex]\rm \:  =  \: \displaystyle\sum_{k=1}^{\infty}\rm \frac{k}{ {2}^{k} }\bigg( \frac{ \frac{1}{2} }{1 - \frac{1}{2} }\bigg)[/tex]

[tex]\rm \:  =  \: \displaystyle\sum_{k=1}^{\infty}\rm \frac{k}{ {2}^{k} }\bigg( \frac{ \frac{1}{2} }{ \frac{2 - 1}{2} }\bigg)[/tex]

[tex]\rm \:  =  \: \displaystyle\sum_{k=1}^{\infty}\rm \frac{k}{ {2}^{k} }\bigg( \frac{ \frac{1}{2} }{ \frac{1}{2} }\bigg)[/tex]

[tex]\rm \:  =  \: \displaystyle\sum_{k=1}^{\infty}\rm \frac{k}{ {2}^{k} }[/tex]

[tex]\rm \:  =  \: \dfrac{1}{2} + \dfrac{2}{ {2}^{2} } + \dfrac{3}{ {2}^{3} } + \dfrac{4}{ {2}^{4} } + - - - \infty [/tex]

Let assume that

[tex]\rm \longmapsto\:S_ \infty   =  \: \dfrac{1}{2} + \dfrac{2}{ {2}^{2} } + \dfrac{3}{ {2}^{3} } + \dfrac{4}{ {2}^{4} } + - - - \infty [/tex]

Now, its an infinite Arithmetico Geometrico Series, So multiply by 1/2 we get

[tex]\rm \longmapsto\:\dfrac{1}{2} S_ \infty   =  \: \dfrac{1}{ {2}^{2} } + \dfrac{2}{ {2}^{3} } + \dfrac{3}{ {2}^{4} } + \dfrac{4}{ {2}^{5} } + - - - \infty [/tex]

On Subtracting above two equations, we get

[tex]\rm \longmapsto\:\dfrac{1}{2} S_ \infty   =  \: \dfrac{1}{2} + \dfrac{1}{ {2}^{2} } + \dfrac{1}{ {2}^{3} } + \dfrac{1}{ {2}^{4} } + - - - \infty [/tex]

[tex]\rm \longmapsto\:\dfrac{1}{2} S_ \infty   =  \: \dfrac{ \dfrac{1}{2} }{1 - \dfrac{1}{2} } [/tex]

[tex]\rm \longmapsto\:\dfrac{1}{2} S_ \infty   =  \: \dfrac{ \dfrac{1}{2} }{ \dfrac{1}{2} } [/tex]

[tex]\rm \longmapsto\:\dfrac{1}{2} S_ \infty   =  \: 1[/tex]

[tex]\bf\implies \:S_ \infty = 2[/tex]

Hence,

[tex] \\ \rm \longmapsto\:\boxed{\tt{ \: \: \: \: \displaystyle\sum_{k=1}^{\infty}\rm \displaystyle\sum_{n=1}^{\infty}\rm \frac{k}{ {2}^{n + k} } = 2 \: \: \: \: }} \\ [/tex]

[tex] \Large\begin{gathered} {\underline{\boxed{ \rm {\red{\pi \: = \: \frac{22}{7} }}}}}\end{gathered}[/tex]

[tex] \Large{{ { \blue{ \rm{{↬}}}}}} \rm \large \: \: \: {{ \Large{ \purple{ \rm{{ \frac{22}{7} \: = \: 3.1415926535 }}}}}} \: [/tex]

Answer:

false

Step-by-step explanation:

absolute value turns the number positive

I-10I=10

Answer:

x=300

Step-by-step explanation:

First you had to find the scale factor of the image to do that you would have to divide 325 by 13 resulting in 25 then you would multiple 12 times 25 resuliting in 300.

Answer:760 lbs

Step-by-step explanation:

The volume of a right rectanglar prism (i.e., a box) is length*width*height.

Volume = (13.5)*(11)*(5.5) = 817 ft^3

Density = 0.93 lb/ft^3

Weight of container contents = (817 ft^3)*(0.93 lg/ft^3) = 760 lbs

Answer:

the slope is 5

Step-by-step explanation:

Answer:

Step-by-step explanation:

slope of ║ line is ( - [tex]\frac{5}{4}[/tex] )

slope of ⊥ line is [tex]\frac{4}{5}[/tex]

Answer:

[tex]-\frac{7}{8}a-\frac{1}{6}[/tex] (the first box is 7/8 and the second box is 1/6)

Step-by-step explanation:

Step 1: Combine like terms.

Therefore, the answer is [tex]-\frac{7}{8}a-\frac{1}{6}[/tex]. (Again, the first box is 7/8 and the second box is 1/6).

sa may picture yong answer

Step-by-step explanation:

sana makatulong

let   −5x+2y=14   be [1]

&        y=3x+2    be [2]  

Finding the value of x

By substituting y in [2] for y in [1]

⇒  −5x + 2(3x+2) = 14         [expand the bracket]

⇒     -5x + 6x + 4 = 14         [subract 4 from both sides and simplify]

⇒                       x = 10

Finding the value of y

Since x =10, we can substitute value of x into [2]

⇒     y = 3(10) + 2

⇒     y = 32

Answer:P2,700,000

Step-by-step explanation:

P100,000 must be added to the purchase price every year from 2009 to 2021.  A formula calculating the value, V, as a function of time, t, where t is years since 2009, would be:

V(t) = P1,500,000 + (t - 2009)*(100,000)

V(2021) = P1,500,000 + (2021 - 2009)*(100,000)

V(2021) = P2,700,000

[Warning:  This prediction assumes no housing bubble drop or general recession.  It also assumes consistent government policies regarding home ownership.  If there were a probability component to the question, it is likely that the overall probability is zero that this is calculation will hold true.  This isn't important to answering the question, but it does allow me to vent a bit.]

Answer:

43.2

26.4

6

Step-by-step explanation:

so first if we know that the loger side's ratio is 6 we divided by 7.2

7.2 divided by 6 which is 1.2

so we mulitply the 5 by 1.2

so the shorter side is 6

6 x 7.2 = 43.2 is the area

14.4 + 12 = 26.4 is the perimeter

Answer:

A∩B = 2,4

A-B = 1,3,5

sin (A+B) = sin(A)cos(B)+cos(A)sin(B)

Step-by-step explanation:

A intersects U means the numbers that are coming to both A and U

set a minus set b of the numbers that are not common to B

multiply the numerator and the denominator by csc(x)

NOTE: I substituted x for theta as I don't have theta on my phone

[tex] \frac{ \csc(x) }{ \csc(x)} \frac{ \tan(x) - \sin(x) }{ \tan(x) + \sin(x) } = \frac{ \sec(x) - 1}{ \sec(x) + 1} [/tex]

[tex] \frac {\csc(x)}{\csc(x)} \frac {\frac ({\sin(x)}{\cos(x)}-\sin(x)} {\frac ({\sin(x)}{\cos(x)} + \sin(x)}) [/tex]

Answer:

[tex]\boxed{\sf x=-3\frac{3}{20}}[/tex]

Step-by-step explanation:

[tex]\sf -4\cfrac{2}{5}=x-1\cfrac{1}{4}[/tex]

Multiply Both sides by 20, Which is the LCM of 5, 4:

[tex]\mapsto \sf (4\times 5+2)=20x-5(4+1)[/tex]

Multiply 4 and 5= 20, and add 20 +2 =22

[tex]\mapsto \sf -4\times 22=20x-5(4+1)[/tex]

Multiply -4 * 22 = -88, and then add 4+1=5:

[tex]\mapsto \sf -88=20x-5\times 5[/tex]

Multiply -5 *5 = -25:

[tex]\mapsto \sf -88=20x-25[/tex]

Now, swap sides:

[tex]\mapsto \sf 20x-25=-88[/tex]

Add 25 to both sides:

[tex]\mapsto \sf 20x=-88+25[/tex]

[tex]\mapsto \sf 20x=-63[/tex]

Divide both sides by 20:

[tex]\mapsto \sf x=\cfrac{-63}{20}[/tex]

Now, convert an improper fraction to a mixed number: →

[tex]\mapsto \sf x= -3\cfrac{3}{20}[/tex]

_____________________________________

Answer:

A, C, and D have been simplified correctly

Answer:

12 2/5   or   12.4

Step-by-step explanation:

Answer:

P=21

Step-by-step explanation:

Add 9 to 12

Answer: Heyy bestie ❤️ The Answer is 21

Step-by-step explanation:

P-9=12

p=12+9

p=21

Answer:

45-45-90, x = -7

Step-by-step explanation:

The triangle is 45-45-90

45 = x + 52

x = -7

Answer:

bbbbbbbbbbbbbbbbbbbbb

Hey there!

2a + 4 = 3

ADD 4 to BOTH SIDES

2a + 4 - 4 = 3 - 4

CANCEL out: 4 - 4 because that gives you 1

KEEP: 3 - 4 because it helps solve for the a-value

2a = 3 - 4

3 - 4 = -1

2a = -1

DIVIDE 2 to BOTH SIDES

2a/2 = -1/2

CANCEL out: 2/2 because it gives you 1

KEEP: -1/2 because it gives you the value of the a-value

a = -1/2

SIMPLIFY IT!

Therefore, your answer is: a = -1/2

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

I'm confused what your asking because 212.65 x 10 does equal 21,265.0

Answer:

Step-by-step explanation:

We can pick the two coordinates again, such as (90,70) and (10,50)

And use the formula m=y1-y2/x1-x2

m= (70-50)/(90-10)

=20/80

=1/4

Step-by-step explanation:

it was measured that the south crawled 6cm in 1 second.

that gets expressed by the ratio

6 cm/sec or formally correct 6/1 cm/sec.

to get that speed in km/h (kilometers per hour), we need to transform the denominator of that ratio to 1 hour.

the only way we can manipulate a fraction or ratio without changing its value is by multiplying numerator and denominator (top and bottom) by the same factor.

like x/y × 3/3 = 3x/3y.

the driver behind a question of this kind is again the denominator. we want the denominator to appear as 1 hour.

so, what do I need to multiply 1 second with to get 1 hour ?

the problem definition tells us : 3600, as there are 3600 seconds in 1 hour.

so, we need to multiply

6/1 × 3600/3600 = (6×3600)/3600 = 21600/3600 =

21600cm/1 hour.

and now, how many km are 21600 cm ?

1 km = 100000 cm

so,

21600cm = 21600/100000 km = 0.216 km

therefore, or full answer is

the sloth's speed was 0.216 km/h

Quinn's way takes a little more time because he didn't chose a good answer to multiply with 8 but gotten the answer anyways. Unlike Jewel, she had a answer that made things much quicker.

I believe the answer to be (-7)

Answer:

-7

Step-by-step explanation:

Step 1: Make an equation.

Step 2: Subtract 9 from both sides.

Step 3: Check if solution is correct.

Therefore, the integer that makes the addition sentence true is -7.

Answer:

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation: (−∞,∞)

Set-Builder Notation: {x|x∈R}

f(x) is continuous on (−∞,0).

The function is continuous.

Step-by-step explanation:

Answer:

3/11

Step-by-step explanation:

because 334443

Answer:

MLEF

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Step-by-step explanation:

I hope this helps...