Find the value of x.

[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]

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).

Answer:

The choice C.

[tex]12 \frac{1}{2} [/tex]

Step-by-step explanation:

[tex]( \frac{4}{5} - \frac{1}{3} ) \times {5}^{2} + \frac{5}{6} \\ \\ ( \frac{12}{15} - \frac{5}{15} ) \times 25 + \frac{5}{6} \\ \\ ( \frac{12 - 5}{15} ) \times 25 + \frac{5}{6} \\ \\ ( \frac{7}{15} ) \times 25 + \frac{5}{6} \\ \\ \frac{35}{3} + \frac{5}{6} \\ \\ \frac{70}{6} + \frac{5}{6} = \frac{75}{6} \\ \\ = \frac{25}{2} = 12 \frac{1}{2} [/tex]

I hope I helped you^_^

Answer:

k=4

Step-by-step explanation:

Answer:

The answer is K=2 100% sure.

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.

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:

{x | 0 < x ≤ 5}

Step-by-step explanation:

The domain of a function describes all the values x could taken on in order to produce an output. You can notice the value of x is farthest left at a value of 0, which has an open dot and the value of x that is farthest right is at 5 with a closed dot. A closed dot includes the value while an open does not. This means x can be equal to 5, but not zero. We can write our domain as follows:

{x | 0 < x ≤ 5}

Answer:

8

Step-by-step explanation:

8

The value of the missing side of the triangle is 24.

Similarity refers to the degree of resemblance or likeness between two or more things, concepts, or ideas. It can be measured in various ways, depending on the context and the characteristics being compared.

Scale factor refers to the ratio of the size of an object in the original form to its size in the scaled or transformed form. It is commonly used in geometry and mathematics to describe how the dimensions of an object have changed after a transformation such as scaling, stretching, or shrinking.

From the given figure the value of the missing number is calculated as,

36 / 24 = x / 16

x = ( 8 x 3 )

x = 24

Therefore, the value of an unknown number is x = 24.

To know more about similarities follow

https://brainly.com/question/25631497

#SPJ2

Answer:

128

Step-by-step explanation:

It’s actually quite simple all you have to do is find out what 20% of 160 is then subtract the 20% by 160 to get your final answer UwU

Answer:

12

Step-by-step explanation:

4 and 12 only share 12 which is the lowest number :D

Answer:

18

Step-by-step explanation:

we can solve this as a ratio, from teaspoons to tablespoon is 3:1. if the tablespoon is 6 then the ratio becomes ?:6. Since we multiplied 1 by 6 we have to multiply 3 by 6 making the ratio 18:6.

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

Answer:

A, C, and D have been simplified correctly

Answer:

false

Step-by-step explanation:

absolute value turns the number positive

I-10I=10

Answer:

12 2/5   or   12.4

Step-by-step explanation:

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:

Cube root of 92 can be represented as 3√92. The value of cube root of one is 92.The nearest previous perfect cube is 64 and the nearest next perfect cube is 125.

Step-by-step explanation:

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:

bbbbbbbbbbbbbbbbbbbbb

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:

sqrt(61)

Step-by-step explanation:

4-(-1) = 5

-3-(-9) = 6

sqrt(5^2+6^2) = sqrt(25+36) = sqrt(61)

Answer:

Is this a graph question?

sa may picture yong answer

Step-by-step explanation:

sana makatulong

[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:

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:

t=5

Step-by-step explanation:

4t+10=20+2t

4t-2t=20-10

2t=10

t=10÷2

=5

Answer:

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