PLEASE ANSWER FOR EXTRA POINTS ⭐️⭐️⭐️!

I bet the sum you're referring to is supposed to be

[tex]\displaystyle \sum_{r=0}^{20} r^2 \times {}^{20}C_r[/tex]

or equivalently,

[tex]\displaystyle \sum_{r=0}^{20} r^2 \binom{20}r[/tex]

where [tex]\binom nk = \frac{n!}{k!(n-k)!}[/tex] is the binomial coefficient.

Recall the binomial series,

[tex](1+x)^\alpha = \displaystyle \sum_{r=0}^\infty \binom\alpha r x^r[/tex]

which is valid for |x| < 1. (Note that if r > α, the binomial coefficient is defined to be zero, so there really are only α many terms when α is a whole number.)

Differentiating both sides with respect to x gives

[tex]\alpha (1+x)^{\alpha-1} = \displaystyle \sum_{r=0}^\infty r \binom\alpha r x^{r-1}[/tex]

Multiply both sides by some arbitrary x in |x| < 1 :

[tex]\alpha x (1+x)^{\alpha-1} = \displaystyle \sum_{r=0}^\infty r \binom\alpha r x^r[/tex]

Repeat:

[tex]\alpha (1+x)^{\alpha-1} + \alpha(\alpha-1) x(1+x)^{\alpha-2} = \displaystyle \sum_{r=0}^\infty r^2 \binom\alpha r x^{r-1}[/tex]

[tex]\alpha x (1+x)^{\alpha-1} + \alpha(\alpha-1) x^2 (1+x)^{\alpha-2} = \displaystyle \sum_{r=0}^\infty r^2 \binom\alpha r x^r[/tex]

Let α = 20, and let x approach 1 from below. The right side converges to the sum we want, while the left side converges to

[tex]20 \times 2^{19} + 20\times19\times 2^{18} = (20 + 10\times19)\times2^{19} = \boxed{210\times2^{19}}[/tex]

In order to solve a proportion, you should cross-multiply:-

[tex]\bf{\displaystyle\frac{3x}{10} =\frac{3}{2}}[/tex]

Multiply 3x times 2 and 10 times 3:-

[tex]\bf{6x=30}[/tex]

Divide both sides by 6:-

[tex]\boxed{\bf{x=5}}[/tex]

Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I'll comment and/or edit my answer :)

Answer:

^EKF and^HKI

Step-by-step explanation:

Answer:

49/3 or 16.33...

Step-by-step explanation:

15 + 4/3.

15/1 + 4/3

45/3 + 4/3.

ANSWER: 49/3

Answer:

3(x-6)=3x-18

Step-by-step explanation:

Answer:

6.25 years

(6 years 3 months)

Step-by-step explanation:

Simple interest formula

A = P(1 + rt)

where:

Given:

Substitute given values into the formula and solve for t:

⇒ 1500 = 1000(1 + 0.08t)

⇒ 1500 = 1000 + 80t

⇒ 500 = 80t

⇒ t = 6.25 years

Answer:

Step-by-step explanation:

In order to determine the correct answer, we need to confirm it first by making the solution below:Costs: $89.95 = New Lamp $239.99 = Comforter 6 3/5% = Sales Tax (convert this to decimal and we get 6.6%)  $351.72 = Total amount the Chang's paidLet's get the total costs first which is $329.946.6% of 329.94 is $21.78The total cost with the tax would be $351.72.Therefore, the Chang's paid the correct amount. The correct answer would be option D. The Chang's family paid the correct amount for their purchases.

The amount that Jo will have less towards next years holiday, if all other expenses, wage and bonus stay the same is $146.88.

The initial amout that Jo paid for the phone is calculated as follows;

amount per month = ($49) / (1 + ¹/₃)

amount per month = ($49) / (1.333)

amount per month = $36.76

For 1 year (12 months), = $36.76 x 12 = $441.12

$49 x 12 = $588

= $588 -  $441.12

= $146.88

Thus, the amount that Jo will have less towards next years holiday, if all other expenses, wage and bonus stay the same is $146.88.

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Answer:

a) we have 5 there 3 times so answer is 3/8

b)

for 8 times rolling 3 times 5 we have

for 40 times rolling will 15 times 5

Step-by-step explanation:

a) we have 5 there 3 times so answer is 3/8

b)

for 8 times rolling 3 times 5 we have

for 40 times rolling will 15 times 5

Answer:

the verbal sentence so it is easier to translate. ... 12 equals p divided by. 4 n. 2. +. 12. = p. ÷. 4. 4. Half of j minus 5 is the sum of k and 13.

Step-by-step explanation:

Answer:

109.2 degrees

Step-by-step explanation:

Use the cos law to find angle F

3.1^2 = 2^2 + 1.8^2 - 2 (2)(1.8) cos F

shows cos f = -.329

arc cos( - .329) = angle F =109.2 degrees

Answer:

-8.5

Step-by-step explanation:

this is because the more negative a number is, the less value it is, hence -8.5 is greater than -15.

Answer:

9

Step-by-step explanation:

700,000

90,000

6,000

100

40

2

Answer:

9

Step-by-step explanation:

796,142

100000  10000    1000  100  10   1

Answer: B (2.9 x 10)

Step-by-step explanation: (4.35 x 10^2)/15 = 29 = 2.9 x 10

Answer:

0.3

Step-by-step explanation:

Start at the beginning, follow the branch to A and then the branch to D (see attached annotated diagram).

When calculating the probability of an event AND another event, multiply the probabilities.

P(A and D) = 0.5 x 0.6 = 0.3

Answer:

Hopefully, this helps you!!

:3

Here's a graph!

Have a great day!!

[tex]Sokkachan[/tex]

Answer:

Point W

Step-by-step explanation:

Answer:

3780/90

what number close to 37 is divisible by 9 ? 36 !!

3600/90=40 or 3690/90=41

3780/90=42

this an underestimate because the compatible numbers 3600 and 3690 are less than 3780

yall be safe

Our estimate is 38. This estimate is an overestimate because we rounded up both numbers, so we expect the actual quotient to be slightly smaller than our estimate.

Compatible numbers are numbers that are simple to mentally work with and can be used to estimate or simplify a more complex calculation.

When performing addition, subtraction, multiplication, or division, for example, it is often helpful to choose numbers that are easy to manipulate in your head or by hand, such as multiples of 10, 100, or 1000.

To estimate the quotient of 3,780 divided by 90 using compatible numbers, we can round 3,780 to 3,800 (which is divisible by 100) and round 90 to 100. Then, we have:

3,800 ÷ 100 = 38

Thus, the estimate is 38. This estimate is an overestimation because we rounded both numbers, so we anticipate that the actual quotient will be slightly lower than our estimate.

For more details regarding Compatible numbers, visit:

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#SPJ2

The marginal tax bracket of Dave shows that the amount of the federal tax is $28000.

Let the federal tax be represented by x.

From the information, Dave’s marginal tax bracket is 25%, and he contributed 7000.

Based on the information, the amount will be:

25% of x = 7000

0.25 × x = 7000

0.25x = 7000

x = 7000/0.25

x = $28000

In conclusion, the amount is $28000.

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We are given with a sequence, which is a GP (Geometric Progression), as the ratio [tex]{\bf{a_{n+1}:a_{n}}}[/tex] is 1/3 for every [tex]{\bf{n\in \mathbb{N}}}[/tex], so 1/3 is the comman ratio r, and we needa find sum till 6 terms, so n = 6, and first term is 6, so putting all the values we will be having ;

[tex]{:\implies \quad \sf S_{6}=\dfrac{6\bigg\{1-{\bigg(\dfrac13\bigg)}^{6}\bigg\}}{1-\dfrac13}}[/tex]

[tex]{:\implies \quad \sf S_{6}=\dfrac{6\bigg(1-\dfrac{1}{3^{6}}\bigg)}{\dfrac{3-1}{3}}}[/tex]

[tex]{:\implies \quad \sf S_{6}=6\bigg(\dfrac{3^{6}-1}{3^{6}}\bigg)\div \dfrac23}[/tex]

[tex]{:\implies \quad \sf S_{6}=6\bigg(\dfrac{3^{6}-1}{3^{6}}\bigg)\times \dfrac32}[/tex]

[tex]{:\implies \quad \sf S_{6}=\dfrac{3^{6}-1}{3^{4}}}[/tex]

[tex]{:\implies \quad \sf S_{6}=\dfrac{3^6}{3^4}-\dfrac{1}{3^4}}[/tex]

[tex]{:\implies \quad \sf S_{6}=3^{2}-\dfrac{1}{81}}[/tex]

[tex]{:\implies \quad \sf S_{6}\approx 9-0.012\approx 8.988\approx \boxed{\bf{8.99}}}[/tex]

Answer:

1/3

Step-by-step explanation:

This problem would be 1/2 x 2/3. The answer would be 1x2 over 2x3.

Answer:

-1.8 kJ

Step-by-step explanation:

Given

Solving

Answer:

2250 J

Step-by-step explanation:

Work done is given by the formula :

work done = force × distance

Substituting values given gives us:

Work done = 45 × 40

Work done = 2250 J

Answer:

No

Step-by-step explanation:

6 time 180 is only 108

108<120

There is not enough chalk.

Answer:

$ 25.86 is the answer

Step-by-step explanation:

ANSWER = 0.48

HOPE IT HELPS :)

Answer: 0.48

Step-by-step explanation:

6 x 8 = 48

we add those decimals back in which would be 0.48

Answer:

Step-by-step explanation:

Since the prices increase at a monthly rate of 0.1% per month. To find the percentage do they increase a year, we need to convert 0.1% to a decimal.

So here how we do it. We put 0.1 percent on the numerator because it a small number which is what we want over 100 like this:

[tex]\frac{0.1}{100}[/tex]

Now when plugging this into your calculator you get:

0.001

.So what do we do with this number?

We now times it by 12 like this:

0.001 x 12 which gives us:

0.012

So we can convert this back to a percentage by moving the decimal by 2 places to the right which gives us 1.2%.

Another way we could of done this without doing the long way to figure it out is by multiplying 0.1 times 12 which still gives us 1.2%

Answer:

Bob

Step-by-step explanation:

Answer:

..............................

Answer:

x = -12

Step-by-step explanation:

⇒ -5x = 60

Isolate the variable "x" by dividing by -5 on each side.

⇒ -5x/-5 = 60/-5

⇒ x = -12

The solution is x = -12

[tex]\boxed{ \sf \bold{x = -12}}[/tex]

Explanation:

[tex]\dashrightarrow \ \ \sf -5x = 60[/tex]

divide both sides by -5

[tex]\dashrightarrow \ \ \sf \dfrac{-5x}{-5} = \dfrac{60}{-5}[/tex]

simplify

[tex]\dashrightarrow \ \ \sf x = -12[/tex]

Step-by-step explanation:

SinP = sin30° = 1/2

sinQ = sin60° = root3/2

cosR = cos90° = 0

cosQ = cos60° = 1/2

sinR = sin90° = 1