Write the fifteenth term of the binomial expansion of (a^2+b)^20

Answers

Answer 1

Answer:

The fifteenth term of the binomial expansion of [tex](a+b)^{20}[/tex] is [tex]38760\cdot a^{6}\cdot b^{14}[/tex].

Step-by-step explanation:

Let be a binomial of the form [tex](a+b)^{n}[/tex], where [tex]a, b\in \mathbb{R}[/tex] and [tex]n\,\in\mathbb{N}^{+}[/tex]. The expansion of this polynomial is defined below:

[tex](a+b)^{n} = \Sigma\limits_{k=0}^{n}\,\frac{n!}{k!\cdot (n-k)!}\cdot (a^{n-k}\cdot b^{k})[/tex] (1)

Where:

[tex]n[/tex] - Number of terms of the expanded polynomial.

[tex]k[/tex] - Index associated to [tex]k[/tex]-th term of the expanded polynomial.

For all [tex]n[/tex]-th binomial, we a sum of [tex]n+1[/tex] terms. If the given binomial has a term of [tex]20[/tex], then we have 21 terms and the fifteenth term of the polynomial corresponds to the [tex]14[/tex]-th term. Then, the fifteenth term of the binomial is:

[tex]c_{14} = \frac{20!}{14!\cdot 6!}\cdot (a^{6}\cdot b^{14})[/tex]

[tex]c_{14} = 38760\cdot a^{6}\cdot b^{14}[/tex]

The fifteenth term of the binomial expansion of [tex](a+b)^{20}[/tex] is [tex]38760\cdot a^{6}\cdot b^{14}[/tex].

Related Questions

Mr Jones bought a snowboard. The 6% sales tax on the snowboard was $32.50. What was the total cost including the sales tax? (rounded to nearest cent)

Answers

Answer: $574

Step-by-step explanation:

First we need to calculate the price of the snowboard before the addition of the tax. This will be represented by x. Therefore,

6% of x = $32.50

0.06 × x = $32.50

0.06x = $32.50

x = $32.50 / 0.06

x = $541.67

Therefore, the total cost including the sales tax will be:

= $541.67 + $32.50

= $574.17

= $574

find the surface area of the prism. 3in , 8in ,5in.

Answers

Answer:

158 in.

Step-by-step explanation:

Surface area of a prism = Area of all the faces added together

So, Face 1 & 2 = 5 x 80 = 40 x 2 = 80

Face 3 & 4 = 8 x 3 = 24 x 2 = 48

Face 5 & 6 = 5 x 3 = 15 x 2 = 30

Therefore, adding them together makes:

80 + 48 + 30 = 158 in.

Solve to figure out what Y is

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Answer:

x = 13 units ; y = 13√2 units

Step-by-step explanation:

The answer is: x = 13

Reflect line AB over the y axis HELP PLS

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Answer:

Here is the answer

And I have a problem

Step-by-step explanation:

Pythagorean Theory

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Answer: 12

Step-by-step explanation:

PLEASEEEE HURRY

For the linear function represented in the table below, determine the value of y if x = 6.

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Answer:

Step-by-step explanation:

The y values increase by 2 every time so 18+2=22

Solve for x.

16 = -2x - 1

Solve for x.

16 = -2x - 1

pls

Answers

Answer:

1. 7

Step-by-step explanation:

Answer:

x = 7 [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Makayla is flying a kite. The angle of elevation from Makayla to the kite is 58º. If 55 ft of kite string has been used, how high above the ground is the kite, to the nearest foot?

Answers

Answer:

I dont know good luck :)

Step-by-step explanation:

peace

question is in picture. Plzzz help me. Due in 2hrs

Answers

Answer:

I think it's line "A"

Step-by-step explanation:

Karl is comparing the interest rates for accounts at two different banks. He will deposit $600 into an account and will not make any additional deposits or withdrawals. Bank Q offers 1% interest compounded annually. Bank R offers 1.5% simple interest.

Answers

Answer: bank R for 1 year

Step-by-step explanation:

Given

Principal deposit is [tex]P=\$600[/tex]

Bank Q offers 1% interest compounded annually

Bank R offers 1.5% simple interest annually

For Bank Q, Compound interest is given by

[tex]\Rightarrow P[1\frac{R}{100}]^t-P[/tex]

for 1 year it is

[tex]\Rightarrow 600[1+\frac{1}{100}]-600=\$6[/tex]

For bank R, simple interest is

[tex]S.I.=\dfrac{P\times R\times T}{100}[/tex]

for 1 year it is

[tex]\Rightarrow S.I.=\dfrac{600\times 1.5\times 1}{100}=\$9[/tex]

Clearly, bank R offers more interest for 1 year

What is the box-and-whiskers plot used to show?
a. a histogram
c. median
b. variability
d. observations

Answers

Answer:

b and c

Step-by-step explanation:

box-and-whiskers plot shows the shape of the distribution, its central value, and its variability.

Solve 7x − 2(x + 1) = 6x + 14. (5 points)

−12

12

−16

16

Answers

Answer:

X=-16

Step-by-step explanation:

HELP ME PLESE IM TIMED NO SNEAKY LINKS ANWSERS ONLY PLZZZ HELP ME

Answers

Answer:

8p=t

Step-by-step explanation: Snap add?

Answer:

8p = t

Step-by-step explanation:

Length of one string = p

Length of all the strings (t) = p × 8

= 8p

Thus, 8p = 7

how do u make 24 out of the numbers(7)(7)(7)(5)
using only [×][-][÷][+]
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Answers

Answer: You add all the numbers.

Step-by-step explanation:

7 + 7 + 5 + 5 = 24.

(7-7/7)*4=24

i know this because i solved it

Of the 16 people attending a seminar, 2 have blond hair.
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Answers

Answer:

1/8

Step-by-step explanation:

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How do I do this

Answers

Answer:

x = 7

Step-by-step explanation:

4x - 2(x + 4) = 22

Distribute:

4x - 2x - 8 = 22

Combine like terms:

2x - 8 = 22

Simplify and solve:

2x = 14

x = 7

Answer:

4x-2x-8=22

2x-8=22

2x=30

x=15

Hiiiooos! Can someone please help me with this!!!❤️❤️❤️❤️:)

Answers

Answer:

Step-by-step explanation:

hopes this helps

Answer: My best guess is 10 (sqrt of 2)

Step-by-step explanation:

What to say back if someone told you that your cute

Answers

Answer:

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Step-by-step explanation:

Answer:

lol id.k

Step-by-step explanation:

if they cute too say " ty u too;)"

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Start at the origin. Move 3 units right and 1 unit up. What is the ordered pair at this point ? for brainlest!!!

Answers

Answer:

(3,1) should be the answer

Step-by-step explanation:

Hope this helps!

The ordered pair at this point is (3,1)

How to draw a shifted figure if the shifts are provided?

Suppose the graph is drawn on the coordinate plane.

Let the shifting be (x,y) → (x+a, y+b)

Then, add 'a' to all x coordinates of the graph's points. Add 'b' to all y coordinates of the graph's points.

The resultant set of new points will be plotted.

Given;

From origin; move to right 3units

move upward 1unit

Moving to right 3units;

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Move upward 1unit;

(3,0)= (3,1)

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https://brainly.com/question/26254258

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Which best proves why the expressions 4 (x + 3) + 2 x and 6 (x + 2) must be equivalent expressions? When x = 3, both expressions have a value of 30. When x = 5, both expressions have a value of 42.

Answers

Answer:

The answer is choice first which is "When x = 3, both expressions have a value of 30".

Step-by-step explanation:

Given:

First expression: [tex]4(x+3)+2x[/tex]

Second expression: [tex]6(x+2)[/tex]

Through the question when we substitute x=3 into its first equation so we get:

[tex]\to 4(3+3)+2(3) \\\\ \to 4\times (6)+6\\\\ \to 24+6\\\\ \to 30[/tex]

The value will be substituted by x=3 into its second expression:

[tex]\to 6(3+2)\\\\ \to 6(5)\\\\ \to 30[/tex]

So, it will prove that both the two expressions are equivalent.

we can ise the distance formula or pythagorean theorem to find the length of a segment? true or false

Answers

Answer:

I think its true

Step-by-step explanation:

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Answers

Answer:

The answer is c

Step-by-step explanation:

Bc I said so answer is always c

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Answers

Answer:

a. 4 (or maybe like 3.5)

b. 6

Step-by-step explanation:

a. Going from x = 0 to x = 8, it is obvious that y goes down 4 or 4.5 units during this stretch. This gives an approximate slope of -3/8. With this in mind, it can be easily calculated that going the remaining distance from x = 8 to x = 10, the value of y will be approximately 4 or so.

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Answers

62%
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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

Step-by-step explanation:

12(5-4)=96

60-48=12 means it's not five

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108-48=60 means it's not 9

12(12-4)=60

144-48=96 so answer is 12

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Answers

Answer:

AAS

Step-by-step explanation:

Angle K is congruent to Angle N (given), Angle H is congruent to itself (reflexive property), and side JH is congruent to side MH (given).

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Answers

Answer:

4000

Step-by-step explanation:

To solve :

36 = 0.9% of w ; solve for w

36 = 0.9/100 * w

36 = 0.009w

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Answers

0=5(4)+b is how the equation needs to be worked out

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Answers

Answer:

slope of line one: 2/4 or 1/2

line two: 6/1

line 3: 6/3 or 2

line 4: -4/1

to find the slope of a line, you have to use rise/run the number of space going along the y-axis is the rise, and the space of the points on the x-axis is the run.

hope this helps!

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