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

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.

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.

PLEASE HELP ME! Which rule explains why this triangle is congruent?( A) SAS (B).ASA ( C.) AAS (D) triangles can not be proven to be congruent.

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).

Indicate in standard form the equation of the line passing through the given point and having the given slope.

R = (4, 0), m = 5

Can someone help with this?

Answers

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

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

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:

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;

(0,0)= (3,0)

Move upward 1unit;

(3,0)= (3,1)

Therefore, the point on graph after shifts will be (3,1)

Learn more about graphs here:

https://brainly.com/question/26254258

#SPJ2

Of the 16 people attending a seminar, 2 have blond hair.
What is the probability that a randomly selected person will have blond hair?

Answers

Answer:

1/8

Step-by-step explanation:

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:

please help ASAP !!
Choose the system of equations that matches the following graph:
Picture included!

Answers

Answer:

Choice 2

Step-by-step explanation:

If im wrong im so sorry

If im right can i hav brainliest plz?

Answer:

Step-by-step explanation:

So you start at x-axis work your way down to the y-axis and you get your answer.

Reflect line AB over the y axis HELP PLS

Answers

Answer:

Here is the answer

And I have a problem

Step-by-step explanation:

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

−12

12

−16

16

Answers

Answer:

X=-16

Step-by-step explanation:

Please help me with this !

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.

b. A dot literally is right next to (6, 6).

Чx-2(x+4)=22

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

Its all in the picture-

Answers

62%
................................

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

PLEASEEEE HURRY

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

Answers

Answer:

Step-by-step explanation:

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

Which answer shows the number that point B represents on the graph? A) 2 1 4 B) 2 1 3 C) 2 1 2 D) 2 3 4° > −11°

Answers

Answer:

The answer is c

Step-by-step explanation:

Bc I said so answer is always c

The answer Is C! Hope this helps

Solve to figure out what Y is

Answers

Answer:

x = 13 units ; y = 13√2 units

Step-by-step explanation:

The answer is: x = 13

From the set {5, 9, 12}, use substitution to determine which value of x makes the equation true. 12(x - 4) = 96

Answers

Answer:

Step-by-step explanation:

12(5-4)=96

60-48=12 means it's not five

12(9-4)=96

108-48=60 means it's not 9

12(12-4)=60

144-48=96 so answer is 12

please help i don’t understand this

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!

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.

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

Write and solve a proportion to answer the question. 36 is 0.9% of what number w? 36/w = .9/100 what is w? w = ?

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

Divide both sides by 0.009

36/0.009 = 0.009w / 0.009

4000 = w

Hence, the number, w equals 4000

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 to say back if someone told you that your cute

Answers

Answer:

your cute to

Step-by-step explanation:

Answer:

lol id.k

Step-by-step explanation:

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

jp I'm bad at giving advice...

how do u make 24 out of the numbers(7)(7)(7)(5)
using only [×][-][÷][+]
frist to get this right gets brainlyest

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

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

Answers

Answer:

I think it's line "A"

Step-by-step explanation:

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:

Pythagorean Theory

I need help...

Answers

Answer: 12

Step-by-step explanation:

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