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].

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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.

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°

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Answer:

The answer is c

Step-by-step explanation:

Bc I said so answer is always c

The answer Is C! Hope this helps

Чx-2(x+4)=22

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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

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What to say back if someone told you that your cute

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Answer:

your cute to

Step-by-step explanation:

Answer:

lol id.k

Step-by-step explanation:

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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).

Pythagorean Theory

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Answers

Answer: 12

Step-by-step explanation:

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

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Answer:

Step-by-step explanation:

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

Step-by-step explanation:

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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 [×][-][÷][+]
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

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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.

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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)

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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

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Answers

Answer:

I think its true

Step-by-step explanation:

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

R = (4, 0), m = 5

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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.

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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

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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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−12

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Answers

Answer:

X=-16

Step-by-step explanation:

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

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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,

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0.06 × x = $32.50

0.06x = $32.50

x = $32.50 / 0.06

x = $541.67

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= $541.67 + $32.50

= $574.17

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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:

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Answers

62%
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Solve for x.

16 = -2x - 1

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Answers

Answer:

1. 7

Step-by-step explanation:

Answer:

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

Step-by-step explanation:

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:

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

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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

Divide both sides by 0.009

36/0.009 = 0.009w / 0.009

4000 = w

Hence, the number, w equals 4000

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Answer:

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Step-by-step explanation:

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Answers

Answer:

Step-by-step explanation:

12(5-4)=96

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108-48=60 means it's not 9

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Answers

Answer:

x = 13 units ; y = 13√2 units

Step-by-step explanation:

The answer is: x = 13

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?

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

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