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nirvana33 [79]
2 years ago
7

What are the coefficients for the binomial expansion of (a + b)^3?

Mathematics
2 answers:
lilavasa [31]2 years ago
7 0
The coefficients are given by \dbinom 3k=\dfrac{3!}{k!(3-k)!} where k\in\{0,1,2,3\}. These are, in order, \{1,3,3,1\}.

So the expansion is

(a+b)^3=1a^3+3a^2b+3ab^2+1b^3
sashaice [31]2 years ago
5 0

Answer:

Required coefficient :coefficient of 1st, 2nd, 3rd and 4th term are 1, 3,3,1 respectively.

Explanation:  

Formula for binomial expansion is (a+b)^n=^nC_0\cdot a^n\cdot b^0+^nC_1\cdota^(n-1)\cdot b^1+------b^n

We will substitute the values a=a, b=b and n=3  in the formula for binomial expansion we will get

^3C_0\cdot a^3\cdot b^0+^3C_1\cdot a^2\cdot b^1+^3C_2\cdot a^1\cdot b^2+^3C_3\cdot a^0\cdot b^3

After simplification of the terms we will get

a^3+3\cdot a^2\cdot b+3\cdot a\cdot b^2+b^3

Since, ^nC_r=\frac{n!}{(r!)(n-r)!}

Therefore the required coefficient : coefficients of 1st, 2nd, 3rd and 4th term are 1, 3,3,1 respectively.

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How to change 17/8 to a proper fraction
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8 can go into 17 twice with one left over so 
the answer is 2 1/8

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3 years ago
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Conditional Distribution, Marginal Distribution, Joint Distribution. <br> What’s the difference?
lutik1710 [3]

Explanation:

Marginal distribution: This distribution gives the probability for each possible value of the Random variable ignoring other random variables. Basically, the values of other variables is not considered in the marginal distribution, they can be any value possible. For example, if you have two variables X and Y, the probability of X being equal to a value, lets say, 4, contemplates every possible scenario where X is equal to 4, independently of the value Y has taken. If you want the probability of a dice being a multiple of 3, you are interested that the dice is either 3 or 6, but you dont care if the dice is even or odd.

Conditional distribution: This distribution contrasts from the previous one in the sense that we are restricting the universe of events to specific condition for other variable, making a modification of our marginal results. If we know that throwing a dice will give us a result higher than 2, then to in order to calculate the probability of the dice being a multiple of 3 using that condition, we have two favourable cases (3 and 6) from 4 total possible results (3,4,5 and 6) discarding the impossible values (1 and 2) from this universe since they dont match the condition given (note that the restrictions given can also reduce the total of favourable cases).

The joint distribution calculates the probabilities for two different events (related to two different random variables) occuring simultaneously. If we want to calculate the joint probability of a dice being multiple of 3 and greater than 2 at the same time, our possible cases in this case are 3 and 6 from 6 possible results. We are not discarding 1 or 2 as possible results because we are not assuming, that the dice is greater than 2, that is another condition that we should met in the combination of events.

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3 years ago
Last PreCalc Question, Need help with writing piecewise functions with graphs. Giving brainliest!
LekaFEV [45]

The piece-wise linear functions can be written as follows:

  • f(x) = x, x \leq -2.
  • f(x) = -x - 7, -2 < x \leq 1.
  • f(x) = 2x - 9, x > 1.

<h3>What is a linear function?</h3>

A linear function is modeled by:

y = mx + b

In which:

  • m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
  • b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

For x equal or less than -2, the line passes through (-3,-3) and (-2,-2), hence the rule is:

f(x) = x, x \leq -2.

For x greater than -2 up to 1, the y-intercept is of -7, and the line also passes through (1,-8), hence the rule is:

f(x) = -x - 7, -2 < x \leq 1.

For x greater than 1, the function goes through (2,-5) and (3,-3), hence the slope is:

m = (-3 - (-5))(3 - 2) = 2.

The rule is:

y = 2x + b.

When x = 2, y = -5, hence:

-5 = 2(2) + b

b = -9.

Hence:

f(x) = 2x - 9, x > 1.

More can be learned about linear functions at brainly.com/question/24808124

#SPJ1

5 0
2 years ago
Last one - Thank you an advance :)
Ivan
Answers:
a. Given
b. Transitive property of congruence
c. Vertical angles are congruent
d. Transitive property of congruence

Let me know if you need any clarification as to how I got those answers. They should be self-explanatory but I'm happy to clarify further if needed. 

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