The solution to the binomial expression by using Pascal's triangle is:
<h3>How can we use Pascal's triangle to expand a binomial expression?</h3>
Pascal's triangle can be used to calculate the coefficients of the expansion of (a+b)ⁿ by taking the exponent (n) and adding the value of 1 to it. The coefficients will correspond with the line (n+1) of the triangle.
We can have the Pascal tree triangle expressed as follows:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
--- --- --- --- --- --- --- --- --- --- --- --- --- --- ---
From the given information:
The expansion of (3x-4y)^11 will correspond to line 11.
Using the general formula for the Pascal triangle:
The solution to the expansion of the binomial (3x-4y)^11 can be computed as:
Learn more about Pascal's triangle here:
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In order for a function to have an inverse that is also a function there are 2 main requirements:
1. The function should be bijective (ie) the function should be one-one ( each element in codomain has not more than 1 pre image in domain) and onto ( Range should be equal to codomain)
2. The inverse function should be defined by a suitable domain and range
Hope this answer helps you..
Answer: point estimate = 3.88
Margin of error = 0.63
Step-by-step explanation:
Confidence interval is written in the form,
(Point estimate - margin of error, Point estimate + margin of error)
The sample mean, x is the point estimate for the population mean. Let m represent the margin of error. Since the confidence interval is given as (3.25 , 4.51), it means that
x - m = 3.25
x + m = 4.51
Adding both equations, it becomes
2x = 7.76
x = 7.76/2
x = 3.88
Substituting x = 3.88 into x + m = 4.51, it becomes
3.88 + m = 4.51
m = 4.51 - 3.88
m = 0.63
Try comparing your solution with the following:
Solution:
Answer:
Check:
![2[10-13(\frac{40}{17})]+9(\frac{40}{17})=-34(\frac{40}{17})+60\\-20=-20](https://tex.z-dn.net/?f=2%5B10-13%28%5Cfrac%7B40%7D%7B17%7D%29%5D%2B9%28%5Cfrac%7B40%7D%7B17%7D%29%3D-34%28%5Cfrac%7B40%7D%7B17%7D%29%2B60%5C%5C-20%3D-20)
<em>Hope this was helpful.</em>
The square root of 81 is 9
