<u>Answer:</u>
The length of VI to the nearest tenth is 4 cm
Solution:
The plot is like a quadrilateral and the fences are built on the diagonal
We know that for quadrilateral both the diagonals are in same height,
So as per the picture, 
Now we know that 
Hence,
<u>Rounding off:</u>
- If the number that we are rounding is followed by 5 to 9, then the number has to be increased to the next successive number.
- If the number that we are rounding is followed by 1 to 4, then the number has to remain the same.
Here the number to be round off is 3.98, 9 belongs to the first category stated above. So, 3 is increased to 4.
Hence, the length of VI = 4 cm.
Answer:
(22.0297, 23.3703)
Step-by-step explanation:
Given that an economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in California.
Let X be per capita income (in thousands of dollars) for a major city in California.
Mean = 22.7
n = 183
Population std dev = 6.3
Since population std dev is known we can use Z critical value.
Std error = 
Z critical =1.44
Marginof error = ±1.44*0.4657=0.6706
Confidence interval 85%
=
The expression given is
The sum of the expression will be,
The sum will be
<span>binomial </span>is an algebraic expression containing 2 terms. For example, (x + y) is a binomial.
We sometimes need to expand binomials as follows:
(a + b)0 = 1
(a + b)1 = a + b
(a + b)2 = a2 + 2ab + b2
(a + b)3 = a3 + 3a2b + 3ab2 + b3
<span>(a + b)4</span> <span>= a4 + 4a3b</span><span> + 6a2b2 + 4ab3 + b4</span>
<span>(a + b)5</span> <span>= a5 + 5a4b</span> <span>+ 10a3b2</span><span> + 10a2b3 + 5ab4 + b5</span>
Clearly, doing this by direct multiplication gets quite tedious and can be rather difficult for larger powers or more complicated expressions.
Pascal's Triangle
We note that the coefficients (the numbers in front of each term) follow a pattern. [This was noticed long before Pascal, by the Chinese.]
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
You can use this pattern to form the coefficients, rather than multiply everything out as we did above.
The Binomial Theorem
We use the binomial theorem to help us expand binomials to any given power without direct multiplication. As we have seen, multiplication can be time-consuming or even not possible in some cases.
<span>Properties of the Binomial Expansion <span>(a + b)n</span></span><span><span>There are <span>\displaystyle{n}+{1}<span>n+1</span></span> terms.</span><span>The first term is <span>an</span> and the final term is <span>bn</span>.</span></span><span>Progressing from the first term to the last, the exponent of a decreases by <span>\displaystyle{1}1</span> from term to term while the exponent of b increases by <span>\displaystyle{1}1</span>. In addition, the sum of the exponents of a and b in each term is n.</span><span>If the coefficient of each term is multiplied by the exponent of a in that term, and the product is divided by the number of that term, we obtain the coefficient of the next term.</span>
The recursive formula would be:
This is because the first term, a₁, is 10. A recursive rule is dependent upon the term before it (a(n-1)) and the common ratio. The common ratio, or the number that each term is multiplied by, is -8.
