Answer:
The integer 27 is an odd number. The integer 27 is a Composite number. 13 is less than 27, so 27 is a deficient number.
Answer:
<u>First question answer:</u> The limit is 69
<u>Second question answer:</u> The limit is 5
Step-by-step explanation:
For the first limit, plug in
in the expression
, that's the answer for linear equations and limits.
So we have:
![9x-3\\9(8)-3\\72-3\\69](https://tex.z-dn.net/?f=9x-3%5C%5C9%288%29-3%5C%5C72-3%5C%5C69)
The answer is 69
For the second limit, if we do same thing as the first, we will get division by 0. Also indeterminate form, 0 divided by 0. Thus we would think that the limit does not exist. But if we do some algebra, we can easily simplify it and thus plug in the value
into the simplified expression to get the correct answer. Shown below:
![\frac{x^2+8x-9}{x^2-1}\\\frac{(x+9)(x-1)}{(x-1)(x+1)}\\\frac{x+9}{x+1}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E2%2B8x-9%7D%7Bx%5E2-1%7D%5C%5C%5Cfrac%7B%28x%2B9%29%28x-1%29%7D%7B%28x-1%29%28x%2B1%29%7D%5C%5C%5Cfrac%7Bx%2B9%7D%7Bx%2B1%7D)
<em>Now putting 1 in
gives us the limit:</em>
![\frac{x+9}{x+1}\\\frac{1+9}{1+1}=\frac{10}{2}=5](https://tex.z-dn.net/?f=%5Cfrac%7Bx%2B9%7D%7Bx%2B1%7D%5C%5C%5Cfrac%7B1%2B9%7D%7B1%2B1%7D%3D%5Cfrac%7B10%7D%7B2%7D%3D5)
So the answer is 5
Given:
The given sets are:
Set a : 200, 104, 100, 160.
Set b: 270, 400, 483, 300, x.
Mean of set a: mean of set b= 3:8
To find:
The value of x.
Solution:
Formula for mean:
![Mean=\dfrac{\text{Sum of observations}}{\text{Number of observation}}](https://tex.z-dn.net/?f=Mean%3D%5Cdfrac%7B%5Ctext%7BSum%20of%20observations%7D%7D%7B%5Ctext%7BNumber%20of%20observation%7D%7D)
The mean of set of a is:
![Mean=\dfrac{200+104+100+160}{4}](https://tex.z-dn.net/?f=Mean%3D%5Cdfrac%7B200%2B104%2B100%2B160%7D%7B4%7D)
![Mean=\dfrac{564}{4}](https://tex.z-dn.net/?f=Mean%3D%5Cdfrac%7B564%7D%7B4%7D)
![Mean=141](https://tex.z-dn.net/?f=Mean%3D141)
The mean of set of b is:
![Mean=\dfrac{270+400+483+300+x}{5}](https://tex.z-dn.net/?f=Mean%3D%5Cdfrac%7B270%2B400%2B483%2B300%2Bx%7D%7B5%7D)
![Mean=\dfrac{1453+x}{5}](https://tex.z-dn.net/?f=Mean%3D%5Cdfrac%7B1453%2Bx%7D%7B5%7D)
![Mean=\dfrac{1453+x}{5}](https://tex.z-dn.net/?f=Mean%3D%5Cdfrac%7B1453%2Bx%7D%7B5%7D)
It is given that,
Mean of set a: mean of set b= 3:8
![\dfrac{141}{\dfrac{1453+x}{5}}=\dfrac{3}{8}](https://tex.z-dn.net/?f=%5Cdfrac%7B141%7D%7B%5Cdfrac%7B1453%2Bx%7D%7B5%7D%7D%3D%5Cdfrac%7B3%7D%7B8%7D)
![\dfrac{705}{1453+x}=\dfrac{3}{8}](https://tex.z-dn.net/?f=%5Cdfrac%7B705%7D%7B1453%2Bx%7D%3D%5Cdfrac%7B3%7D%7B8%7D)
![8\times 705=3\times (1453+x)](https://tex.z-dn.net/?f=8%5Ctimes%20705%3D3%5Ctimes%20%281453%2Bx%29)
![5640=4359 +3x](https://tex.z-dn.net/?f=5640%3D4359%0A%2B3x)
Isolate the variable x.
![5640-4359 =3x](https://tex.z-dn.net/?f=5640-4359%0A%3D3x)
![1281 =3x](https://tex.z-dn.net/?f=1281%0A%3D3x)
Divide both sides by 3.
![\dfrac{1281}{3} =x](https://tex.z-dn.net/?f=%5Cdfrac%7B1281%7D%7B3%7D%0A%3Dx)
![427 =x](https://tex.z-dn.net/?f=427%0A%3Dx)
Therefore, the value of x is 427.
<span>1, 2, 3, 6, 9, 18, 27, & 54
</span>
It looks floppy but you said you need this fast so yeah