<h2><em><u>Solution</u></em> : </h2>
let the last number be x
we know,
![\boxed{mean = \frac{sum \: \: of \: \: all \: \: observations}{number \: \: of \: \: observations} }](https://tex.z-dn.net/?f=%20%5Cboxed%7Bmean%20%3D%20%20%5Cfrac%7Bsum%20%5C%3A%20%20%5C%3A%20of%20%5C%3A%20%20%5C%3A%20all%20%5C%3A%20%20%5C%3A%20observations%7D%7Bnumber%20%5C%3A%20%20%5C%3A%20of%20%5C%3A%20%20%5C%3A%20observations%7D%20%7D)
So,
![\hookrightarrow \: 8 = \dfrac{22 + x}{4}](https://tex.z-dn.net/?f=%20%5Chookrightarrow%20%5C%3A%208%20%3D%20%20%5Cdfrac%7B22%20%2B%20x%7D%7B4%7D%20)
![\hookrightarrow \: 8 \times 4 = 22 + x](https://tex.z-dn.net/?f=%20%5Chookrightarrow%20%5C%3A%208%20%5Ctimes%204%20%3D%2022%20%2B%20x)
![\hookrightarrow \: 32 = 22 + x](https://tex.z-dn.net/?f=%20%5Chookrightarrow%20%5C%3A%2032%20%3D%2022%20%2B%20x)
![\hookrightarrow \: x = 32 - 22](https://tex.z-dn.net/?f=%20%5Chookrightarrow%20%5C%3A%20x%20%3D%2032%20-%2022)
![\hookrightarrow \: x = 10](https://tex.z-dn.net/?f=%20%5Chookrightarrow%20%5C%3A%20x%20%3D%2010)
therefore, the last number is 10.
Answer is x= -14 because you divide each term by -3 and then simplify
Answer: 1692
Step-by-step explanation:
Formula to find the sample size :
![n=p(1-p)(\dfrac{z_{\alpha/2}}{E})^2](https://tex.z-dn.net/?f=n%3Dp%281-p%29%28%5Cdfrac%7Bz_%7B%5Calpha%2F2%7D%7D%7BE%7D%29%5E2)
Given : Confidence level : ![(1-\alpha)=0.90](https://tex.z-dn.net/?f=%281-%5Calpha%29%3D0.90)
⇒ significance level =![\alpha= 0.10](https://tex.z-dn.net/?f=%5Calpha%3D%200.10)
z-value for 90% confidence interval (using z-table)=![z_{\alpha/2}=1.645](https://tex.z-dn.net/?f=z_%7B%5Calpha%2F2%7D%3D1.645)
Prior estimate of the population proportion (p) of customers who keep up with regular vehicle maintenance is unknown.
Let we take p= 0.5
Margin of error : E= 2%=0.02
Now, the required sample size will be :
![n=0.5(1-0.5)(\dfrac{1.645}{0.02})^2](https://tex.z-dn.net/?f=n%3D0.5%281-0.5%29%28%5Cdfrac%7B1.645%7D%7B0.02%7D%29%5E2)
Simplify , we get
![n=(0.25)(6765.0625)=1691.265625\approx1692](https://tex.z-dn.net/?f=n%3D%280.25%29%286765.0625%29%3D1691.265625%5Capprox1692)
Hence, the required sample size = 1692
Answer:
It should be "one solution"
Step-by-step explanation:
After graphing the equations, the two lines only intersect at one point which makes it "one solution." Hope this helps.
<u>Given</u><u> </u><u>info:</u><u>-</u>If the radius of a right circular cylinder is doubled and height becomes 1/4 of the original height.
Find the ratio of the Curved Surface Areas of the new cylinder to that of the original cylinder ?
<u>Explanation</u><u>:</u><u>-</u>
Let the radius of the right circular cylinder be r units
Let the radius of the right circular cylinder be h units
Curved Surface Area of the original right circular cylinder = 2πrh sq.units ----(i)
If the radius of the right circular cylinder is doubled then the radius of the new cylinder = 2r units
The height of the new right circular cylinder
= (1/4)×h units
⇛ h/4 units
Curved Surface Area of the new cylinder
= 2π(2r)(h/4) sq.units
⇛ 4πrh/4 sq.units
⇛ πrh sq.units --------(ii)
The ratio of the Curved Surface Areas of the new cylinder to that of the original cylinder
⇛ πrh : 2πrh
⇛ πrh / 2πrh
⇛ 1/2
⇛ 1:2
Therefore the ratio = 1:2
The ratio of the Curved Surface Areas of the new cylinder to that of the original cylinder is 1:2