Answer:
the 90% confidence interval is ( 48.684 , 51.316 )
Step-by-step explanation:
Given that :
the sample size = 36
Sample Mean = 50
standard deviation = 4.80
The objective is to calculate a 90% confidence interval.
At 90% confidence interval ;
the level of significance = 1 - 0.9 = 0.1
The critical value for ![z_{\alpha/2} = z_{0.1/2}](https://tex.z-dn.net/?f=z_%7B%5Calpha%2F2%7D%20%3D%20z_%7B0.1%2F2%7D)
= 1.645
The standard error S.E = ![\dfrac{\sigma}{\sqrt{n}}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D)
=![\dfrac{4.8}{\sqrt{36}}](https://tex.z-dn.net/?f=%5Cdfrac%7B4.8%7D%7B%5Csqrt%7B36%7D%7D)
![=\dfrac{4.8}{6}](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B4.8%7D%7B6%7D)
= 0.8
The Confidence interval level can be computed as:
![\bar x \ \pm z \times \ \dfrac{ \sigma }{\sqrt{n}}](https://tex.z-dn.net/?f=%5Cbar%20x%20%20%5C%20%5Cpm%20z%20%5Ctimes%20%5C%20%5Cdfrac%7B%20%5Csigma%20%7D%7B%5Csqrt%7Bn%7D%7D)
For the lower limit :
![\bar x \ - z \times \ \dfrac{ \sigma }{\sqrt{n}}](https://tex.z-dn.net/?f=%5Cbar%20x%20%20%5C%20-%20z%20%5Ctimes%20%5C%20%5Cdfrac%7B%20%5Csigma%20%7D%7B%5Csqrt%7Bn%7D%7D)
![=50 \ - 1.645 \times \ \dfrac{ 4.8 }{\sqrt{36}}](https://tex.z-dn.net/?f=%3D50%20%5C%20-%201.645%20%20%5Ctimes%20%5C%20%5Cdfrac%7B%204.8%20%7D%7B%5Csqrt%7B36%7D%7D)
![=50 \ - 1.645 \times \ 0.8 }}](https://tex.z-dn.net/?f=%3D50%20%5C%20-%201.645%20%20%5Ctimes%20%5C%200.8%20%7D%7D)
=50 - 1.316
= 48.684
For the upper limit :
![\bar x \ - z \times \ \dfrac{ \sigma }{\sqrt{n}}](https://tex.z-dn.net/?f=%5Cbar%20x%20%20%5C%20-%20z%20%5Ctimes%20%5C%20%5Cdfrac%7B%20%5Csigma%20%7D%7B%5Csqrt%7Bn%7D%7D)
![=50 \ + 1.645 \times \ \dfrac{ 4.8 }{\sqrt{36}}](https://tex.z-dn.net/?f=%3D50%20%5C%20%2B%201.645%20%20%5Ctimes%20%5C%20%5Cdfrac%7B%204.8%20%7D%7B%5Csqrt%7B36%7D%7D)
![=50 \ + 1.645 \times \ 0.8 }}](https://tex.z-dn.net/?f=%3D50%20%5C%20%2B%201.645%20%20%5Ctimes%20%5C%200.8%20%7D%7D)
=50 + 1.316
= 51.316
Thus, the 90% confidence interval is ( 48.684 , 51.316 )
We are given three vertices, but we do not know which two are adjacent. We could draw these points to find out. But that is not neccesary.
In a parallelogram we can draw four types of lines. Two types are sides and two types are diagonals. Diagonals are lngre than sides. This helps us to solve this problems. If we find distance between all points we will take only two smaller numbers because they represent sides.
Distance between two points is given by:
![d= \sqrt{ ( x_{2}- x_{1} )^{2} + (y_{2}- y_{1})^{2} }](https://tex.z-dn.net/?f=d%3D%20%5Csqrt%7B%20%28%20x_%7B2%7D-%20x_%7B1%7D%20%20%29%5E%7B2%7D%20%2B%20%28y_%7B2%7D-%20y_%7B1%7D%29%5E%7B2%7D%20%7D%20)
For points (3,2) and (4,4) distance is:
![d= \sqrt{ ( 4- 3 )^{2} + (4-2)^{2} } = \sqrt{1+4} = \sqrt{5}](https://tex.z-dn.net/?f=d%3D%20%5Csqrt%7B%20%28%204-%203%20%29%5E%7B2%7D%20%2B%20%284-2%29%5E%7B2%7D%20%7D%20%3D%20%5Csqrt%7B1%2B4%7D%20%3D%20%5Csqrt%7B5%7D%20)
For points (3,2) and (6,1) distance is:
![d= \sqrt{ ( 6- 3 )^{2} + (1-2)^{2} } = \sqrt{9+1} = \sqrt{10}](https://tex.z-dn.net/?f=d%3D%20%5Csqrt%7B%20%28%206-%203%20%29%5E%7B2%7D%20%2B%20%281-2%29%5E%7B2%7D%20%7D%20%3D%20%5Csqrt%7B9%2B1%7D%20%3D%20%5Csqrt%7B10%7D)
For points (4,4) and (6,1) distance is:
![d= \sqrt{ ( 6-4 )^{2} + (1-4)^{2} } = \sqrt{4+9} = \sqrt{13}](https://tex.z-dn.net/?f=d%3D%20%5Csqrt%7B%20%28%206-4%20%29%5E%7B2%7D%20%2B%20%281-4%29%5E%7B2%7D%20%7D%20%3D%20%5Csqrt%7B4%2B9%7D%20%3D%20%5Csqrt%7B13%7D)
Last distance is greatest and it represents a diagonal. Other two distances represent sides.
Perimeter of a parallelogram is given by:
Answer:
The First one is an Acute angle 90 degrees
Step-by-step explanation <em>The second one is an Equitateral angle has three equal sides. The third one is an obtuse greater than 90. and the last one is an right angle. has one right side.</em>
Answer:
V =64 ft^3
Step-by-step explanation:
The volume of a cube is given by
V = s^3 where s is the side length
V = 4^3
V =64 ft^3