1) 452.6
2)175.666666667 or 175.7
3) There will be approximately 2,639 bottles in each box.
From diameter you get radius by halving the diamter
radius = 14/2 = 7 cm
volume, height, and radius of a cylinder are all related by formula for volume of cylinder:
V = <span>πr²h
If we want to solve for h, we divide both sides by </span><span>πr² and get
h = V/(</span><span>πr²)
since V = 112</span><span>π and r = 7, h is equal to
h = (112</span>π)/(<span>π*7²) = 112/49 = 16/7 cm
height is C 16/7 cm
</span>
Answer:
![z= \frac{p- \mu_p}{\sigma_p}](https://tex.z-dn.net/?f=%20z%3D%20%5Cfrac%7Bp-%20%5Cmu_p%7D%7B%5Csigma_p%7D)
And the z score for 0.4 is
![z = \frac{0.4-0.4}{\sigma_p} = 0](https://tex.z-dn.net/?f=%20z%20%3D%20%5Cfrac%7B0.4-0.4%7D%7B%5Csigma_p%7D%20%3D%200)
And then the probability desired would be:
![P(p](https://tex.z-dn.net/?f=%20P%28p%3C0.4%29%20%3D%20p%28z%3C0%29%20%3D0.5)
Step-by-step explanation:
The normal approximation for this case is satisfied since the value for p is near to 0.5 and the sample size is large enough, and we have:
![np = 45*0.4= 18 >10](https://tex.z-dn.net/?f=%20np%20%3D%2045%2A0.4%3D%2018%20%3E10)
![n(1-p) = 45*0.6= 27 >10](https://tex.z-dn.net/?f=%20n%281-p%29%20%3D%2045%2A0.6%3D%2027%20%3E10)
For this case we can assume that the population proportion have the following distribution
Where:
![\mu_{p}= \hat p = 0.4](https://tex.z-dn.net/?f=%5Cmu_%7Bp%7D%3D%20%5Chat%20p%20%3D%200.4)
![\sigma_p = \sqrt{\frac{p(1-p)}(n} =\sqrt{\frac{0.4(1-0.4)}(45}= 0.0703](https://tex.z-dn.net/?f=%5Csigma_p%20%3D%20%5Csqrt%7B%5Cfrac%7Bp%281-p%29%7D%28n%7D%20%3D%5Csqrt%7B%5Cfrac%7B0.4%281-0.4%29%7D%2845%7D%3D%200.0703)
And we want to find this probability:
![P(p](https://tex.z-dn.net/?f=%20P%28p%20%3C0.4%29)
And we can use the z score formula given by:
![z= \frac{p- \mu_p}{\sigma_p}](https://tex.z-dn.net/?f=%20z%3D%20%5Cfrac%7Bp-%20%5Cmu_p%7D%7B%5Csigma_p%7D)
And the z score for 0.4 is
![z = \frac{0.4-0.4}{\sigma_p} = 0](https://tex.z-dn.net/?f=%20z%20%3D%20%5Cfrac%7B0.4-0.4%7D%7B%5Csigma_p%7D%20%3D%200)
And then the probability desired would be:
![P(p](https://tex.z-dn.net/?f=%20P%28p%3C0.4%29%20%3D%20p%28z%3C0%29%20%3D0.5)
<h2>
AREA</h2>
The formula for finding area of a square is:
![length \times width](https://tex.z-dn.net/?f=%20length%20%5Ctimes%20width%20)
In a square, all the sides are the same. Each side is 6 meters long. Plug in 6 to the formula.
![length \times width \rightarrow 6 \times 6](https://tex.z-dn.net/?f=%20length%20%5Ctimes%20width%20%5Crightarrow%206%20%5Ctimes%206%20)
Multiply:
![6 \times 6 = 36](https://tex.z-dn.net/?f=%206%20%5Ctimes%206%20%3D%2036%20)
The area of the square is 36 m²
<h2>PERIMETER</h2>
Perimeter is the distance around a shape. To find perimeter, you have to add all all the side lengths. The formula for finding perimeter is:
![2(l) \times 2(w)](https://tex.z-dn.net/?f=%202%28l%29%20%5Ctimes%202%28w%29%20)
Remember that squares have 4 sides, and all length(s) and width(s) measure the same. The length and width measure the same. Plug in the numbers into the formula:
![2(l) + 2(w) \rightarrow 2(6) + 2(6)](https://tex.z-dn.net/?f=%202%28l%29%20%2B%202%28w%29%20%5Crightarrow%202%286%29%20%2B%202%286%29%20)
Simplify:
![2(6) + 2(6) = 12 + 12](https://tex.z-dn.net/?f=%202%286%29%20%2B%202%286%29%20%3D%2012%20%2B%2012%20)
Add:
![12 + 12 = 24](https://tex.z-dn.net/?f=%2012%20%2B%2012%20%3D%2024%20)
The perimeter of the square is 24 m
Answer:
Base line: x + 2y = 6
Parallel: Continous, never touching
Perpendicular: Create a right angle when touching
y= -1/2x -5 : Parallel
-2x+y=-4 : Pependicular
-x+2y=2 : Neither
x+2y=-2 : Parallel