Answer:
a) 14960 bottles
b) 502 bottles
Step-by-step explanation:
Given that:
Mean (μ) = 24 ounces, standard deviation (σ) = 0.14 ounces
a) From empirical rule (68−95−99.7%) , 68% of the population fall within 1 standard deviation of the mean (μ ± 1σ).
Therefore 68% fall within 0.14 ounces of the mean
the number of bottle = 22,000*68% = 14960 bottles
b) To solve this we are going to use the z score equation given as:
where x is the raw score = 23.72
![z=\frac{x-\mu}{\sigma}=\frac{23.72-24}{0.14} =-2](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%3D%5Cfrac%7B23.72-24%7D%7B0.14%7D%20%3D-2)
From the normal probability distribution table: P(X < 23.72) = P (Z < -2) = 0.0228
The number of rejected bottles = 22000 × 0.0228 = 502 bottles
Answer:
Step-by-step explanation:
Given data:
The given table.
The expression for the average temperature is,
![\begin{gathered} 86^{\circ}F=\frac{84^{\circ}F+92^{\circ}F+79^{\circ}F+x+82^{\circ}F+93^{\circ}F}{6} \\ 516^{\circ}F=430^{\circ}F+x \\ x=86^{\circ}F \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%2086%5E%7B%5Ccirc%7DF%3D%5Cfrac%7B84%5E%7B%5Ccirc%7DF%2B92%5E%7B%5Ccirc%7DF%2B79%5E%7B%5Ccirc%7DF%2Bx%2B82%5E%7B%5Ccirc%7DF%2B93%5E%7B%5Ccirc%7DF%7D%7B6%7D%20%5C%5C%20516%5E%7B%5Ccirc%7DF%3D430%5E%7B%5Ccirc%7DF%2Bx%20%5C%5C%20x%3D86%5E%7B%5Ccirc%7DF%20%5Cend%7Bgathered%7D)
Thus, the value of x is 86 degree Fahrenheit.
Given :
One company buys a new bulldozer for $130800.
The company depreciates the bulldozer linearly over its useful life of 20 years. It salvage value at the end of 20 years is $19800.
To Find :
The value of the Bulldozer, V, as a function of how many years old it is, t.
Solution :
Let, the equation is :
V = mt + c .....1)
For, t = 0 years
V = m(0) +c = $130800.00
c = $130800.00
For, t = 20 years
V = 20m + c = $19800.00
Putting value of c in above equation, we get :
20m + $130800.00 = $19800.00
m = (19800.00-130800.00 )÷20
m = -5550
Putting value of m and c in equation 1, we get :
V = -5550t + 130800
Hence, this is the required solution.
Answer:
Packaging with cube will be more efficient.
Step-by-step explanation:
Given:
A cube and a sphere where the diameter of the sphere is equal to the height of the cube.
Let the height of the cube "x"
Radius of the sphere =
Formula to be used:
Surface area of the cube =
and Surface area of the sphere = ![4\pi (r)^2](https://tex.z-dn.net/?f=4%5Cpi%20%28r%29%5E2)
Volume of the cube =
and Volume of the sphere = ![\frac{4\pi r^3}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B4%5Cpi%20r%5E3%7D%7B3%7D)
We have to compare the ratio of SA and Volumes.
Ratio of SA : Ratio of their volumes :
⇒
⇒ ![\frac{Volume \ of \ cube\ (V_1)}{Volume\ of\ sphere\ (V_2)}](https://tex.z-dn.net/?f=%5Cfrac%7BVolume%20%5C%20of%20%5C%20cube%5C%20%28V_1%29%7D%7BVolume%5C%20of%5C%20sphere%5C%20%28V_2%29%7D)
⇒
⇒ ![\frac{x^3}{\frac{4 \pi r^3}{3} }](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E3%7D%7B%5Cfrac%7B4%20%5Cpi%20r%5E3%7D%7B3%7D%20%7D)
⇒
⇒ ![\frac{x^3}{\frac{4 \pi (\frac{x}{2})^3}{3} }](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E3%7D%7B%5Cfrac%7B4%20%5Cpi%20%28%5Cfrac%7Bx%7D%7B2%7D%29%5E3%7D%7B3%7D%20%7D)
⇒
⇒ ![\frac{x^3}{\frac{4 \pi (\frac{x^3}{8})}{3} }](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E3%7D%7B%5Cfrac%7B4%20%5Cpi%20%28%5Cfrac%7Bx%5E3%7D%7B8%7D%29%7D%7B3%7D%20%7D)
⇒
⇒ ![\frac{6}{\pi}](https://tex.z-dn.net/?f=%5Cfrac%7B6%7D%7B%5Cpi%7D)
⇒ approx
⇒ approx ![2](https://tex.z-dn.net/?f=2)
⇒
⇒ ![V_1=2V_2](https://tex.z-dn.net/?f=V_1%3D2V_2)
Packaging of the toy with the cube will be more efficient as it has more volume comparatively.