Answer:
(a)Length =2 feet
(b)Width =2 feet
(c)Height=3 feet
Step-by-step explanation:
Let the dimensions of the box be x, y and z
The rectangular box has a square base.
Therefore, Volume of the box
Volume of the box

The material for the base costs
, the material for the sides costs
, and the material for the top costs
.
Area of the base 
Cost of the Base 
Area of the sides 
Cost of the sides=
Area of the Top 
Cost of the Base 
Total Cost, 
Substituting 

To minimize C(x), we solve for the derivative and obtain its critical point
![C'(x)=\dfrac{0.6x^3-4.8}{x^2}\\Setting \:C'(x)=0\\0.6x^3-4.8=0\\0.6x^3=4.8\\x^3=4.8\div 0.6\\x^3=8\\x=\sqrt[3]{8}=2](https://tex.z-dn.net/?f=C%27%28x%29%3D%5Cdfrac%7B0.6x%5E3-4.8%7D%7Bx%5E2%7D%5C%5CSetting%20%5C%3AC%27%28x%29%3D0%5C%5C0.6x%5E3-4.8%3D0%5C%5C0.6x%5E3%3D4.8%5C%5Cx%5E3%3D4.8%5Cdiv%200.6%5C%5Cx%5E3%3D8%5C%5Cx%3D%5Csqrt%5B3%5D%7B8%7D%3D2)
Recall: 
Therefore, the dimensions that minimizes the cost of the box are:
(a)Length =2 feet
(b)Width =2 feet
(c)Height=3 feet
MP3 players in the shipment which are likely to be defective is 330.
Step-by-step explanation:
• Probability is event of an occurrence which is uncertain.
• Probability always lies between 0 to 1.
• The sample of 50 MP3 has 6 defective, to solve it has to be converted.
• Convert percentage in 100 multiply numerator and denominator by 2.
• Result is 6/50 converted to 12/100, bring it to 0.12%.
• 12% is defected in 100% of sample.
• It is found here that 2750 is the population and 12% of 2750.
• 2750 * 0.12 = 330, defective pieces in 2750.
• There are three types of Classical,Empirical or Experimental.
• Classical are ‘n’ number of events find the probability occurrence.
• Empirical or experimental is purely based on events.