Answer:
- Base Length of 84cm
- Height of 42 cm.
Step-by-step explanation:
Given a box with a square base and an open top which must have a volume of 296352 cubic centimetre. We want to minimize the amount of material used.
Step 1:
Let the side length of the base =x
Let the height of the box =h
Since the box has a square base
Volume, 
Surface Area of the box = Base Area + Area of 4 sides
Step 2: Find the derivative of A(x)
Step 3: Set A'(x)=0 and solve for x
![A'(x)=\dfrac{2x^3-1185408}{x^2}=0\\2x^3-1185408=0\\2x^3=1185408\\$Divide both sides by 2\\x^3=592704\\$Take the cube root of both sides\\x=\sqrt[3]{592704}\\x=84](https://tex.z-dn.net/?f=A%27%28x%29%3D%5Cdfrac%7B2x%5E3-1185408%7D%7Bx%5E2%7D%3D0%5C%5C2x%5E3-1185408%3D0%5C%5C2x%5E3%3D1185408%5C%5C%24Divide%20both%20sides%20by%202%5C%5Cx%5E3%3D592704%5C%5C%24Take%20the%20cube%20root%20of%20both%20sides%5C%5Cx%3D%5Csqrt%5B3%5D%7B592704%7D%5C%5Cx%3D84)
Step 4: Verify that x=84 is a minimum value
We use the second derivative test
Since the second derivative is positive at x=84, then it is a minimum point.
Recall:
Therefore, the dimensions that minimizes the box surface area are:
- Base Length of 84cm
- Height of 42 cm.
The answer will be 40 feet because w = 10 feet’s so it will decrease into 100
Answer: 38.41 minutes
Step-by-step explanation:
The standard error for the difference in means is given by :-
where , 
= Standard deviation for sample 1.
= Size of sample 1.
= Standard deviation for sample 2.
= Size of sample 2.
Let the sample of Latino name is first and non -Latino is second.
As per given , we have
The standard error for the difference in means will be :
Hence, the standard error for the difference in means =38.41 minutes
The question is incomplete. The complete question is :
Tests for adverse reactions to a new drug yielded the results given in the table. Drug Placebo headaches No headaches 11 7 91 73 The data will be analyzed to determine if there is sufficient evidence to conclude that an association exists between the treatment (drug or placebo) and the reaction (whether or not headaches were experienced. The results of the test are X2 = 1.798 P-value = .1799. Identify the correct conclusion. O Do not reject the null hypothesis. Report that there insufficient evidence to conclude that treatment and reaction are dependent. O Fail to reject the null hypothesis. Report that there insufficient evidence to conclude that the distribution of headaches is uniform for the drug and placebo. O Reject the null hypothesis. Report that there is sufficient evidence to conclude that treatment and reaction are dependent. O Reject the null hypothesis. Report that there is insufficient evidence to conclude that treatment and reaction are dependent.
Solution :
Given :
Drugs Placebo
Headaches 11 7
No headaches 73 91
The results of the test are :
The P value is given as = 0.1799
The hypothesis test given for dependent or association between the two variables.
: There is no association between the treatment and the reaction
: There is association between the treatment and the reaction.
If the P value is greater than the alpha value, i.e. when
P value > α (0.05), then we reject the .
Therefore, Do not 
. Report that 
evidence to conclude that 
as well as 
.
