<span>The area of the base is x^2> The height is h. Each side of the box has area xh. There are 4 sides of the box so the total surface area of the box is x^2+4xh and that is equal to 1000. Solve that equation for h:
x^2+4xh = 1000 h = (1000-x^2)/4x so the Volume = x^2[(1000-x^2)/4x]
Simplify and get V = 250x-x^3/4
The volume will be a maximum when its first derivative is 0.
V' = 250-3/4x^2
Set to 0 and solve. x=18.26
Now plug into the volume function to find the maximum volume:
V=250(18.26)-(18.26)^3/4
V= 4564.35 - 1522.10 =3042.25</span>
Answer:
Reject Null Hypothesis given that P-value < ∝
Step-by-step explanation:
Applying the Five ( 5 ) step model and assuming ∝ = 0.05
First step : determine the Null hypothesis
H0 : Age and support for Anti-smoking = independent
Second step : Determine the alternate hypothesis
Ha : Age and support for Anti-smoking ≠ independent
Thirdly : Identify significance level ( ∝ ) = 0.05
4th step : Calculate the Test statistic and P-value
Chi-squared test = 36.1429 using excel function
P-value = 1 - CHISQ.DIST(36.1429, 1, TRUE) < 0.0001
finally : we can conclude that Age and support for Anti -smoking are not Independent hence we Reject The Null hypothesis. Given that
P-value < ∝
