. The article "Wind-Uplift Capacity of Residential Wood Roof-Sheathing Panels Retrofitted with Insulating Foam Adhesive" (P. Datin, D. Prevatt, and W. Pang, Journal of Architectural Engineering, 2011:144–154) presents a study of the failure pressures of roof panels. Following are the failure pressures, in kPa, for five panels constructed with 6d smooth shank nails. These data are consistent with means and standard deviations presented in the article. 3.32 2.53 3.45 2.38 3.01 Find a 95% confidence interval for the mean failure pressure for this type of roof panel.

The 95% confidence interval  is  

Step-by-step explanation:

From the question we are told that

   The sample size is  n =  5

    The sample  data is  3.32  2.53  3.45  2.38   3.01

Gnerally the sample mean is mathematically represented as

=>    

=>    

Generally the standard deviation is mathematically represented as

=>

=>    

Generally the degree of freedom is mathematically represented  as

=>  

=>      

From the question we are told the confidence level is  95% , hence the level of significance is  

=>  

Generally from the t distribution table the critical value  of   at a degree of freedom of    is  

Generally the margin of error is mathematically represented as  

Generally 95% confidence interval is mathematically represented as  

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb