Each edge of a right triangular prism is 8 inches in length. What is the surface area of the right triangular prism?
1 answer:
Check the picture below.
since each edge is 8 inches, that simply means the right-triangle has a base of 8 and a height/altitude of 8 as well.
and since the triangular prism is really just two triangles and 3 rectangles, as you see there, we can simply get the area of each figure and sum them up, and that's the surface area of the prism.
![\bf \stackrel{\textit{area of the two triangles}}{2\left[ \cfrac{1}{2}(\stackrel{base}{8})(\stackrel{height}{8}) \right]}~+~\stackrel{\textit{area of the 3 rectangles}}{3(8\cdot 8)}\implies 64+192\implies 256](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7B%5Ctextit%7Barea%20of%20the%20two%20triangles%7D%7D%7B2%5Cleft%5B%20%5Ccfrac%7B1%7D%7B2%7D%28%5Cstackrel%7Bbase%7D%7B8%7D%29%28%5Cstackrel%7Bheight%7D%7B8%7D%29%20%5Cright%5D%7D~%2B~%5Cstackrel%7B%5Ctextit%7Barea%20of%20the%203%20rectangles%7D%7D%7B3%288%5Ccdot%208%29%7D%5Cimplies%2064%2B192%5Cimplies%20256)
since each edge is 8 inches, that simply means the right-triangle has a base of 8 and a height/altitude of 8 as well.
and since the triangular prism is really just two triangles and 3 rectangles, as you see there, we can simply get the area of each figure and sum them up, and that's the surface area of the prism.
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Answer:
Option B is correct.
Use the difference in sample means (10 and 8) in a hypothesis test for a difference in two population means.
Step-by-step Explanation:
The clear, complete table For this question is presented in the attached image to this solution.
It should be noted that For this question, the running coach wants to test if participating in weekly running clubs significantly improves the time to run a mile.
In the data setup, the mean time to run a mile in January for those that participate in weekly running clubs and those that do not was provided.
The mean time to run a mile in June too is provided for those that participate in weekly running clubs and those that do not.
Then the difference in the mean time to run a mile in January and June for the two classes (those that participate in weekly running clubs and those that do not) is also provided.
Since, the aim of the running coach is to test if participating in weekly running clubs significantly improves the time to run a mile, so, it is logical that it is the improvements in running times for the two groups that should be compared.
Hence, we should use the difference in sample means (10 and 8) in a hypothesis test for a difference in two population means.
Hope this Helps!!!
