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:
The test statistic value is 1.474.
Step-by-step explanation:
In this case we need to determine whether the plant is making a higher than expected number of irregular t-shirts.
If more than 8% of the t-shirts manufactured at a plant are classified as irregular, the manager has to do an investigation to try to find the source of the increased mistakes in the manufacturing process..
The hypothesis for this test can be defined as follows:
<em>H₀</em>: The proportion of irregular t-shirts is 8%, i.e. <em>p</em> = 0.08.
<em>Hₐ</em>: The proportion of irregular t-shirts is more than 8%, i.e. <em>p</em> > 0.08.
The information provided is:
<em>n</em> = 100
<em>X</em> = number of irregular t-shirts = 12
Compute the sample proportion as follows:
Compute the test statistic as follows:
Thus, the test statistic value is 1.474.