Find the surface area
1 answer:
If you notice, the figure has two hexagonal faces and 6 rectangles.
now the rectangles are just 4x9 each, so their area is just 6(4*9) for all 6.
the hexagons has a distance from the center perpendicular to a side of 7.8, namely the apothem is 7.8, and since each side is 9 km long, the perimeter is 9+9+9+9+9+9.
since the area of a regular polygon is (1/2)(apothem)(perimeter), we can simply get the area of those two hexagons and the area of the rectangles, sum them up, and that's the surface area of the hexagonal prism.
![\bf \stackrel{\textit{6 rectangles}}{6(4\cdot 9)}~~~~+~~~~\stackrel{\textit{2 hexagons}}{2\left[ \cfrac{1}{2}(7.8)(54) \right]}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7B%5Ctextit%7B6%20rectangles%7D%7D%7B6%284%5Ccdot%209%29%7D~~~~%2B~~~~%5Cstackrel%7B%5Ctextit%7B2%20hexagons%7D%7D%7B2%5Cleft%5B%20%5Ccfrac%7B1%7D%7B2%7D%287.8%29%2854%29%20%5Cright%5D%7D)
now the rectangles are just 4x9 each, so their area is just 6(4*9) for all 6.
the hexagons has a distance from the center perpendicular to a side of 7.8, namely the apothem is 7.8, and since each side is 9 km long, the perimeter is 9+9+9+9+9+9.
since the area of a regular polygon is (1/2)(apothem)(perimeter), we can simply get the area of those two hexagons and the area of the rectangles, sum them up, and that's the surface area of the hexagonal prism.
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Answer:
a.
b.
c. Not mutually exclusive.
d. Not independent events
Step-by-step explanation:
a. When two six-sided fair dice are rolled one time,
Total possible outcomes, n(S) = 6 × 6 = 36,
If A be the event that the first die is odd and the second is a 4, 5, or 6
Then, A = {(1, 4), (3, 4), (5, 4), (1, 5), (3, 5), (5, 5), (1, 6), (3, 6), (5, 6)}
i.e. n(A) = 9,
Thus, the probability of event A,
b. if B be the event that the sum of the two dice is 10,
Then B = {(4, 6), (5, 5), (6, 4)}
i.e. n(B) = 3,
Thus, the probability of event B,
c. Two event are called mutually exclusive events,
If they are disjoint,
i.e. A and B are mutually exclusive,
If A ∩ B = ∅
∵ {(1, 4), (3, 4), (5, 4), (1, 5), (3, 5), (5, 5), (1, 6), (3, 6), (5, 6)} ∩ {(4, 6), (5, 5), (6, 4)}
= {(5, 5)} ≠ ∅
So, they are not mutually exclusive events.
d. Two events are called independent if the occurrence of one event does not affect the occurrence of other event.
Also, A and B are independent events,
If P(A ∩ B) = P(A) × P(B)
n(A∩ B) = 1,
∵
Hence, they are not independent events.