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Nat2105 [25]
3 years ago
9

Find the total area of the prism. 144 sq. in. 576 sq. in. 864 sq. in.

Mathematics
1 answer:
anastassius [24]3 years ago
7 0

Answer:

864\ in^{2}

Step-by-step explanation:

The figure is a cube

The surface area of a cube is equal to

S=6b^{2}

where

b is the length side of the cube

In this problem we have

b=12\ in

substitute

S=6(12^{2})=864\ in^{2}


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Cylinder (A):
-Surface area: adding all areas of all faces of the shape.

*10 x 6= 60m^3
*3.14 x 3^2 = 28.274 m^2. Then We times it by 2 since we have 2 circles. Which equals to 56.55m^2

Total surface area: 60 + 56.55 = 116.55m^2

-Volume: 3.14 x r^2 x h, then substitute.

*3.14 x 3^2 x 10 = 282.74m^3

(B):
-surface area:

*7 x 11= 77
*5 x 11 = 55
*11 x 11 = 121
*7 x 5 = 35/2 = 17.5 > then again we times it by 2 cuz we have 2 triangles. Which equals to 35.

Total surface area: 77 + 55 + 121 + 35 = 288 cm^2

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Make sure to check the units!!!
Hope this helped :)
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3 years ago
Anna has 4 bags of 100 crackers, bags of 10 crackers, and 3 crackers that aren’t in bags. How many crackers does she have
sweet-ann [11.9K]

Answer:1,100??

Step-by-step explanation:

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3 years ago
Suppose that two teams play a series of games that ends when one of them has won ???? games. Also suppose that each game played
Musya8 [376]

Answer:

(a) E(X) = -2p² + 2p + 2; d²/dp² E(X) at p = 1/2 is less than 0

(b) 6p⁴ - 12p³ + 3p² + 3p + 3; d²/dp² E(X) at p = 1/2 is less than 0

Step-by-step explanation:

(a) when i = 2, the expected number of played games will be:

E(X) = 2[p² + (1-p)²] + 3[2p² (1-p) + 2p(1-p)²] = 2[p²+1-2p+p²] + 3[2p²-2p³+2p(1-2p+p²)] = 2[2p²-2p+1] + 3[2p² - 2p³+2p-4p²+2p³] =  4p²-4p+2-6p²+6p = -2p²+2p+2.

If p = 1/2, then:

d²/dp² E(X) = d/dp (-4p + 2) = -4 which is less than 0. Therefore, the E(X) is maximized.

(b) when i = 3;

E(X) = 3[p³ + (1-p)³] + 4[3p³(1-p) + 3p(1-p)³] + 5[6p³(1-p)² + 6p²(1-p)³]

Simplification and rearrangement lead to:

E(X) = 6p⁴-12p³+3p²+3p+3

if p = 1/2, then:

d²/dp² E(X) at p = 1/2 = d/dp (24p³-36p²+6p+3) = 72p²-72p+6 = 72(1/2)² - 72(1/2) +6 = 18 - 36 +8 = -10

Therefore, E(X) is maximized.

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