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PtichkaEL [24]
3 years ago
15

In how many orders can four girls and four boys walk through a doorway single file if

Mathematics
1 answer:
RideAnS [48]3 years ago
7 0

Answer:

(a) 40,320

(b) 576

Step-by-step explanation:

(a) We are asked to find the number of orders in which four girls and four boys can walk through a doorway single file if  there are no restrictions.

Since there are 8 people in total, so they can walk in 8! ways.

8!=8\cdot7\cdot6\cdot5\cdot4\cdot 3 \cdot 2\cdot1=40,320

Therefore, four girls and four boys walk through a doorway single file in 40,320 ways.

(b) To find the number of ways in which four girls and four boys can walk through a doorway single file if  the girls walk through before the boys.

The total number of ways would be equal to product of 4 girls walking first and 4 boys walking after.

4 girls can walk first in 4! ways and boys can walk after in 4! ways as well.

4!\cdot 4!=4\cdot 3\cdot 2\cdot 1\cdot 4\cdot 3\cdot 2\cdot 1=576

Therefore, four girls and four boys can walk through a doorway single file if  the girls walk through before the boys, in 576 ways.

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Step-by-step explanation:

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4 0
3 years ago
The rectangular bar is connected to the support bracket with a 10-mm-diameter pin. The bar width is w = 70 mm and the bar thickn
german

Answer:

P_max = 9.032 KN

Step-by-step explanation:

Given:

- Bar width and each side of bracket w = 70 mm

- Bar thickness and each side of bracket t = 20 mm

- Pin diameter d = 10 mm

- Average allowable bearing stress of (Bar and Bracket) T = 120 MPa

- Average allowable shear stress of pin S = 115 MPa

Find:

The maximum force P that the structure can support.

Solution:

- Bearing Stress in bar:

                                       T = P / A

                                       P = T*A

                                       P = (120) * (0.07*0.02)

                                       P = 168 KN

- Shear stress in pin:

                                        S = P / A

                                        P = S*A

                                        P = (115)*pi*(0.01)^2 / 4

                                        P = 9.032 KN

- Bearing Stress in each bracket:

                                       T = P / 2*A

                                       P = T*A*2

                                       P = 2*(120) * (0.07*0.02)

                                       P = 336 KN

- The maximum force P that this structure can support:

                                      P_max = min (168 , 9.032 , 336)

                                      P_max = 9.032 KN

3 0
3 years ago
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morpeh [17]

Answer:

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Step-by-step explanation:

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