The sandwich shop has 6 employees, but only 3 people need to work at any one time. The manager wants to have a different group of people work together every day for two weeks. Is that possible?

Yes

Step-by-step explanation:

Given that:

Number of employees (n) = 6

Number of employees who can work at a time (r) = 3

To know of its possible for different groups of employees to work for two wweka, then, the number of different groups or combination must be greater Than or equal to 14 (two weeks) ; Assume (1 week = 14 days)

Using the combination formula :

nCr = n! ÷ (n - r)!r!

6C3 = 6! ÷ (6 - 3)!3!

6C3 = 6! ÷ 3!3!

6C3 = (6*5*4) ÷ (3*2*1)

6C3 = 120 / 6

6C3 = 20 ways

Hence, 20 different groups of 3 employees can be made from all 6 employees. Hence, it is possible to have different groups work for two weeks

answer: cos [   arcsin (3/5) - arccos (1/2) ] =

step-by-step explanation: × = 3/5 = 0.6--> x = 36.87 and x = 180 - 36.87 = 143.13 deg

cos y = 1/2 --> y = +- 60 deg a. cos (x - y) = cos (143.13 - 60) = cos 83,13  

=

0.12

b. cos (36.87 - 60) = cos (-23.23) = 0.92