Each person, in an it department of 60 people, works on at least one of 3 major projects: system security, program implementation, platform development. 23 people work on system security, 28 work on program implementation, and 26 work on platform development. 7 people work on system security and platform development, 12 people work on program implementation and platform development, and 6 people work on all three projects. how many people work only on system security and program implementation (i. e., not all three projects)?
answer either: 4, 5 or 6

4

Step-by-step explanation:

Given: total persons in IT department=60,23 people work on system security, 28 work on program implementation, and 26 work on platform development. 7 people work on system security and platform development, 12 people work on program implementation and platform development, and 6 people work on all three projects.

To Find: number of people working only on system security and program implementation.

Solution:

let people in system security be=,

let people in  program implementation be=,  

let people in platform development be=,

persons working in and = ∩, ∩=

persons working in and = ∩, ∩=

persons working in and = ∩=

persons working in , and =∩∩, ∩∩=6

Now,

we know that

∪∪= ++-∩-∩-∩+∩∩

on putting values,

60=23+28+26-7-12-∩+6

∩=64-60

∩=4

hence, the number of persons working in system security and program implementation are=4

x = -3

y = -18

step-by-step explanation:

to solve by substitution, substitute one variable and solve for the other. then substitute again to find the remaining variable.

x-1/3(3x-9) = -3 since y=3x-9 substittute y.

x-1/3(3x-9)=-3

x + x +3 = -3

2x+3=-3

2x+3-3= -3-3

2x=-6

x=-3

substitute again into y=3x-9

y=3(-3)-9

y=-9-9

y=-18

x ≥ 18 is your answer

step-by-step explanation:

let "a number" = x

(2/3)x + 17 ≥ 29

isolate the variable (x). do the opposite of pemdas (parenthesis, exponent (& root), multiplication, division, addition, subtraction).

first, subtract 17 from both sides.

(2/3)x + 17 (-17) ≥ 29 (-17)

(2/3)x ≥ 29 - 17

(2/3)x ≥ 12

next, multiply 3/2 to both sides to isolate the x

(3/2)(2/3)x ≥ 12(3/2)

x ≥ 12(3/2)

simplify. multiply, then divide

x ≥ (12 * 3)/2

x ≥ (36)/2

x ≥ 18

x ≥ 18 is your answer

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