If you’re good with probability math 30 please help with questions 33 and 35! real answers only

 33) b      34) a        35) none

Step-by-step explanation:

33)

Filling in the Venn Diagram (from Left to right, including outside of circles):

T only           = 13

(T ∩ F)only   =  6

F only           = 21

(T ∩ D) only  =  3

T ∩ F ∩ D     =  5

(F ∩ D) only  =  8

D only           = 15

(T ∪ F ∪ D)'    = 11  

   TOTAL      = 82

34)

Red  = 26

Face  = 12

Red ∩ Face = 6

Total cards = 52

R ∪ F = R + F - (R ∩ F)

        = 26 + 12 - 6

        = 32

35) Note that the total is 34 + 17 + 8 + 3 + 9 + 4 + 5 = 80

I think the teacher made an error, if so, then the answer is "d".

answer

the correct answer is

explanation

the given function is

the excluded values are obtained by solving:

we factor to obtain:

the excluded values are

reduce the friction between its moving parts

step-by-step explanation:

in fact, by reducing the friction between the moving parts of the machine, it is possible to reduce the energy wasted due to this friction; therefore, more input energy is converted into useful work, and this will improve the efficiency of the machine.