4. The mean of 12 numbers is 5.5. Eleven
of the numbers are 5, 6,5,3,4,5,7,6,9,
7 and 5. Find
a) the twelfth number.
b) the mode of the twelve numbers.
c) the sum of the mode and the mean.

A) 4

B) Mode is 5

C) 10.5

Step-by-step explanation:

A) 62+x/12

(62 + x) ÷ 12 = 5.5 ×12

62 + x = 66

×= 66-62

×=4

B) mode is the highest occuring no which is 5

C) mean has been given as 5.5; mean plus mode= 10.5

a) 4

b) 5

c) 9

Step-by-step explanation:

a) let the 12th number b x

Mean = sum/n

5.5 = (5+6+5+3+4+5+7+6+9+7+5+x)/12

5.5×12 = 62+x

66 = 62+x

x = 4

b) set is: 3,4,4,5,5,5,5,6,6,7,7,9

Mode is 5 (most frequent)

c) mode+mean = 5+4 = 9

step-by-step explanation:

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.