Find (a) the range and (b) the standard deviation for the given sample

The range is the difference between the highest and lowest value:

Highest value: 85.63

Lowest value : 84.25

Range= 85.63-84.25 = 1.38

Standard deviation:

First, find the mean

Mean = sum of the values / number of values

M = (85.54+84.33+85.15+85.63+84.25+85.18+84.78+85.36+85.04) /9 = 85.03

For each value, subtract the mean and square the result:

85.54-85.03 = 0.51 = 0.51^2 = 0.26

84.33-85.03 = -0.7= 0.49

85.15-85.03 =0.12 = 0.014

85.63-85.03= 0.6 = 0.36

84.25-85.03=-0.78=0.61

85.18-85.03 = 0.15 = 0.02

84.78-85.03=-0.25=0.06

85.36-85.03=0.33 = 0.11

85.04-85.03=0.01 = 0.0001

Calculate the mean of the results ( add results and divide by 9)

1.9241/9=0.21

Square root of that value:

√0.21 = 0.46 (standard deviation)

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.

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation: