Young's modulus is a quantitative measure of stiffness of an elastic material. suppose that for aluminum alloy sheets of a particular type, its mean value and standard deviation are 70 gpa and 1.6 gpa, respectively (values given in the article "influence of material properties variability on springback and thinning in sheet stamping processes: a stochastic analysis" (intl. j. of advanced manuf. tech., 2010: 117– (a) if x is the sample mean young's modulus for a random sample of n = 64 sheets, where is the sampling distribution of x centered, and what is the standard deviation of the x distribution?

0.2 GPa

Step-by-step explanation:

Data provided:

Mean value = 70 GPa

Standard deviation, σ = 1.6 GPa

Now,

a) sample, n = 64

From central limit theorem,

The sample of n = 64 will have the same mean i.e 70 GPa

and,

The standard deviation

σ' =

on substituting the respective values, we get

σ' =

or

σ' = 0.2 GPa

6, 10

9, -13

12, -21

18, -23

step-by-step explanation:

you just add 6 to the x-coordinate and subtract 10 from the y-coordinate.

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.