Establishing the properties of materials is an important problem in identifying a suitable substitute for biodegradable materials in the fast food packaging industry. consider the following data on product density (g/cm3) and thermal conductivity k-factor (w/mk) published in materials research and innovation (1999, pp 2-8). thermal conductivity, y product density, x 0.049000 0.185000 0.053500 0.23 0.055000 0.235000 0.054500 0.236000 0.058000 0.26 0.062000 0.286500 (a) create a scatter diagram of the data. what do you anticipate will be the sign of the sample correlation coefficient? (b) compute to 4 decimal places the sample correlation. hint: carry all calculations out to six (6) significant digits.

(a) see below for a scatter plot; we anticipate a positive sign

(b) 0.9928

Step-by-step explanation:

The plotting and calculations are best performed by a spreadsheet or graphing calculator. The attached shows the use of the free on-line Desmos graphing calculator for the purpose.

answer: it is d

step-by-step explanation:

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.