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.

Lorne subtracted 6x3 – 2x + 3 from –3x3 + 5x2 + 4x – 7. use the drop-down menus to identify the steps lorne used to find the difference.

Write the expression as a single natural logarithm. 2 in a - 4 in y

Carla was trying to decide what to do saturday evening. she has $100 available to spend for the evening. she has narrowed her choices down to these events: braves game, a concert of an artist she likes, or the georgia aquarium. admission to the braves game is $25, hot dogs cost $10, sodas cost $5. the concert costs $25 for admission, $20 for a souvernir t-shirt, and $10 for a soda. the georgia aquarium has the show of a lifetime with an all you can eat and drink that costs $100. carla does not want to take any driving chances, so in addition to the cost of the aquarium, she will also need to pay for her uber/lyft, which is $15 each way. which option should carla choose if she wants to spend the least? based on that choice, what then is carla's oppotunity cost? fully explain your answer in at least one paragraph.