In this unit, you worked with geometric proofs. a proof is a logical sequence of justified conclusions that lead from a hypothesis to a final conclusion. in your opinion, why are mathematical proofs important? suppose that a conclusion within a proof isn’t justified or is inaccurate. in geometry, what might be the consequences of the inaccuracy? now think about different kinds of proofs that take place outside the world of geometry, and list a few examples. what might be the consequences of having an unjustified conclusion surface in such proofs? who might be affected and how?

Farmers know that driving heavy equipment on wet soil compresses the soil and injures future crops. here are data on the "penetrability" of the same type of soil at two levels of compression. penetrability is a measure of how much resistance plant roots will meet when they try to grow through the soil. compressed soil 2.85 2.66 3 2.82 2.76 2.81 2.78 3.08 2.94 2.86 3.08 2.82 2.78 2.98 3.00 2.78 2.96 2.90 3.18 3.16 intermediate soil 3.17 3.37 3.1 3.40 3.38 3.14 3.18 3.26 2.96 3.02 3.54 3.36 3.18 3.12 3.86 2.92 3.46 3.44 3.62 4.26 use the data, omitting the high outlier, to give a 95% confidence interval for the decrease in penetrability of compressed soil relative to intermediate soil. compute degrees of freedom using the conservative method. interval: to