Theorem: the sum of any two even integers equals 4k for some integer k. "proof: suppose m and n are any two even integers. by definition of even, m = 2k for some integer k and n = 2k for some integer k. by substitution, m + n = 2k + 2k = 4k. this is what was to be shown." what's the mistakes in this proof?

The number of electoral votes each state is assigned is determined by the size of its population every ten years. the chart shows the number of electoral votes california was assigned each decade of the past century. what is the 3rd quartile of the data?

Explain how you can find the missing fraction in 3 4/5 / (blank) 2 5/7. then find the missing fraction.

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