Select the correct answer from each drop-down menu.
complete the statements about the closure of sets.

1. the set {0, 2, 5} is (closed; not closed) under addition, as is illustrated by the fact that adding 2 and 5 results in 7, which is not included in the set.

2. the set of all integers is closed under addition, as is illustrated by the fact that adding -20 and 6 result in -14, which is (included; not included) in the set.

3. the set of all polynomials is (closed; not closed) under addition, which is illustrated by the fact that adding 3x2 − 2 and 7x4 + 4x results in 7x4 + 3x2 + 4x − 2, which is in the set.

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