Find an expression for a cubic function f if f(4) = 96 and f(-4) = f(0) = f(5) = 0. part 1 of 4 a cubic function generally has the form f(x) = ax3 + bx2 + cx + d. if we know that for some x-value x = p we have f(p) = 0, then it must be true that x − p is a factor of f(x). since we are told that f(5) = 0, we know that x-5 correct: your answer is correct. seenkey x-5 is a factor. part 2 of 4 similarly, since f(−4) = 0, then f(x) has the factor x+4 correct: your answer is correct. seenkey x+4 , and since f(0) = 0, then f(x) has the factor x correct: your answer is correct. seenkey x .

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