The vector wequals=aiplus+bj is perpendicular to the line axplus+byequals=c and parallel to the line bxminus−ayequals=c. it is also true that the acute angle between intersecting lines that do not cross at right angles is the same as the angle determined by vectors that are either normal to the lines or parallel to the lines. use this information to find the acute angle between the lines below. startroot 3 endroot3xminus−nothingyequals=22, nothingxminus−startroot 3 endroot3yequals=8

Which number produces a rationale number when multiplied by 1/5

Do more republicans (group a) than democrats (group b) favor a bill to make it easier for someone to own a firearm? two hundred republicans and two hundred democrats were asked if they favored a bill that made it easier for someone to own a firearm. how would we write the alternative hypothesis?

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