The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states.
\begin{tabular}{|r|r|r|r|r|r|r|r|r|}
\hline$x$ & 11.9 & 8.2 & 7.2 & 3.5 & 2.9 & 2.3 & 2.5 & 0.8 \\
\hline$y$ & 14.4 & 11 & 10.3 & 7.1 & 6.5 & 6.2 & 6 & 4.7 \\
\hline
\end{tabular}
$x=$ thousands of automatic weapons
$y=$ murders per 100,000 residents
This data can be modeled by the equation $y=0.87 x+4.01$. Use this equation to answer the following;
A) How many murders per 100,000 residents can be expected in a state with 2.9 thousand automatic weapons?
Answer =
Round to 3 decimal places.
B) How many murders per 100,000 residents can be expected in a state with 4.2 thousand automatic weapons?
Answer $=$ Round to 3 decimal places.

Step 1 ：The problem provides us with a linear equation \(y=0.87 x+4.01\), where \(x\) is the number of automatic weapons in thousands and \(y\) is the number of murders per 100,000 residents.

Step 2 ：For part A, we are asked to find the expected number of murders per 100,000 residents in a state with 2.9 thousand automatic weapons. We can find this by substituting \(x=2.9\) into the equation and solving for \(y\).

Step 3 ：Substituting \(x=2.9\) into the equation gives us \(y=0.87(2.9)+4.01\).

Step 4 ：Solving the equation gives us \(y=6.533\). So, the expected number of murders per 100,000 residents in a state with 2.9 thousand automatic weapons is \(\boxed{6.533}\).

Step 5 ：For part B, we are asked to find the expected number of murders per 100,000 residents in a state with 4.2 thousand automatic weapons. We can find this by substituting \(x=4.2\) into the equation and solving for \(y\).

Step 6 ：Substituting \(x=4.2\) into the equation gives us \(y=0.87(4.2)+4.01\).

Step 7 ：Solving the equation gives us \(y=7.664\). So, the expected number of murders per 100,000 residents in a state with 4.2 thousand automatic weapons is \(\boxed{7.664}\).