A box with a mass of [m] kg is acted upon by two forces, F1 = [F1] N and F2​ = [F2] N. Assuming the block moves on a frictionless surface, determine the magnitude of the box’s acceleration. Express your answer in m/s2. The view in the figure is from above.

We want to add a state category variable to the regression analysis. The state category variable has four possible answers (MO =1, FL =2, WA =3, NY = 4). In this case, we need to convert the state category variable into _________________ dummy variables for regression analysis.

A force of [F] N pushes a [m] kg box along the +x axis on a horizontal frictionless surface. The figure shows the velocity and displacement of the box. At time t = 0, the box is at displacement x1 = [x1] m and moves with an initial velocity of v0 = +[v0] m/s. Given x2 = [x2] m, determine the magnitude of the velocity v1 in m/s. Note that the positive directions of force, displacement, and velocity are all toward the right.

The spring constant of a massless spring can be determined from the force-displacement graph, which shows the force applied to the spring and the corresponding displacement. x1 = [x] m and F2 = [F] N. A person pulls the spring slowly until it is stretched by [dx] m. Determine the work done by the person to stretch the spring. Express your answer in joules.

WORD PROBLEM #1 A sample of n = 81 is selected from a normal population with  

Look at the distribution for this word problem and determine if X =100 is a score that is noticeably different from the mean.  In your answer indicate 1) yes or no 2) explain why you selected your answer (i.e., back up with reasoning from facts learned in this class). 

In terms of goodness of model-fit, (1)_______________ (a. model 1 b. model 2, c. model 3; 2 points) is the best model based on (2)_____________ (a. R-squared / b. Adjusted R-squared; 2 points).

What z-score represents X = 115?  Use the mean and standard deviation you just calculated in the preceding questions to arrive at your answer.  

WORD PROBLEM #3 Find the z‑score corresponding to each of the following scores.  To receive full credit, please use notebook paper and pencil to solve the word problem.  Make sure you specifically show all work in each of the steps. Then answer the next 7 questions.  X   100 105 110 115 120  

Decision Tree (DF) for classification selects a feature and threshold to split feature space in each node that minimize impurity measures. Please select the two impurity measures of DT for classification:_____________