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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.

A variable force F is applied to a block, and the relationship between the force and the block’s displacement is shown in the figure. x1 = [x1] m, x2 = [x2] m, x3= 30 m, F1= [F1] N, F2= 30 N, and F3= [F3] N. The positive directions of the force and displacement are the same (toward right). Calculate the work done by the force as the block moves from position x1 to position x2. Express your answer in joules (J). 

A [m] kg box is moving on a horizontal surface in the +x direction (toward the right). The coefficient of kinetic friction is [mu]. An unknown force F, parallel to the surface, is applied to the box. The velocity as a function of time is shown in the figure. Given t1 = [t1] s, t2 = [t2] s, v1 = [v1] m/s, and v3 = [v3] m/s, determine the magnitude of the force F during the time interval from t1 to t2. Express your answer in newtons.

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.

What z-score represents X = 100?  Use the mean and standard deviation you just calculated in the preceding questions to arrive at your answer.  

Based on the above binary logit model in Q9, the probability of buy (i.e., P(buy=1) in the city 3 (i.e., C(city)[T.3]=1, St. Louis) is (1)___________(a. higher, b. smaller; 1 points) than that of the base group (2)__________(a. Rolla,   b. Kansas City, c. St. Louis; 2 points) at statistically (3) _______________ (a. insignificant, b. significant 10%, c. significant 5%, d. significant 1%; 1 point).

Based on the above example of the decision tree (DT) for the binary classification (0: candy 1: wine), the predicted class in the terminal node  is (1)____________(a. candy, b. wine; 2 points), and the predicted class in the terminal node  is (2)____________(a. candy, b. wine; 2 points).

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:_____________ 

Let’s assume that an economist wants to investigate consumer choices for an energy saving device as follows:

Decision Tree (DF) for regression selects a feature and threshold to split feature space in each node that minimize __________________ (one answer; 4 points).