Chapter 3.3, Problem 12E

(6 points) Let S be the surface z = 1 − x² - y², x² + y² ≤1. The boundary OS of S is the unit circle x² + y² = 1. Let F(x, y, z) = (x², y², z²). Use the Stokes' Theorem to calculate the line integral Hint: First calculate V x F. Jos F F.ds.

Q5. Manager of car dealership is trying to see how number of sale associates can affect number of final sales in his dealership. He collects the following information: Number of cars Number of working sale associates per day sold in one day 2 2 3 5 3 3 4 1 3 1 2 4 5 Calculate the correlation coefficient for this data set using the equation given on slide#77? Comment on the association of the two variables. ΣΥ) - Σ) × Σ(Υ) (X) E(Y) N 2 (Σ(x²) - 2x²) × (Σ(12) - ²) N N

You are provided with data that includes all 50 states of the United States. Your task is to draw a sample of: 20 States using Random Sampling (2 points: 1 for random number generation; 1 for random sample) 10 States using Systematic Sampling (4 points: 1 for random numbers generation; 1 for generating random sample different from the previous answer; 1 for correct K value calculation table; 1 for correct sample drawn by using systematic sampling) (For systematic sampling, do not use the original data directly. Instead, first randomize the data, and then use the randomized dataset to draw your sample. Furthermore, do not use the random list previously generated, instead, generate a new random sample for this part. For more details, please see the snapshot provided at the end.) You are provided with data that includes all 50 states of the United States. Your task is to draw a sample of: o 20 States using Random Sampling (2 points: 1 for random number generation; 1 for random sample) o…