### Sign of correlation coefficient to correlate two variables

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How can a non-linear relationship among two variables influence the correlation coefficient? For example, ability to pay attention and the level of stimulation in the environment do not demonstrate a linear relationship. At some point, too much stimulation will limit the ability to focus and pay attention. What would happen to the size and the sign of the correlation coefficient if we correlated these two variables? How can researchers work around this issue?

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 Problem regarding investment projects : All of this working capital would be recovered at the end of the life of the machine. The company requires a minimum pretax return of 13% on all investment projects. The net present value of the proposed project is closest to: Change of variables : Let R be the elliptical region in the first quadrant bounded by x^2/3^2 +y^2/2^2 =1. Use the change of variables, x =3u , y =2v , to evaluate the area of R . How much energy (in kilojoules) is needed : How much energy (in kilojoules) is needed to heat 3.60 of ice from -14.5 to 26.0? The heat of fusion of water is 6.01, and the molar heat capacity is 36.6 for ice and 75.3 for liquid water. Write equations for the reaction : Write equations for the reaction of each of the following with (1) Mg in ether followed by (2) additione of D2O to the resulting solution: Sign of correlation coefficient to correlate two variables : What would happen to the size and the sign of the correlation coefficient if we correlated these two variables? How can researchers work around this issue? Center of mass of lamina : Find the center of mass of the lamina bounded by y = x^2 and y=2x and the density is ?(x,y) = xy. Subtraction rule : When you subtract one number from another, the answer is always less than both of the numbers in the subtraction problem. Support or disprove this statement with examples. Problem associated to minimum pretax return : The company requires a minimum pretax return of 15% on all investment projects. The net present value of the proposed project is closest to: What mass of p4 is produced : What mass of P4 is produced when 41.5 g of Ca3(PO4)2, 26.5 g of SiO2 and 7.80 g of C are reacted according to the equation:  2Ca3(PO4)2 + 6SiO2 + 10C ¼ P4 + 6CaSiO3 + 10C

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