Applied Mathematics for Construction and the Built Environment Assignment No. 1 Determine resource reguirement for construction projects ]P1.1l 1. The outer surface of the buildings in a private housing estate is painted. The amount of paint used ()2) depend on the surface area of the buildings (x). The relationship between them is shown as follow Amount ofpaint used 12.1 23.8 36.4 47.9 61 73.2 83.8 (liter) Surface area ofthe building 205 395 612 804 988 1192 1413 1600 (m2) (a) Find the Value of product moment correlation coefficient between x and y. Describe and interpret the correlation between the amount of paint used and surface area of the building base on these data. (b) Use least square methods to find out the relationship between amount of paint used and surface area of the building (i.e. find the regression line of y on x). (c) Estimate the amount of paint needed for painting a surface of 750 m2. Show your steps clearly. The cost (in million) for construct a building depends on three factors, that are, number of labour (x), material used (y) and the plant used (z). The relation between them can refer to the three completed projects as following SK -1- 433² -i- 22 = 28 32: + Ty + 43 = 4-4 3:: -i- y -i- 82 = 59 (d) By using matrix method, find out the ratio of X, y, and z.