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- Briefly describe how co-ordinates can be stored for a simple vector data structure for i) points ii) lines iii) polygonsLet x and y be linearly independent vectors in R2.If | |x | |= 2 and | |y | | = 3, what, if anything, can weconclude about the possible values of |xTy|?For which value of k is { (1, 2, 3), (1, 0, 1), (2, k, 8) } a linearly dependent set?
- (5) Please explain in words how a student would determine the normal vector to the direction vector D[2, -1]The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. xx 11.6 8.5 7.2 3.6 2.6 2.3 2.1 0.4 yy 13.8 11.4 9.9 7.1 5.9 5.8 5.8 4.7 xx = thousands of automatic weaponsyy = murders per 100,000 residentsThis data can be modeled by the equation y=0.84x+4.02.y=0.84x+4.02. Use this equation to answer the following;Special Note: I suggest you verify this equation by performing linear regression on your calculator.A) How many murders per 100,000 residents can be expected in a state with 4.9 thousand automatic weapons?Answer = Round to 3 decimal places.B) How many murders per 100,000 residents can be expected in a state with 10.3 thousand automatic weapons?Answer = Round to 3 decimal places.(A) The linearity between two variables X and Y, in pairs, defined as X=[4,2,3,5,2,4] and Y=[6,4,6,8,5,10] is equal to? (B)An outbreak of certain illness was attributed to ice creams produced at a certain factory. Scientists measured the level of the illness causing factor in 10 randomly sampled batches of ice cream. The levels were: 0.583, 0.242, 0.129, 0.691, 0.231, 0.693, 0.619, 0.392, 0.418. What is the estimated interval of population mean at 0.05 level of significance? (C) The population standard deviation for the age of a certain University students is 13 years. If we want to be 90% confident that the sample mean age is within 3 years of the true population mean age of the University students, then how many randomly selected students must be surveyed?
- The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. xx 11.3 8.6 7.1 3.3 2.4 2.3 2.4 0.7 yy 13.7 11.1 10.4 6.9 6.4 6.2 6.1 4.9 xx = thousands of automatic weaponsyy = murders per 100,000 residentsThis data can be modeled by the equation y=0.83x+4.28.y=0.83x+4.28. Use this equation to answer the following;Special Note: I suggest you verify this equation by performing linear regression on your calculator.A) How many murders per 100,000 residents can be expected in a state with 10.7 thousand automatic weapons?Answer = Round to 3 decimal places.B) How many murders per 100,000 residents can be expected in a state with 1.6 thousand automatic weapons?Answer = Round to 3 decimal places.The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. xx 11.3 8.6 7.1 3.3 2.4 2.3 2.4 0.7 yy 13.7 11.1 10.4 6.9 6.4 6.2 6.1 4.9 xx = thousands of…The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. xx 11.8 8.6 7.1 3.9 2.5 2.6 2.4 0.4 yy 14.3 11.5 9.8 7.6 6.2 6.5 6.4 4.1 xx = thousands of automatic weaponsyy = murders per 100,000 residentsThis data can be modeled by the equation y=0.86x+4.07.y=0.86x+4.07. Use this equation to answer the following; Special Note: I suggest you verify this equation by performing linear regression on your calculator.A) How many murders per 100,000 residents can be expected in a state with 3 thousand automatic weapons?Answer = Round to 3 decimal places.B) How many murders per 100,000 residents can be expected in a state with 4.1 thousand automatic weapons?Answer = Round to 3 decimal places.Use this data and create a model that estimates a student's giving rate as an alumni based on the three parameters provided. If a class has a graduation rate of 74, the % of classes under 20 student equal to 55, and a Student=Faculty Ratio of 19, what should we expect our Alumni Giving Rate to be? (Enter a whole number) University Graduation Rate % of Classes Under 20 Student-Faculty Ratio Alumni Giving Rate Boston College 85 39 13 25 Brandeis University 79 68 8 33 Brown University 93 60 8 40 California Institute of Technology 85 65 3 46 Carnegie Mellon University 75 67 10 28 Case Western Reserve Univ. 72 52 8 31 College of William and Mary 89 45 12 27 Columbia University 90 69 7 31 Cornell University 91 72 13 35 Dartmouth College 94 61 10 53 Duke University 92 68 8 45 Emory University 84 65 7 37 Georgetown University 91 54 10 29 Harvard University 97 73 8 46 Johns Hopkins University 89 64 9 27 Lehigh University 81 55 11 40 Massachusetts Inst.…