Persediaan below.pets A- 2JB4))) wederal ACD Premium of AD Db Cr4 13-) Calculate the value ofrir AD || BC 1.1.2 What type of quadrilateral is ABCD? Determine the coordinates of P.) 1.1.3 (2) Prove that HP IAD. 12) 1.1.5 Determine the equation of the circle passing through PBA in the form (x-a) i Cu-b8² = r² (5 1.1.6 Calculate the maximum radius of the circle having equation +y? - 2xcos8 - 4y cos8 --2 for any value of e. (5
5) Prove et CY), = a c= CA),
(5) Show Corr(aX + b, cY + d) = Corr(X, Y). Hint: Use results for the covariance and variance.]
(5) Show Corr(aX + b, cY + d) = Corr(X, Y). Hint: Use results for the covariance and variance.]
(5) Show Corr(aX + b, cY + d) = Corr(X, Y). Hint: Use results for the covariance and variance.]
Problem 10.4. Prove that if akąbk € R, ax + a and bk + b, and ax <bk for all k € N, then a Sb. Problem 10.5. Prove or give a counter-example to the statement in Problem 10.4, with both replaced by <.
(a) Prove that l-x」=-[al and「-2] =- (b) Give a proof by cases that 142] = 1x1+ 1xH + 1x-si + 1x+1 . 3
6. Give 5 examples that can shift the AD to the right 7. Give 5 examples that can shift the AD to the left 8. Give 5 examples that can shift the SRAS & LRAS to the right 9. Give 5 examples that can shift the SRAS & LRAS to the left
solve using Least Square Method
Hw 1019119 Quadratic Ean: z-ax²+bxac R²=cy-z) ² 1) cost (2,4) (4,1) (6,61 (8,7 n=5
1. Prove the following results and give the logical explanation. a. E(aX) = aE (X), where a is a constant. b. E(X + b) = E(X) + b, where b is a constant. You are interested in studying the distribution of the workout days of 100 students. The 2. collected data is summarized in the table below: Workout Days 15 18 20 24 Students Count 10 17 33 20 12 8 Calculate the average number of workout days for students?...
11. (adapted from 1.6 8) Prove the characteristic polynomial of matrix A - is p(x) = 12 - (a+d)X + ad-bc = 0. Show that p(A) = A - (a + d) A+ (ad - bc)1 = 0. 12. (adapted from 1.6 14) Suppose A has eigenvalues 0,0,3 with independent eigenvectors u, v,w. (a) Give the vectors span the nullspace and the column space. (b) Find a particular solution to Ax=w. Find all solutions. (c) Does w + u in...