5. Prove the folowing divergence property div(4a,-(grade)-a + φ div a 6. Prove 7. Compute 8....
#6 table 2 8 LABORATORY REPORT 1C. TIME/DIV-S IC VOLTS/DIV-SV A VOLTS/DIV V ov o v 0 s 2A. TIME/DIN-S2B. TIME/DIV 2C TIME/DIV-mS 2C. VOLTS/DIV o V 0 s 60033 0 s 3A. TIME/DIV-m 3A, VOLTS/DIV=-, 3B. TIME/DIV-1m 3B. VOLTS/DIV o v 0 s 0 s 388 Physics Laboratory Mamual Loyd A. TIME/DIV- ms 4A. VOLTS/DIV-LV o v ov 0 s 0 s 0 s Data Table 1 X Data Table 2 Voltmeter (V Voltmeter V 1.00 2.00 3.00 4.00...
4 6 5 5 5 3 7 2 2 8 7 A) Compute the population variance and the sample variance using the formula B) Compute the population standard deviation and the sample standard deviation using the formula Please show the work on paper not excel.
13. (i) For each of the following equations, find all the natural numbers n that satisfy it (a) φ(n)-4 (b) o(n) 6 (c) ф(n) 8 (d) φ(n) = 10 (ii) Prove or disprove: (a) For every natural number k, there are only finitely many natural num- bers n such that ф(n)-k (b) For every integer n > 2, there are at least two distinction integers that are invertible modulo n (c) For every integers a, b,n with n > 1...
7. Prove or disprove: If we know that 2X +6=4 (mod 8), then X +3 = 2 (mod 8). 8. Prove or disprove: If we know that 2X+6 = 4 (mod 7), then X+3 = 2 (mod 7). 9. Let S be the set {311, 254, -172,45,2019, 111,3}. Find a subset T such that the sum of the elements in divisible by 7
9 – in 5. Prove that lim n+ 8 + 13n -7 13
I need help with problem #9 For Questions 5 through 7, determine convergence or divergence of the series using any test of your choice. If the series is geometric, give its sum. You must verify that all assumptions of the test you choose are satisfied. 5. (8 points) § (193) 6. (10 points) { $s 8. Find the radius of convergence and interval of convergence for the series below: (a) (6 points) mal (b) (6 points) { }(22+1)* sin 9....
Compute the sign of the following permutations: (a) (1, 4, 3, 6, 7)(5, 8, 9, 10). (b) σ ∈ Sn, i 7→ n + 1 − i. (c) Show that this initial configuration of the 15 puzzle is not solvable 3 1 15 13 2 8 5 9 12 7 11 4 14 6 10 − (d) Suppose that (i, j) ∈ Sn is a transposition and that i < j. Find an expression (in terms of i and j...
On the provided answer sheet, compute BY HAND the final course grade for a student with the following scores: Homework average-85, Quiz average- 72, Project average-88, Test 1-75, Test 2-54, Test 3- 95, Test 4 -79. SHOW YOUR WORK. 2. 1 Category Weight Score 2 Homework 20.00% 3 Quizzes 4 Projects 5 Test 1 6 Test 2 7 Test 3 8 Test 4 9 Final Grade 20.00% 15.00% 11.25% 11.25% 11.25% 11.25%
Given then following data pointsx(1) = (2, 8); x(2) = (2, 5); x(3) = (1, 2); x(4) = (5, 8)x(5) = (7, 3); x(6) = (6, 4); x(7) = (8, 4); x(8) = (4, 7)Compute 2 iterations of the K-Means algorithm by hand using the Forgy’s initialisation choosing x(3), x(4) and x(6). Calculate the loss function in each iteration.
5. Use mathematical induction to prove that for n 2 1, 1.1! +2.2!+3.3++ n n! (n +1)!-1 7. Prove: If alb and al(b +c) then alc. Prove that for all sets A and B, P(An 6. 8. (a) Find the Boolean expression that corresponds to the circuit 5. Use mathematical induction to prove that for n 2 1, 1.1! +2.2!+3.3++ n n! (n +1)!-1 7. Prove: If alb and al(b +c) then alc. Prove that for all sets A and...