2. Given the following Bayesian network which shows that Fire Smoke and Heat. (F=Fire, S=Smoke. causes H= Heat) P(F) P(-F) 0.1 0.9 P(H) P(-H) F| P(S) P(-S) S H F 0.001 0.999 T 0.99 F 0.01 0.99 0.01 0.9 0.1 What is the probability of fire if smoke has been seen? Hint (use Bayes' Rule for Single Event).
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- 'roof: given that f(0) exists, we must show that limx-o f(x)-f(0), or equivalently nat lim f(0+h)+f(0)(if h#0, then.,. ......(Continue h.w)Let L be a line in the xy plane. If L is a vertical line, its equation is x=afor some real number a. Suppose L is not a vertical line and its slope is m. Then the equation of L is y=mx + b, where b is the y-intercept. If L passes through the point (x0,y0), the equation of L can be written as y –y0=m(x –x0). If (x1,y1)and (x2,y2)are two points in the xy plane and x1≠x2, the slope of the line passing through these points is m = (y2-y1)/ (x2-x1). Write a program that prompts the user to enter two points in the xy plane. The program outputs the equation of theline and uses ifstatements to determine and output whether the line is vertical, horizontal, increasing, or decreasing. If L is a nonvertical line, output its equation in the form y=mx + b.Correct answer will be upvoted else downvoted. Computer science. You are given a grid a comprising of positive integers. It has n lines and m segments. Develop a framework b comprising of positive integers. It ought to have a similar size as a, and the accompanying conditions ought to be met: 1≤bi,j≤106; bi,j is a various of ai,j; the outright worth of the contrast between numbers in any nearby pair of cells (two cells that share a similar side) in b is equivalent to k4 for some integer k≥1 (k isn't really something similar for all sets, it is own for each pair). We can show that the appropriate response consistently exists. Input The primary line contains two integers n and m (2≤n,m≤500). Every one of the accompanying n lines contains m integers. The j-th integer in the I-th line is ai,j (1≤ai,j≤16). Output The output ought to contain n lines each containing m integers. The j-th integer in the I-th line ought to be bi,j.
- Let l be a line in the x-yplane. If l is a vertical line, its equation is x = a for some real number a. Suppose l is not a vertical line and its slope is m. Then the equation of l is y = mx + b, where b is the y-intercept. If l passes through the point (x₀, y₀), the equation of l can be written as y - y₀ = m(x - x₀). If (x₁, y₁) and (x₂, y₂) are two points in the x-y plane and x₁ ≠ x₂, the slope of line passing through these points is m = (y₂ - y₁)/(x₂ - x₁). Instructions Write a program that prompts the user for two points in the x-y plane. Input should be entered in the following order: Input x₁ Input y₁ Input x₂Let l be a line in the x-y plane. If l is a vertical line, its equation is x 5a for some real number a. Suppose l is not a vertical line and its slope is m. Then the equation of l is y 5mx 1b, where b is the y-intercept. If l passes through the point (x0, y0,), the equation of l can be written as y 2y0 5m(x 2x0 ). If (x1, y1) and (x2, y2) are two points in the x-y plane and x1 ≠ x2, the slope of line passing through these points is m 5(y2 2y1 )/(x2 2x1 ). Write a program that prompts the user two points in the x-y plane. The program outputs the equation of the line and uses if statements to determine and output whether the line is vertical, horizontal, increasing, or decreasing. If l is a non-vertical line, output its equation in the form y 5mx 1b.Given A = {1,2,3} and B={u,v}, determine. a. A X B b. B X B
- Using JAVA solve the below problem Amitabh had a magical cat. That cat once fell down an empty well. As the walls of the well were not completely vertical, the cat could climb up the well. In one day, the cat can climb 1 unit height and the height of the well is h units. The cat starts at the bottom. Every day, a cat would divide into 2 cats. One of them would climb up 1 unit. The other would wait for help. But while waiting it would fall asleep and roll down 1 unit, unless it is already at the bottom, in which case it just remains there. When a cat would reach the top, it would run home toAmitabh. (Schrodinger doesn't know that some of the cats are in a well and so he can't rescue them). It has been d days since the cat fell into the well. How many cats would come out of the well today? You would notice that the number of cats grows very large with each passing day, so output the answer modulo 10^9+7. d = 0 means that the cat has fallen just now and so there's just one cat at the…Correct answer will be upvoted else downvoted. Computer science. positive integer is the gcd of that integer with its amount of digits. Officially, gcdSum(x)=gcd(x, amount of digits of x) for a positive integer x. gcd(a,b) means the best normal divisor of an and b — the biggest integer d to such an extent that the two integers an and b are detachable by d. For instance: gcdSum(762)=gcd(762,7+6+2)=gcd(762,15)=3. Given an integer n, track down the littlest integer x≥n to such an extent that gcdSum(x)>1. Input The primary line of input contains one integer t (1≤t≤104) — the number of experiments. Then, at that point, t lines follow, each containing a solitary integer n (1≤n≤1018). All experiments in a single test are unique. Output Output t lines, where the I-th line is a solitary integer containing the response to the I-th experiment.Prove (A n B) n A = Ø. (An B)nĀ = (Bn A)NĀ ? = Bn (AnĀ) ? = BnØ ? = Ø ? > >
- Please help me Josephus Problem is a theoretical problem related to a certain counting-out game. On thiscase, people are standing in a circle waiting to be executed. After a specified number ofpeople are skipped, the next person is executed. The procedure is repeated with theremaining people, starting with the next person, going in the same direction and skippingthe same number of people, until one person remains, and is freed.Arrange the numbers 1 , 2, 3 , ... consecutively (say, clockwise) in a circle. Now removenumber 2 and proceed clockwise by removing every other number, among those thatremain, until one number is left. (a) Let denote the final number which remains. Find formula for .(b) If there are 70 people, what is the safe number (the number that remains)?The Harvard robotics club has organized a Robothon. n robots are placed alongthe edge of a circular area at the middle of the OAT(open air theatre). Each robot will move along arbitrary tracksinside the circle while leaving behind a heat signature along its trail. However, they have beenprogrammed not to cross their own trail or the trail of another robot, neither will they ever moveout of the circle. In case a pair of robots i and j meet at any point, they are removed from the sceneand the club will pay a reward sum of M[i, j] to the owners of these robots. Note that some robotscan keep moving infinitely without ever meeting another one. Given the reward matrix M whereM[i, j] = M[j, i], design a polynomial time algorithm that determines the maximum money theclub might potentially end up spending. For this particular problem, give a very brief justificationof the recurrence. Give pseudo-code for a dynamic program which solves the recurrence efficiently Youdo not need to prove…If anyone is a honest politician, Mary is. F: a is honest. G: a is a politician. A: Mary v Choose. Ax [Fx A Gx]→ FA A GA Vx (Fx A Hx → Ix) A Vx (Gx A Hx + Ix) Vx(Hx Λ Fx Λ Gx)HA Λ FAΛ GA Лх [Fx Л Gx-> FA Л GA] Joe bought a big house, even though Mary bought it too. F: Joe bought a H: a is a house. Ix: a is big G: Mary bought a Ax (Fx A Hx → Ix)A Ax (Gx A Hx > Ix) Ax ((Fx v Gx ) → Hx) Not all dogs bite without provocation. Лх (Fx Л Gx) > Нх) - Ax (Fx → Gx) Vx (Fx A Hx A Ix) A Vx (Gx A Hx A Ix) -Ax (Fx → -Gx) F: a is a dog. G: a bites without provocation Vx (Fx Л Нx Л \xЛ Gx) Vx (Fx A Hx A Ix → Gx )