Question . Consider the following contingency table. B 𝐵𝐵𝑐𝑐 A 26 34 𝐴𝐴𝑐𝑐 14 26 a. Convert the contingency table into a joint probability table. b. What is the probability that A occurs? c. What is the probability that A and B occur? d. Given that B has occurred, what is the probability that A occurs? e. Given that 𝐴𝐴𝑐𝑐 has occurred, what is the

[10 points] Problem 1. An ant starts from the origin of a 2-D grid, at the point (0,0). Then each time it moves either i) right by one unit distance, e.g., from (0,0) to (1,0), ii) up by one unit distance, e.g., from (0,0) to (0,1), or iii) stay still, with probabilities 0.3, 0.2, and 0.5, respectively. After 10 moves, what is the probability that the ant settles down at point (2,5)?

5.8 Let Y, and Y, have the joint probability density function given by kynyz. Os y < 1,0 < y2 < 1, f(y1, y) = 0, elsewhere. a Find the value of k that makes this a probability density function. b Find the joint distribution function for Y, and Y2. c Find P(Yi < 1/2, Y2 < 3/4). <

(a) Consider the cell Hg(1)Hg,SO. () FeSO (aq,a = 0.01000) Fe(s). Pertimbangkan sel Hg(1)| Hg,SO. (3)| FeSO. (aq,a = 0.01000) Fe(s). (i) Write the cell reaction. Tuliskan tindak balas sel. (ii) Calculate the cell potential (E), the equilibrium constant for the cell reaction (K), and AG at 25°C. Kirakan keupayaan sel (E), keseimbangan tetap untuk tindak balas sel (K) dan AGrindak bali pada 25 °C. (10 marks/markah) (b) Consider the equilibrium CH (g) CH4(g) + H2(g). At 1000 K and a constant total pressure of 1 bar, CyH6g) is introduced into a reaction vessel. At equilibrium, the composition of the mixture in mole percent is H2(g): 26%, CH4(g): 26%, and CyH6(g): 48%. Calculate Ko at 1000 K. (b) If AH reaction = 137.0 kJ mol-', calculate the value of K, at 298.15 K. (c) Calculate AG reaction for this reaction at 298.15 K.

I am stuck on how to do partsF and G here. Thanks so much in advance for any helphere! e. In the boxes below, draw the initial momentum, the change in momentum, and the final momentum for each astronaut in the three experiments. The initial momentum is shown for astronaut A. Draw the other vectors using the same scale. MOOD Initial Sit to be Change bar Final > Astronaut A Expt. 1 20 20 LU 1 Astronaut B Expt. 1 Astronaut A Expt. 2 Astronaut B Expt. 2 25 23 BOSTE Astronaut A Expt. 3 20 15 Astronaut B TH Expt. 3 The following questions: f. Generalize from your results above to answer the following questions: ano ang sist so If the net force on a system of two colliding objects is zero, how does the change in momentum of one object compare to the change in momentum of the other object: • in magnitude? 2.DE color . in direction? g. Explain how your answers to part f are consistent with Newton's third law and the impulse- momentum theorem ( ĒDe N = - Ap) for: Bhes • each astronaut considered separately, and do o bottom holds . for the system of both astronauts together. iboto

a. Objects withmasses m1 = 12.0 kg and m2 = 9.0 kgare connected by a light string that passes over a frictionlesspulley as in the figure below. If, when the system starts fromrest, m2 falls 1.00 min 1.43 s, determine the coefficient of kineticfriction between m1 and thetable. (a) Objects with masses mi - 12.0 kg and m29.0 kg are connected by a light string that passes over a frictionless pulley as in the figure below. If, when the system starts from rest, m2 falls 1.00 m in 1.43 s, determine the coefficient of kinetic friction between m1 and the table. 494 Express the friction force in terms of the coefficient of kinetic friction. Obtain an expression for the acceleration in terms of the masses and the net force, including friction, and solve for the coefficient of kinetic friction. mg (b) What If? What would the minimum value of the coefficient of static friction need to be for the system not to move when released from rest?

Produce graphs of f that reveal all the important aspects of the curve. Then use calculus to find the following. (Enter your answers using interval notation. Round your answers to two decimal places.) f(x) = 4x4 - 32x3 + 89x2 - 95x + 34 Find the interval of increase. x Find the interval of decrease. x Find the inflection points of the function. (x, y) = (smaller x-value) (x, y) = (larger x-value) Find the interval where the function is concave up. Find the interval where the function is concave down.