If n what is a x and x x x n

ring. a) Calculate the work done to compress the spring. (2 marks) b) What happens to the work done on the spring ? (1 mark) c) If the spring is released, what happens to the energy of the spring? (1 mark) d) Calculate the total mechanical energy of the ball at the instant it leaves the spring. (2 marks) e) What will be the speed of the ball at the instant it leaves the spring? (2 marks) f) If the ball is fired up into the air by the spring, how much gravitational potential energy will it gain? (1 mark) g) What will be the maximum height of the ball? (2 marks

2,3,4,7). If it lands tails, a fair six-sided die is thrown (with values 3,4,5,6,7,9). Regardless of which die is used, Alice eats n grains of rice, where n is the largest prime factor of the die result (for example, the largest prime factor of 9 is 3). (a) What is the conditional probability that the coin lands heads, given that Alice eats three grains of rice? (b) Suppose that the entire experiment is conducted twice on the following day (starting with a new coin toss on the second run-through). What is the conditional probability that the coin lands heads on both run-throughs, given that Alice eats a total of five grains of rice during the two run-throughs? (Do not count the two grains from part (a) in part (b); we assume two brand new experiments, each with a new coin toss. Start your solution by defining a suitable partition of the sample space. Please use an appropriate notation and/or justification in words, for each value that you give as part of your solution.) Exercise 5) Alice and Bob throw an unfair coin repeatedly, with probability 2/5 of landing heads. Alice starts with £2 and Bob starts with £3 . Each time the unfair coin lands heads, Alice gives Bob £1 . Each time the unfair coin lands tails, Bob gives Alice £1 . The game ends when one player has £5 . (a) Draw a labelled Markov chain describing the problem, and write down a transition matrix P. Write down the communication classes, and classify them as either recurrent or transient. (b) Using the transition matrix, calculate the probability that Alice loses all of her money in exactly four tosses of the unfair coin. (c) Calculate the (total) probability that Alice loses all of her money (before Bob loses all of his). (d) Calculate the expected (mean) number of tosses of the unfair coin, for the game to end.

34.0 N when it’s not in the water. When it’s submerged in water (the density of water is 1.00 x 103 kg/m3) the scale now reads 27.0 N. (a) What is the density of the block? (b) If you suspended another object from the block that has a density of 3.20 x 103 kg/m3, with both objects submerged, what would the object's mass need to be for the scale to once again read 34.0 N? Note: Part (a) is worth 7 points, and part (b) is worth 8 points.

f the students make their choices independently and each is as likely to pick one integer as any other, what is the probability that 8 or more will select 4,5 or 6? b Having observed eight students who selected 4, 5, or 6, what conclusion do you draw based on your answer to part (a)?A missile protection system consists of n radar sets operating independently, each with a probability of .9 of detecting a missile entering a zone that is covered by all of the units. a If n = 5 and a missile enters the zone, what is the probability that exactly four sets detect the missile? At least one set? b How large must n be if we require that the probability of detecting a missile that enters the zone be .999?

ng the snow. The first child exerts a force of F1 = 11 N at an angle θ1 = 45° counterclockwise from the positive x direction. The second child exerts a force of F2 = 6 N at an angle θ2 = 30° clockwise from the positive x direction. Find the magnitude (in N) and direction of the friction force acting on the sled if it moves with constant velocity. magnitude direction (counterclockwise from the +x-axis) What is the coefficient of kinetic friction between the sled and the ground? What is the magnitude of the acceleration (in m/s2) of the sled if F1 is doubled and F2 is halved in magnitude?