From the following data compute 3 yearly moving averages. Plot original and trend values on the same graph.
`{:("Year",2006,2007,2008,2009,2010,2011,2012,2013,2014,2015),("Value",50,36.5,43.0,44.5,38.9,38.1,32.6,41.7,41.1,33.8):}`

Following is a data sample in ascending order. The data has mean 4.1 and mode 4.9. Find the missing numbers. 2.4 3.1 3.8 X 4.9 Y 5.4

A psychologist selected a random sample of 20 students. He grouped them in 10 pairs so that the students in each pair have nearly equal scores in an intelligence test. In each pair, one student was taught by method A and the other by method B and examined after the course. The marks obtained by them after the course are as follows. {:("Pairs","Method A","Method B"),(1,34,38),(2,36,43),(3,28,39),(4,34,45),(5,40,43),(6,30,50),(7,34,52),(8,28,39),(9,32,40),(10,42,42):} Calculate spearman's Rank correlation

The following data gives the weights of 30 persons (in kg) 70.0,69.4,49.4,64.5,59.4,72.4,47.5,48.8,62.3,64.2,66.8,70.3,71.3,56.3,52.7,66.6,59.9,64.7,44.6,60.3,50.3,54.3,62.3,56.3,45.0,45.7,49.8,60.5,67.8,50.1, (i) Construct a frequency distribution such that the last class is 72-76. (ii) State the upper class limits of last three class intervals. (iii) State the maximum weight that can be included in the fourth class interval. (iv) State the class mark of each of the classes. (v) Find the range of the given weights. (vi) If 60kg is the weight of a person then in which class interval, it will be taken.

Direction : Resistive force proportional to object velocity At low speeds, the resistive force acting on an object that is moving a viscous medium is effectively modeleld as being proportional to the object velocity. The mathematical representation of the resistive force can be expressed as R = -bv Where v is the velocity of the object and b is a positive constant that depends onthe properties of the medium and on the shape and dimensions of the object. The negative sign represents the fact that the resistance froce is opposite to the velocity. Consider a sphere of mass m released frm rest in a liquid. Assuming that the only forces acting on the spheres are the resistive froce R and the weight mg, we can describe its motion using Newton's second law. though the buoyant force is also acting on the submerged object the force is constant and effect of this force be modeled by changing the apparent weight of the sphere by a constant froce, so we can ignore it here. Thus mg - bv = m (dv)/(dt) rArr (dv)/(dt) = g - (b)/(m) v Solving the equation v = (mg)/(b) (1- e^(-bt//m)) where e=2.71 is the base of the natural logarithm The acceleration becomes zero when the increasing resistive force eventually the weight. At this point, the object reaches its terminals speed v_(1) and then on it continues to move with zero acceleration mg - b_(T) =0 rArr m_(T) = (mg)/(b) Hence v = v_(T) (1-e^((vt)/(m))) In an experimental set-up four objects I,II,III,IV were released in same liquid. Using the data collected for the subsequent motions value of constant b were calculated. Respective data are shown in table. {:("Object",I,II,II,IV),("Mass (in kg.)",1,2,3,4),(underset("in (N-s)/m")("Constant b"),3.7,1.4,1.4,2.8):} A small sphere of mass 2.00 g is released from rest in a large vessel filled with oil. The sphere approaches a terminal speed of 10.00 cm/s. Time required to achieve speed 6.32 cm/s from start of the motion is (Take g = 10.00 m//s^(2) ) :

Which of the following are AP's ? If they form an AP, find the common difference d and write three more terms. (i) 2, 4, 8, 16, . . . (ii) 2,5/2,3,7/2,. . . (iii) -1.2 ,- 3.2 ,- 5.2 ,- 7.2 ,... (iv) -10 ,-6,-2,2.... (v) 3,3+sqrt2,3+2sqrt2,3+3sqrt2,..." " (vi) 0.2,0.22,0.222,0.2222,..." " (vii) 0,-4,-8,-12,..." " (viii) -(1)/(2),-(1)/(2),-(1)/(2),-(1)/(2),..." " (ix) 1,3,9,27,..." " (x) a,2a,3a,4a,..." " (xi) a,a^(2),a^(3),a^(4),..." " (xii) sqrt2,sqrt8,sqrt18,sqrt32,..." " (xiii) sqrt3,sqrt6,sqrt9,sqrt12,..." " (xiv) 1^(2),3^(2),5^(2),7^(2),..." " (xv) 1^(2),5^(2),7^(2),73,...

Over the past 200 working days, the number of defective parts produced by a machine is given in the following table : |{:("Number of","0 1 2 3 4 5 6 7 8 9 10 11 12 13"),("defective parts",),("Days","50 32 22 18 12 12 10 10 10 8 6 6 2 2"):}| Determine the probability that tomorrow's output will have : (i) no defective part. (ii) at least one defective part,(iii) more than 13 defective parts.

A student performs an experiment to determine how the range of a ball depends on the velocity with which it is projected. The "range" is the distance between the points where the ball lends and from where it was projected, assuming it lands at the same height from which it was projected. It each trial, the student uses the same baseball, and launches it at the same angle. Table shows the experimental results. |{:("Trail","Launch speed" (m//s),"Range"(m)),(1,10,8),(2,20,31.8),(3,30,70.7),(4,40,122.5):}| Based on this data, the student then hypothesizes that the range, R, depends on the initial speed v_(0) according to the following equation : R=Cv_(0)^(n) , where C is a constant and n is another constant. Based on this data, the best guess for the value of n is :-

A student performs an experiment to determine how the range of a ball depends on the velocity with which it is projected. The "range" is the distance between the points where the ball lends and from where it was projected, assuming it lands at the same height from which it was projected. It each trial, the student uses the same baseball, and launches it at the same angle. Table shows the experimental results. |{:("Trail","Launch speed" (m//s),"Range"(m)),(1,10,8),(2,20,31.8),(3,30,70.7),(4,40,122.5):}| Based on this data, the student then hypothesizes that the range, R, depends on the initial speed v_(0) according to the following equation : R=Cv_(0)^(n) , where C is a constant and n is another constant. The student performs another trial in which the ball is launched at speed 5.0 m//s . Its range is approximately:

Following are the weights (in kg) of 10 new born babies in a hospital on a particular day: 3.4, 3.6, 4.2, 4.5, 3.9, 4.1, 3.8, 4.5, 4.4, 3.6. Find the mean .

Following are the weights (in kg) of 10 new born babies in a hospital on a particular day: 3.4, 3.6, 4.2, 4.5, 3.9, 4.1, 3.8, 4.5, 4.4, 3.6. Find the mean .