The weight of coffee in 70 jars is shown in the following table: Weight (in grams):, `200-201` , `201-202` , `202-203` , `203-204` , 204-205, 205-206 `F r e q u e n c y` , 13, 27, 18, 10, 1, 1 Determine the variance and standard deviation of the above distribution.

The weights of a coffee in 70 jars are shown in the following table . .Determine variance and standard deviation of the above distribution.

A die is thrown 1000 times with the frequencies for the outcomes 1, 2, 3,4, 5 and 6 as given in the following table : O u t com e1 2 3 4 5 6F r e q u e c n y 179 150 157 149 175 190 Find the probability of getting each outcome.

A die is thrown 1000 times with the following frequencies for the outcomes 1, 2, 3, 4, 5 and 6 as given below: O u t com e : 1 2 3 4 5 6 F r e q u e n c y : 179 150 157 149 175 190 Find the probability of happening of each outcome.

For his 18th birthday in February Peter plants to turn a hut in the garden of his parents into a swimming pool with an artifical beach. In order to estimate the consts for heating the water and the house , peter obtains the data for the natural gas combustion and its price. What is the total energy (in MJ) needed for Peter's "winter swimming pool" calculated in 1.3 and 1.4? How much natural gas will he need, if the gas heater has an efficiency of 90.0% ? What are the different costs for the use of either natural gas or electricity ? Use the values given by PUC for your calculations and assume 100% efficiency for the electric heater. Table 1: Composition of natural gas {:("Chemical substance","mol fraction x",D_(1)H^(@)(KJ mol^(-1))^(-1),S^(@)(J mol^(-1)K^(-1))^(-1),C_(p)^(@)(J mol^(-1)K^(-1))^(-1)),(CO_(2(g)),0.0024,-393.5,213.6,37.1),(N_(2(g)) ,0.0134,0.0,191.6,29.1),(CH_(2(g)),0.9732,-74.6,186.3,35.7),(C_(2)H_(3 (g)),0.0110,-84.0,229.2,52.2),(H_(2)O_(g),-,-285.8,70.0,75.3),(H_(2)O_(g),-,-241.8,188.8,33.6),(H_(2)O_(g),-,0.0,205.2,29.4):} Equation J=E(A.Deltat)^(-1) =!! lambda "wall" . DeltaT. d^(-1) , where J= energy flow E along a temperature gradient (wall direction Z) par area A and time Deltat , d-wall thickness , lambda wall -heat conductivity , DeltaT - difference in temperature between the inside and the outside of the house.

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) ) :

A very large, charged plate floats in deep space. Due to the charge on the plate, a constant electric field E exists everry above the plate. An object with mass m and charge q is shot upward from the plate with a velocity v and at an angle theta . It follows the path shown reaching a height h and a ramge R. Assume the effects of gravity to be negligible. Suppose E is 10 N//C , m is 1 kg, q is -1C , v is 100 m//s and theta is 30^(@) . What is h?

Let y(x) be a solution of the differential equation (1+e^x)y^(prime)+y e^x=1. If y(0)=2 , then which of the following statements is (are) true? (a) ( b ) (c) y(( d ) (e)-4( f ))=0( g ) (h) (b) ( i ) (j) y(( k ) (l)-2( m ))=0( n ) (o) (c) ( d ) (e) y(( f ) x (g))( h ) (i) has a critical point in the interval ( j ) (k)(( l ) (m)-1,0( n ))( o ) (p) (q) ( r ) (s) y(( t ) x (u))( v ) (w) has no critical point in the interval ( x ) (y)(( z ) (aa)-1,0( b b ))( c c ) (dd)

Consider the family of all circles whose centers lie on the straight line y=x . If this family of circles is represented by the differential equation P y^+Q y^(prime)+1=0, where P ,Q are functions of x , y and y^(prime)(h e r ey^(prime)=(dy)/(dx),y^=(d^2y)/(dx^2)), then which of the following statements is (are) true? (a) ( b ) (c) P=y+x (d) (e) (b) ( f ) (g) P=y-x (h) (i) (c) ( d ) (e) P+Q=1-x+y+y +( f ) (g)(( h ) (i) y^(( j )prime( k ))( l ) ( m ))^(( n )2( o ))( p ) (q) (r) (s) ( t ) (u) P-Q=x+y-y -( v ) (w)(( x ) (y) y^(( z )prime( a a ))( b b ) ( c c ))^(( d d )2( e e ))( f f ) (gg) (hh)

In a binomial expansion (x+y)^n gretest term means numericaly greatest term and therefore greatest term in (x-y)^n and (x+y)^n are ame. I frth therm t_r be the greatest term in the expansion of (x+y)^n whose therms are all ositive, then t_rget_(r+1) and t_rget_=(r-1)i.e. t_r/t_mge1 and t_r/t_(r-)ge1 ON the basis of above information answer the following question: Greatest term in the expansion of (2+3x0^10, whern x= 3/5 is (A) ^10C_5(18/5)^5 (B) ^10C_6(18/5)^6 (C) ^10C_4(18/5)^4 (D) none of these

A curve is such that the mid-point of the portion of the tangent intercepted between the point where the tangent is drawn and the point where the tangent meets the y-axis lies on the line y=xdot If the curve passes through (1,0), then the curve is (a) ( b ) (c)2y=( d ) x^(( e )2( f ))( g )-x (h) (i) (b) ( j ) (k) y=( l ) x^(( m )2( n ))( o )-x (p) (q) (c) ( d ) (e) y=x-( f ) x^(( g )2( h ))( i ) (j) (k) (d) ( l ) (m) y=2(( n ) (o) x-( p ) x^(( q )2( r ))( s ) (t))( u ) (v)