Math Answers

find the range, standard deviation and range of 8 10 22 18 17 11 15 28 16 16

PROVE that N (a) is a subgroup of G Where N (a) is a normalizer of a in G

Supposed three coins are tossed. Let X be the random variable representing the number of heads occur . Construct a table that shows the sample space and values of the random variable X

The equations of two Regressions lines are

7𝑥 − 16𝑦 + 9 = 0 and 5𝑦 − 4𝑥 − 3 = 0.

Find the coefficient of correlation and the means of x and y

Given 𝑑𝑦

𝑑𝑥

= 𝑥 𝑥

2 + 𝑦

2

𝑒

−𝑥

and 𝑦(0) = 1, 𝑦(0.1) = 1.005, find

i) 𝑦 0.2 by Euler’s method

ii) 𝑦 0.3 by Modified Euler’s method

iii) 𝑦(0.4) by Milne’s predictor - corrector method.

Apply Runge-Kutta method of 4th order method to find the approximate

value of 𝑦 for 𝑥 = 0.1, if 𝑑𝑦

𝑑𝑥

= 𝑥 + 𝑦

2 given that 𝑦 = 1 where 𝑥 = 0.

A coin is tossed four times.

b. Suppose the outcome of the first two tosses are heads, and Y represents the number of heads landed, what are the possible values of Y?

A differential equation for the velocity v of a falling mass m subjected to air resistance

proportional to the square of the instantaneous velocity is:

𝑚 (𝑑𝑣/𝑑𝑡) = mg-kv²

Where k >0 is a constant of proportionality. The positive direction is downward.

(a) Solve the equation subject to the initial condition v(0)=v₀.

(b) Use the solution in part (a) to determine the limiting, or terminal, velocity of the mass.

(c) If the distance s, measured from the point where the mass was released above ground, is

related to velocity v by ds/dt=v(t), find an explicit expression for s(t) if s(0)= 0.

If ux² + y² +2²,v=x+y+z₁w=xy+yz+zx, then the value of the jacobian is d(u,v,w)/d(x,y,z)

Jac tossed an unbiased coin. If the coin lands with head up on each toss, he wins ₱50. However, if it lands

with tail up, he loses ₱60. If he continues to play the game, how much can he expect to win or lose in the

game?