Find the solutions for the following system of equations. 5x + 3y = 18 and 2y -2x = -4 and explain Solution Given the system: 5x + 3y = 18 ...........(1) 2y - 2x = -4 We will divide by 2: ==> y - x = -2 .............(2) Now we will use the substitution method to solve for x and y. First, we will rewrite equation (2). ==> y = x - 2 Now we will substitute y= x -2 into equation (1). ==> 5x + 3y = 18 ==> 5x + 3(x-2) = 18 ==> 5x + 3x - 6 = 18 ==> 8x = 24 ==> x = 24/8 = 3 ==> x= 3 Now we to find y, we will substitute into y= x-2 ==> y= x- 2 = 3 - 2 = 1 ==> y= 1 Then, the solution for the system is the pair ( 3, 1).

1. Find the standard deviation, for the binomial distribution which has the stated values of n and p.
Round your answer to the nearest hundredth.
Problem - n=2815, p=.63
Solution
We know for a binomial distibution with probability function,
P(x = r) = nCr * p^r *(1-p)^(n-r), the mean = np and variance = np(1-p).
Standard deviation, s= (variance)^(1/2) ={np(1-p)}^(1/2).
Standard deviation , s = (np(1-p)}^(1/2)....(1)
So we substitute n = 2815, p = 0.63, in the formula at (1).
Standard deviation = {2815*0.63*(1-0.63)}^(1/2).
Standard deviation = {2815*0.63*0.37}^(1/2) = 25.6159 = 25.62.
So the required standard deviation for the give binomial distribution is 25.62