1. <span>4x – 20 = 5y
so 5y = </span><span>4x – 20
divide both sides by 5
y = (4/5)x - 4
2. x-intercept is at y=0
so (4/5)x - 4 = 0
x = 5
so it is (5,0)
3. y-intercept is at x=0, y = 0 - 4 = -4
so it is (0,-4)
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The number of tissues that can fit the container will be given by:
[volume of the container]/[volume of tissue box]
volume of container:
V=length×width×height
V=19.5×39×19.5
V=14829.75
Volume of tissue box:
v=6.5×6.5×6.5
v=274.625
Number of tissues in the container:
14829.75/274.625
=54
Answer: 54 tissue paper boxes
7/11 = 0.64 because 7+4 = 11 and then divid 7 by the total number
The solution is at what point the two lines intersect.
Plug y into the other equation to get: 5x-4(5-3x)=-3
Multiply it out: 5x+12x-20=-3
Combine like terms and add 20 to both sides: 17x=17
Divide both sides by 17: x=1
Now plug the x value back into any equation to get the y value.
So you get y=5-3(1) --> y=2
The solution is (1, 2)
Answer:
a. 
.
b. 
Step-by-step explanation:
By the definition, the expected value of a random variable X with probability mass function p is given by 
where the sum runs over all the posible values of X. Given a function g, the random variable Y=g(X) is defined. Note that the function g induces a probability mass function P' given by P'(Y=k) = P(X=g^{-1}(k)) when the function g is bijective.
a. Note that for 1/3ln(2)+1/6ln(5) by choosing the function g(x) = ln(x) the expression coincides with E(g(x)), because if Y = g(x) then E(Y) = P'(Y=1)*ln(1)+P'(Y=2)*ln(2)+P'(Y=5)*ln(5) = P(X=1)*ln(1)+P(X=2)*ln(2)+P(X=5)*ln(5).
b. On the same fashion, the function g(x) = xe^{xt} fullfills the expression of E[g(X)]
