The anwser is 5.05 cm hahahahahahahahahahahahah 
        
             
        
        
        
So I'll start with the mixed number to improper fraction. 
Step one - multiply the denominator and the whole number.
Step two- take your product and add it to the numerator 
Step three- the sum is the numerator of the mixed number and the original denominator is the denominator 
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Now for improper fraction to mixed number 
Step one- see how many times the denominator goes into the numerator (ex. 2 goes into 9, 4 times With one left over) 
Step two -the 4 becomes the whole number and the 1 the numerator
Step three- use the same denominator 
        
             
        
        
        
Given:
One time payment, <em>p </em>= $300
Payment per month, <em>q = </em>$65
Number of months paid, <em>n</em> = 5
The objectiv is to find the amount she paid in 5 months.
Let <em>x </em>be the amount she paid in 5 months. Then the the formula is,

Let's substitute the values.

Hence, total amount paid in 5 months is $625.
 
        
             
        
        
        
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.
 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)]