A system of linear equations in two variables can have _____ solutions.
1 answer:
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Answer:
Mom would required 1 lbs of Sugar and 4 lbs of water.
Step-by-step explanation:
Given:
Amount of Sugar syrup Mom wants to make = 5 lbs
Percentile amount of syrup she needs to make = 20%
Solution:
Let amount of sugar to make 20% syrup be 'x'.
So by definition of proportion we get;
Now Multiplying both side by 5 we get;
So we can say that;
Amount of water =
Hence Mom would required 1 lbs of Sugar and 4 lbs of water.
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)]