Bob earns $60,000 a year at an accounting firm. Each year, he receives a raise. Bob has determined that the probability that he receives a 10% raise is 0.7, the probability that he earns
a 3% raise is 0.2, and the probability that he earns a 2% raise is 0.1.

A competing company has offered Bob a similar position for $65,000 a year. Bob wonders if he
should take the new job or take his chances with his current job. SHOW ALL WORK!

A) Find the mathematical expectation of the dollar amount of his raise at his current job.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

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step-by-step explanation:

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