1. Miguel is playing a game in which a box contains four chips with numbers written on them. Two of the chips have the number 1, one chip has the number 3, and the other chip has the number 5.
Miguel must choose two chips, and if both chips have the same number, he wins $2. If the two
chips he chooses have different numbers, he loses $1 (-$1).
a. Let X = the amount of money Miguel will receive or owe. Fill out the missing values in the
table. (Hint: The total possible outcomes are six because there are four chips and you are
choosing two of them.)
X
2
-1
P(x)
b.
What is Miguel's expected value from playing the game?

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

the answer is d

step-by-step explanation:

solve systems of equations by graphing. a system of linear equations contains two or more equations e.g. y=0.5x+2 and y=x-2. the solution of such a system is the ordered pair that is a solution to both equations. to solve a system of linear equations graphically we graph both equations in the same coordinate system

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step-by-step explanation:

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