Four students attempt to register online at the same time for an Introductory Statistics class that is full. Two are psychology majors and two are biology majors. They are put on a wait list. Prior to the start of the semester, two enrolled students drop the course, so the professor randomly selects two of the four wait list students and gives them seats in the class. What is the probability that both students selected have different majors?

2/3

Step-by-step explanation:

If all outcomes are listed,

{P1P2, P1B1, P1B2, P2B1, P2B2, B1B2}

then 4/6 of the outcomes have different majors.

this can be simplified to 2/3.

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

step-by-step explanation:

this can be solved first with pythagorean theorem, which tells us to square both legs of the triangle and sum it. this will be equal to the square of the hypotenuse.

the hypotenuse is the side "opposite" the 90 degree angle, which is x.

so we can write using pythagorean theorem,

simplifying:

to further simplify this radical, we need to use the property  

thus