16. in a group of 68 students, each student is registered for at least one of three classes – history, math and english. twenty-five students are registered for history, twenty-five students are registered for math, and thirty-four students are registered for english. if only three students are registered for all three classes, how many students are registered for exactly two classes?

[tex[ two groups=-68+25+25+34 -6=10[/tex]

Step-by-step explanation:

For this case we have a diagram of the situation on the figure attached.

And for this case we can us the following rule from probability:

Or equivalently:

We know the total on this case total=68, the people for history is A=25, for math B=25 and for english C=34, and the people in all the groups 3, so we can replace:

And if we solve for the poeple in two groups we got:

[tex[ two groups=-68+25+25+34 -6=10[/tex]

step-by-step explanation:

x^2 -12x + 36 + y^2 = 36

x^2 + y^2 = 12x

r^2 = 12rcos(theta)

r = 12 cos(theta)

on a coordinate grid, point a is at (−4.0, −2.4) and point b is at (4.0, −2.4). point b is a reflection of point a across the –axis. input either a lowercase x or i think is the right awnser

step-by-step explanation: