How many combinations of 4 students can a teacher choose from 30 students?

a. 27,405

b. 657,720

c. 120

d.810,000

b.  27,405

Step-by-step explanation:

So, we have a total population of 30 (n) and we sample 4 (r) from it.

Now, is it a combination or a permutation?  Does the order matter?  Is it important that the teacher picked John before Andrew?  No.  So, it's a combination:

C(n,r)=C(30,4)

So, the teacher has 27,405 ways to combine groups of 4 students from his 30-student class.

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form