The formula for the number of multisets is (n k−1)! divided by a product of two other factorials. we want to use the quotient principle to explain why this formula counts multisets. the formula for the number of multisets is also a binomial coefficient, so it should have an interpretation that involves choosing k items from n k−1 items. the parts of the problem that follow lead us to these explanations. a. in how many ways can you place k red checkers and n−1 black checkers in a row?

a box 3 3/4 feet long or 4+ feet.

step-by-step explanation:

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.

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm