Aclass with n kids lines up for recess. the order in which the kids line up is random with each ordering being equally likely. there are three kids in the class named hubert, celia and felicity. the use of the word "or" in the description of the events, should be interpreted as the inclusive or. that is "a or b" means that a is true, b is true or both a and b are true. give an expression for each of the probabilities below as a function of n. simplify your final expression as much as possible so that your answer does not include any expressions of the form (ab). (a) what is the probability that celia is first in line or felicity is first in line? (b) what is the probability that celia is first in line or felicity is last in line? (c) what is the probability that celia is not next to felicity in line? (d) what is the probability that hubert is next to celia or felicity in line? (e) what is the probability that hubert is not next to either celia or felicity in line?

- 2 + 10x³ - 21x² + 19x - 4

step-by-step explanation:

each term in the second factor is multiplied by each term in the first factor

x²(- 2x² + 4x - 1) - 3x(- 2x² + 4x - 1) + 4(- 2x² + 4x - 1) ← distribute

= - 2 + 4x³ - x² + 6x³ - 12x² + 3x -8x² + 16x - 4

collect like terms

= - 2 + 10x³ - 21x² + 19x - 4 ← in standard form

b

step-by-step explanation:

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is

if you was gonna solve for a, a is a   < -12