2. How many outcome sequences are possible when a die is rolled four times, where we say, for instance, that the outcome is 3, 4, 3, 1 if the first roll landed on 3, the second on 4, the third on 3, and the fourth on 1

the required number of possible outcomes on the is 1296

Step-by-step explanation:

Given the data in the question;

the possible number of outcomes on a dice is n = 6[ 1, 2, 3, 4, 5, 6 ]

we know that if a dice is rolled for example x number of times,

then the possible outcomes will be N = nˣ

now given outcome are 3, 4, 3, 1

if the dice is rolled 4 times, i.e our x is 4

then the total number of possible outcomes on the dice will be;

N = nˣ

N = 6⁴

N = 1296

Therefore, the required number of possible outcomes on the is 1296

2 equivalent expressions to represent the area of a rectangle and the top is n-3 and the side is 2

area of the rectangle = length * width

given length = n - 3

width = 2

replace it in the area

so area of the rectangle = (n-3) *2

= 2(n-3)

one of the expression is 2(n-3)

to get another expression we distribute 2 inside the parenthesis

2(n-3) is 2n - 6

so another expression is 2n - 6

two equivalent expression are

2(n - 3)   , 2n - 6

it would be 0.18 because when the other choices are converted they equal those two numbers.   hope this !