A fair 66-sided die is rolled 77 times and the resulting sequence of 77 numbers is recorded. A) How many different sequences are possible?B) How many different sequences consist entirely of even numbers? C) How many different sequences are possible if the first, third, and fourth numbers must be the same? D) How many sequences are there where every number is different? E) How many sequences are there where there are at least two numbers that are the same?

A. 279936 sequences.

B. 2187 sequence.

C. 7776 sequence.

D. 46656 sequence

E. 64 sequence.

Step-by-step explanation:

Given data:

A 6 sided fair die

No of time rolled = 7

Resulting sequence recorded = 7.

Solution.

A.) No of different possible sequence

= 6^7

= 279936 sequences.

B.) Sequence consisting of only even number

= there are 3 even numbers between 1 and 7 ( 2,4,6).

= 3^7

= 2187 sequence.

C.) possible sequences are when the first, third, and fourth numbers must be the same.

= 6* 6 ^n

where n = 4

= 6*6^4

= 7776 sequence.

D.) sequence when every number is different.

There are 6 sides of a die, so when every number is different it is.

= 6^6

= 46656 sequence

E.) sequence when atleast there are two numbers that are the same.

= 2^6

= 64 sequence.

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.

answer: median

step-by-step explanation:

the median is the middle value when a data set is ordered from least to greatest