There are 720 total different combinations, and 24 of those will have the letters DAY consecutively within all those combinations.
<u>Explanation:</u>
FRIDAY is a six letter word.
To form all combinations of letters, we would have six choices of letters to fill the first spot. Whatever letter you choose for the first spot, you then have five choices of letters to fill the second spot. Four choices of letters to fill the third spot. And so on.
So, the total number of different combinations of the six letters would be 6!
6! = 6 X 5 X 4 X 3 X 2 X 1
= 720
DAY could appear consecutively starting in 4 different spots: the 1st, 2nd, 3rd, and 4th spots of all combinations. DAY will appear consecutively 6 times in each of those 4 starting spots.
6 X 4 = 24.
So, there are 720 total different combinations, and 24 of those will have the letters DAY consecutively within all those combinations.
Answer & Step-by-step explanation:
First, we will multiply 5 by 28 to find out the total number of ages in the room.
5 * 28 = 140
Now, we will multiply 6 by 29 to find out the total number of ages in the room after the new person comes in.
6 * 29 = 174
Now, in order for us to find the age of the new person, then we will subtract 140 from 174.
174 - 140 = 34
So, the person that entered the room is 34 years old.
Answer: 116 Degrees
Step-by-step explanation:
540 is what the pentagon equals! You add up all of the sides, the square equals 90 degrees because it's a right angle. 121+115+98+90 equals 424. You subtract 540 - 424 and you get 116, which is x! Good luck!
Answer:
--- test statistic
--- p value
Conclusion: Fail to reject the null hypothesis.
Step-by-step explanation:
Given


--- Null hypothesis
---- Alternate hypothesis

Solving (a): The test statistic
This is calculated as:

So, we have:






Solving (b): The p value
This is calculated as:

So, we have:

Look up the z probability in the z score table. So, the expression becomes


Solving (c): With
, what is the conclusion based on the p value
We have:

In (b), we have:

By comparison:

i.e.

So, we fail to reject the null hypothesis.