Answer:
Number of combinations = 56
Step-by-step explanation:
Points to remember
nCₐ = n!/(r!(n - r)!)
The given word is "FRIENDLY"
F R I E N D L Y is a 8 letter word.
<u>To find the number of combinations</u>
5 letters can be selected from 8 letter = 8C₅
8C₅ = 8!/(8 - 5)!5!
= 8!/3!5!
= (8 * 7 * 6* 5!)/(1 * 2 * 3 * 5!)
= 8 * 7
= 56
5 letter combinations can be created from the letters in the world “friendly = 56
First, the need to determine if the statements are true or false.
1) January is the first month of the year. (This statement is true)
2) December is the last month of the year. (This statement is also true)
With this in mind we can determine that what will illustrate the truth value would be:
T T -> T
In other words, since the first statement is true and the second statement is also true then conjunction of both statements would be true.
Answer:
-586
Step-by-step explanation:
Add 538 to both sides
p-538+538=-1124+538=
p=-1124-538
=-586
Y-3=5(x-2)
y-3=5x-10
y=5x-13
the slope is 5
Answer:
The third score must be larger than or equal to 72, and smaller than or equal 87
Step-by-step explanation:
Let's name "x" the third quiz score for which we need to find the values to get the desired average.
Recalling that average grade for three quizzes is the addition of the values on each, divided by the number of quizzes (3), we have the following expression for the average:

SInce we want this average to be in between 80 and 85, we write the following double inequality using the symbols that include equal sign since we are requested the average to be between 80 and 85 inclusive:

Now we can proceed to solve for the unknown "x" treating each inaquality at a time:

This inequality tells us that the score in the third quiz must be larger than or equal to 72.
Now we study the second inequality to find the other restriction on "x":

This ine
quality tells us that the score in the third test must be smaller than or equal to 87 to reach the goal.
Therefore to obtained the requested condition for the average, the third score must be larger than or equal to 72, and smaller than or equal 87: