Answer: 120 ways
Step-by-step explanation: In this problem, we're asked how many ways can 5 people be arranged in a line.
Let's start by drawing 5 blanks to represent the 5 different positions in the line.
Now, we know that 5 different people can fill the spot in the first position. However, once the first position is filled, only 4 people can fill the second spot and once the second spot is filled, only 3 people can fill the third spot and so on. So we have <u>5</u> <u>4</u> <u>3</u> <u>2</u> <u>1</u>.
Now, based on the counting principle, there are 5 x 4 x 3 x 2 x 1 ways for all 5 spots to be filled.
5 x 4 is 20, 20 x 3 is 60, 60 x 2 is 120, and 120 x 1 is 120.
So there are 120 ways for all 5 spots to be filled which means that there are 120 ways that 5 people can be arranged in a line.
I have also shown my work on the whiteboard in the image attached.
The answer is -17 hope this helps
Answer:
.
Step-by-step explanation:
Notice that the first two factors are in the form
, which is equal to
. Start by combining and expanding these two factors:
Let
.
.
.
This expression can now be expressed as
.
stands the unit imaginary number, where
. Unless
is raised to a certain power other than
, it can be treated just like a constant.
Expand this expression using FOIL:
.
-.8,2/33,1/11,.4 good luck
<span>
Answer: PQ=5, QR=radical 61= 7.81, angle: 50degrees,</span>Why:PQ=|-3|+2=5PR=6<span>angle Alfa, so there is right angle triangle PQR so I can use following formula:</span>PQ^2 + RP^2=QR^2;25 + 36=QR^2;QR=radical 61<span>also I can use: sinus (angle)=PR/QR;</span><span>sin(angle)=6/radical61=0.76822 which gives angle to be little bit more than 50 degrees{sinus 50 degrees=<span>0,7660</span>}. </span>