How many ways can 5 people be arranged in a line?
1 answer:
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.
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Answer:
x = -4
y = 7
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Step-by-step explanation:
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We'll first simplify both sides of the expression to get (simply using the distributive property):
Then, we can simplify a little bit:
To solve for n, we have to isolate it. Let's subtract 3n from both sides to further simplify it:
Then, add 18 to both sides to get the value of n:
And that's your answer. If you have questions on how I got that, feel free to ask!
Then, we can simplify a little bit:
To solve for n, we have to isolate it. Let's subtract 3n from both sides to further simplify it:
Then, add 18 to both sides to get the value of n:
And that's your answer. If you have questions on how I got that, feel free to ask!
Answer:
Step-by-step explanation:
<u>Use trigonometry (shown in image below) to find the 3 side-lengths:</u>
- The side opposite of θ =
- The base side adjacent to θ = 11
- The hypotenuse = 12
<u>According to right triangle trigonometry:</u>
cos θ =
<u>Substitute in the values:</u>
cos θ =
