Answer:
6 swimmers in the first heat can be arranged in 1716 different ways.
Step-by-step explanation:
A swim meet has 13 contestants signed up. To calculate the arrangement of first 6 swimmers in first heat we will use combinations because order doesn't matter.
So to select 6 swimmers out of 13 contestants number of different ways
= ![^{13}C_{6}](https://tex.z-dn.net/?f=%5E%7B13%7DC_%7B6%7D)
= ![\frac{13!}{(6!)(13-6)!}](https://tex.z-dn.net/?f=%5Cfrac%7B13%21%7D%7B%286%21%29%2813-6%29%21%7D)
= ![\frac{13\times 12\times 11\times 10\times 9\times 8\times 7!}{6!\times 7!}](https://tex.z-dn.net/?f=%5Cfrac%7B13%5Ctimes%2012%5Ctimes%2011%5Ctimes%2010%5Ctimes%209%5Ctimes%208%5Ctimes%207%21%7D%7B6%21%5Ctimes%207%21%7D)
= ![\frac{13\times 12\times 11\times 10\times 9\times 8}{6\times 5\times 4\times 3\times 2\times 1}](https://tex.z-dn.net/?f=%5Cfrac%7B13%5Ctimes%2012%5Ctimes%2011%5Ctimes%2010%5Ctimes%209%5Ctimes%208%7D%7B6%5Ctimes%205%5Ctimes%204%5Ctimes%203%5Ctimes%202%5Ctimes%201%7D)
= ![\frac{1235520}{720}](https://tex.z-dn.net/?f=%5Cfrac%7B1235520%7D%7B720%7D)
= 1716
Therefore, 6 swimmers in the first heat can be arranged in 1716 different ways.
Answer: X = t or minus 4 square root 3 and X= 4 square root 3 Explanation: add 48 on both sides bring down x squared = 48 take the square root on both sides you get X= t or - 4 square root 3 and X=4 square root 3) Animex yw
Answer:
1/4
25%
Step-by-step explanation:
Robert has 1/2 of the candy bar
If he gave his sister half, she has 1/2 x 1/2 = 1/4 of the candy bar
To convert 1/4 to percentage, multiply by 100
1/4 x 100 = 25%
Answer:
In the pic
Step-by-step explanation:
If you have any questions about the way I solved it, don't hesitate to ask me in the comments below =)
Answer: E, A, D, C, B
Step-by-step explanation:
First, we need to get y alone. So we will add 7 to the side of the equation that has the 4y in it.
So the first one will be.
<em><u>Add 7 to both sides of the equation.</u></em>
Now the second one is
<em><u>4y = 25 + 7 </u></em>Because what you do to one side of the equation, you do to the other. So we add 7 to 25.
Then the 3rd one will be <u><em>4y = 32 </em></u>because 25+7 is equal to 32. But we still have that 4y on the other side of the equation. So the next equation is 4y = 32.
The second to last step is <em><u>Divide both sides by 4 </u></em>because thats
how you isolate y. So once you divide both sides by 4. You will get 8. Leading you into the next and final step.
<em><u>Y = 8</u></em>
And thats how you do it!