Answer:
B: Permutation; Number of ways = 60
Step-by-step explanation:
First we have to decide if this is a problem of permutation or combination. The rule is:
- If the order matters, permutations will be used
- If order does not matter, combinations will be used
In this problem, they order of awarding the medals matters, so this is a permutation problem.
We have to award 3 medals among 5 runners. So this can be done in 5P3 ways:
![nPr=\frac{n!}{(n-r)!}\\ \\ so\\ \\ 5P3=\frac{5!}{(5-3)!}=60](https://tex.z-dn.net/?f=nPr%3D%5Cfrac%7Bn%21%7D%7B%28n-r%29%21%7D%5C%5C%20%5C%5C%20so%5C%5C%20%5C%5C%205P3%3D%5Cfrac%7B5%21%7D%7B%285-3%29%21%7D%3D60)
Therefore, there are 60 ways to award the medal. Therefore, the correct answer is B.
Answer:
X= (300 s + 200 b + 42 d )mg
Step-by-step explanation:
Amount of spinach=300 ml
Amount of berries =200 ml
amount of dressing = 42 ml
Vitamin C in one ml of spinach = s mg
Vitamin C in 300 ml of spinach = 300 s mg
Vitamin C in one ml of berries=b mg
Vitamin C in 200 ml of berries = 200 b mg
Vitamin C in one ml of dressing = d mg
Vitamin C in 42 ml of dressing = 42 d mg
Let total vitamin C be = x
Then
X= (300 s + 200 b + 42 d )mg
is the required expression
Answer:
Step-by-step explanation:
F(x)=x³-27/x²-9
F(x)=(-9)³-27/(-9)²-9
F(x)=-729-27/-81-9
F(x)=-756/-90
F(x)=42/5
1) <span>Which of the following shows that polynomials are closed under subtraction when polynomial x + 5 is subtracted from 3x2 + 2x − 6?
3x^2+2x-6-(x+5)=3x^2+2x-6-x-5=3x^2+x-11
Answer: Second option: </span><span>3x^2 + x − 11 will be a polynomial
2) </span><span>Which of the following shows that polynomials are closed under subtraction when polynomial 3x2 + 4 is subtracted from x2+ 2x + 5?
x^2+2x+5-(3x^2+4)=x^2+2x+5-3x^2-4=-2x^2+2x+1
Answer: Third option </span><span>−2x^2 + 2x + 1 will be a polynomial</span>
For this case we have the following functions:
![y = 2 y = 3x](https://tex.z-dn.net/?f=y%20%3D%202%0A%0Ay%20%3D%203x)
To find the algebraic solution we must equal both equations.
We have then:
![2 = 3x ](https://tex.z-dn.net/?f=2%20%3D%203x%0A)
Clearing x we have:
![x = 2/3 ](https://tex.z-dn.net/?f=x%20%3D%202%2F3%0A)
Then, the ordered pair solution is:
Answer:
(x, y) = (2/3, 2)
See attached image.