there are 15 finalist in a singing competition. the top five singers receive prizes. how many ways can the singer finish first t
1 answer:
Answer:
The singers can finish first through fifth in 360360 ways.
Step-by-step explanation:
The order of the singers is important, because they are ranked by positions. So we use the permutations formula to solve this question.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
In this question:
Top five singers, from 15 finalists. So
The singers can finish first through fifth in 360360 ways.
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1. a. Pretty much, you just have to rearrange it so that the highest power is in the front. So, here's your answer:
b. It's a 4th-degree polynomial. A degree means that "what's the highest power?"
c. It's a trinomial. It has 3 terms, hence it's a trinomial.
2. a. Since it's an odd power and a negative coefficient, it will be:
x→∞, f(x)→-∞
x→-∞, f(x)→∞
b. The degree is even and the coefficient is negative, so it will be:
x→∞, f(x)→-∞
x→-∞, f(x)→-∞
3. a. This basically means that if you solve for x, you should get -2, 1, and 2. So, to do this, you can just write it in factored form and multiply inwards using any method of your choice (remember that in the parentheses, you should get the above value if you solve for x):
If you multiply it out, you get (also your answer):
4. The zeros are at x = 3, 2 and -7. Multiplicity of 3 is 1, for 2 it's 2, and for -7 it's 3.
Hope this helps!
b. It's a 4th-degree polynomial. A degree means that "what's the highest power?"
c. It's a trinomial. It has 3 terms, hence it's a trinomial.
2. a. Since it's an odd power and a negative coefficient, it will be:
x→∞, f(x)→-∞
x→-∞, f(x)→∞
b. The degree is even and the coefficient is negative, so it will be:
x→∞, f(x)→-∞
x→-∞, f(x)→-∞
3. a. This basically means that if you solve for x, you should get -2, 1, and 2. So, to do this, you can just write it in factored form and multiply inwards using any method of your choice (remember that in the parentheses, you should get the above value if you solve for x):
If you multiply it out, you get (also your answer):
4. The zeros are at x = 3, 2 and -7. Multiplicity of 3 is 1, for 2 it's 2, and for -7 it's 3.
Hope this helps!