I think that this is a combination problem. From the given, the 8 students are taken 3 at a time. This can be solved through using the formula of combination which is C(n,r) = n!/(n-r)!r!. In this case, n is 8 while r is 3. Hence, upon substitution of the values, we have
C(8,3) = 8!/(8-3)!3!
C(8,3) = 56
There are 56 3-person teams that can be formed from the 8 students.
Answer:
20 to the 5th power
Step-by-step explanation:
Answer:
Part 1) The domain of the quadratic function is the interval (-∞,∞)
Part 2) The range is the interval (-∞,1]
Step-by-step explanation:
we have
![f(x)=-x^2+14x-48](https://tex.z-dn.net/?f=f%28x%29%3D-x%5E2%2B14x-48)
This is a quadratic equation (vertical parabola) open downward (the leading coefficient is negative)
step 1
Find the domain
The domain of a function is the set of all possible values of x
The domain of the quadratic function is the interval
(-∞,∞)
All real numbers
step 2
Find the range
The range of a function is the complete set of all possible resulting values of y, after we have substituted the domain.
we have a vertical parabola open downward
The vertex is a maximum
Let
(h,k) the vertex of the parabola
so
The range is the interval
(-∞,k]
Find the vertex
![f(x)=-x^2+14x-48](https://tex.z-dn.net/?f=f%28x%29%3D-x%5E2%2B14x-48)
Factor -1 the leading coefficient
![f(x)=-(x^2-14x)-48](https://tex.z-dn.net/?f=f%28x%29%3D-%28x%5E2-14x%29-48)
Complete the square
![f(x)=-(x^2-14x+49)-48+49](https://tex.z-dn.net/?f=f%28x%29%3D-%28x%5E2-14x%2B49%29-48%2B49)
![f(x)=-(x^2-14x+49)+1](https://tex.z-dn.net/?f=f%28x%29%3D-%28x%5E2-14x%2B49%29%2B1)
Rewrite as perfect squares
![f(x)=-(x-7)^2+1](https://tex.z-dn.net/?f=f%28x%29%3D-%28x-7%29%5E2%2B1)
The vertex is the point (7,1)
therefore
The range is the interval
(-∞,1]
I just had a test on this lol perfect timing. Anyways the answer would be 3 times bigger bc the circumference of a circle with the radius of 3 is 6pi and the circumference of a circle with the radius of 1 is 2pi which makes the first circle 3 times bigger