You have in total 5 pets and you have $22.00 To spend what you do is divide . Like this
Different
slot method
1st slot has 6 options to chose from
2nd slot has 5 since 1 is gone to slot 1
3rd slot has 4 since 2 are gone to 1st and 2nd slots
so it is
6 times 5 times 4=120
answer is 120 ways
Answer:
See verification below
Step-by-step explanation:
Remember that the Intermediate Value Theorem (IVT) states that if f is a continuous function on [a,b] and f(a)<M<f(b), there exists some c∈[a,b] such that f(c)=M.
Now, to apply the theorem, we have that f(0)=0²+0-1=-1, f(5)=5²+5-1=29, then f(0)=-1<11<29=f(5). Additionally, f is continous since it is a polynomial. Then the IVT applies, and such c exists.
To find, c, solve the quadratic equation f(c)=11. This equation is c²+c-1=11. Rearranging, c²+c-12=0. Factor the expression to get (c+4)(c-3)=0. Then c=-4 or c=3. -4 is not in the interval, then we take c=3. Indeed, f(3)=3²+3-1=9+3-1=11.
