Apopulation of coyotes is known to show periodic behavior over time. the table shows the population of coyotes in a specific area over time.

second  option  

Step-by-step explanation:

We have a function of the form

We know that the cos(x) function is periodic.

That's why      when

Where k is an even number.

Also    when

Where k is an odd integer.

Finally when and k is an odd integer.

With this information we can evaluate the options given for the function f(x) with the values presented in the attached table and see which one is more similar.

For example, for the point (0, 25) we have Acos(0) = A.

Then A + h = 25

Of the options presented, the one that best approximates this result is:

Because:

If we try another point, for example (3, 75) we have:

We know that

So:

In point (6, 26) we have:

Finally the answer is the second  option

6 adults and 9 children went.

a + c = 15

12a + 9c = 153

12(6) + 9(9) = 153

72 + 81 = 153

asnwer is (g o h o f)(x) = 2x - 6/x + 7

step-by-step explanation:

given,

f(x) = x - 3/x

g(x) = x + 3

h(x) = 2x + 1

we need to find : (g o h o f)(x)

we can write (g o h o f)(x) = g[ h{ f(x) } ]

so first we find h{f(x)}

h{f(x)} = f(x) + 3 = (x - 3/x) + 3

h{f(x)} = x - 3/x + 3

now we find g[ h{ f(x) } ].

g[ h{ f(x) } ] = g(x - 3/x + 3)       {plug h{f(x)} = x - 3/x + 3 in g[h{f(x)}] }

g(x - 3/x + 3) = 2 (x - 3/x + 3) + 1

                    = 2x - 6/x + 6 + 1

                    = 2x - 6/x + 7

hence we get (g o h o f)(x) = 2x - 6/x + 7