Answer:
Felipe is correct
Step-by-step explanation:
Note the difference between consecutive terms is constant, that is
16 - 24 = 8 - 16 = 0 - 8 = - 8
This indicates the sequence is arithmetic
The explicit formula for an arithmetic sequence is
f(n) = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 24 and d = - 8, thus
f(n) = 24 - 8(n - 1) = 24 - 8n + 8 = 32 - 8n ← Felipe's answer
Answer:

And we can set equal this derivate to 0 in order to find the critical point and we got:


And we can calculate the second derivate and we got:

So then w can conclude that the value of t = 3.4375 represent the minimum value for the function and we can replace in the original function and we got:

So then the minimum annual income occurs at t = 3.43 (between 2008 and 2009) and the value is 25.094
Step-by-step explanation:
For this case we have the following function:

Where P represent the annual net income for the period 2007-2011 and 
And t represent the time in years since the start of 2005
In order to find the lowet income we need to use the derivate, given by:

And we can set equal this derivate to 0 in order to find the critical point and we got:


And we can calculate the second derivate and we got:

So then w can conclude that the value of t = 3.4375 represent the minimum value for the function and we can replace in the original function and we got:

So then the minimum annual income occurs at t = 3.43 (between 2008 and 2009) and the value is 25.094
Answer:
364 inches cubed
Step-by-step explanation:
There are 10 seniors in the class, from which 4 should be chosen by the teacher. The order of the chosen students does not matter. This means that we speak of combinations. THe equation for calculating the number of possible combinations is:
C=N!/R!(N-R), where N is the total number of objects and R is the number of objects we select from the N
In our case, N=10, R=4.
C= 10!/4!*6!=10*9*8*7*6!/6!*4*3*2*1=<span>10*9*8*7/24=5040/24=210
There are 210 different ways for the teacher to choose 4 seniors in no particular order.</span>
Answer:
x can only be 0
Step-by-step explanation: