Answer:
see below
Step-by-step explanation:
-33, -27, -21, -15,....
-33 +6 = -27
-27+6 = -21
-21+6 = -15
This is an arithmetic sequence
The common difference is +6
explicit formula
an=a1+(n-1)d where n is the term number and d is the common difference
an = -33 + ( n-1) 6
an = -33 +6n -6
an = -39+6n
recursive formula
an+1 = an +6
10th term
n =10
a10 = -39+6*10
= -39+60
=21
sum formula
see image
The sum will diverge since we are adding infinite numbers
Just multiply man 2*4 2*3 1.5*4 and 1.5*3.
<h3>
Answer: A) 1/4</h3>
Explanation: There are four equal sections, one of which is red. So the probability of landing in the red space is 1/4.
We're given
![\displaystyle \int_4^{-10} g(x) \, dx = -3](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint_4%5E%7B-10%7D%20g%28x%29%20%5C%2C%20dx%20%3D%20-3)
which immediately tells us that
![\displaystyle \int_{-10}^4 g(x) \, dx = 3](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint_%7B-10%7D%5E4%20g%28x%29%20%5C%2C%20dx%20%3D%203)
In other words, swapping the limits of the integral negates its value.
Also,
![\displaystyle \int_4^6 g(x) \, dx = 5](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint_4%5E6%20g%28x%29%20%5C%2C%20dx%20%3D%205)
The integral we want to compute is
![\displaystyle \int_{-10}^6 g(x) \, dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint_%7B-10%7D%5E6%20g%28x%29%20%5C%2C%20dx)
which we can do by splitting up the integral at x = 4 and using the known values above. Then the integral we want is
![\displaystyle \int_{-10}^6 g(x) \, dx = \int_{-10}^4 g(x) \, dx + \int_4^6 g(x) \, dx = 3 + 5 = \boxed{8}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint_%7B-10%7D%5E6%20g%28x%29%20%5C%2C%20dx%20%3D%20%5Cint_%7B-10%7D%5E4%20g%28x%29%20%5C%2C%20dx%20%2B%20%5Cint_4%5E6%20g%28x%29%20%5C%2C%20dx%20%3D%203%20%2B%205%20%3D%20%5Cboxed%7B8%7D)