Answer:
Tomorrow = 25 students
In 2 days = 44 students
In 40 days = 40 students
Step-by-step explanation:
Let A = watch more than an hour
B = watch less than an hour
First of all we need to make a transition matrix
![P = \begin{bmatrix}0 & 1\\ 0.25 & 0.75\end{bmatrix} \binom{A}{B}](https://tex.z-dn.net/?f=P%20%3D%20%5Cbegin%7Bbmatrix%7D0%20%26%201%5C%5C%200.25%20%26%200.75%5Cend%7Bbmatrix%7D%20%5Cbinom%7BA%7D%7BB%7D)
Also we are given,
X = [100, 100]
A B
Therefore,
![XP=\begin{bmatrix}100 & 100\end{bmatrix} \times \begin{bmatrix}0 & 1\\ 0.25 & 0.75\end{bmatrix}](https://tex.z-dn.net/?f=XP%3D%5Cbegin%7Bbmatrix%7D100%20%26%20100%5Cend%7Bbmatrix%7D%20%5Ctimes%20%5Cbegin%7Bbmatrix%7D0%20%26%201%5C%5C%200.25%20%26%200.75%5Cend%7Bbmatrix%7D)
= [25, 175]
Thus, 25 students will watch television for an hour or more tomorrow.
Now for 2 days,
![XP^2=\begin{bmatrix}100 & 100\end{bmatrix} \times \begin{bmatrix}0 & 1\\ 0.25 & 0.75\end{bmatrix} \times \begin{bmatrix}0 & 1\\ 0.25 & 0.75\end{bmatrix}](https://tex.z-dn.net/?f=XP%5E2%3D%5Cbegin%7Bbmatrix%7D100%20%26%20100%5Cend%7Bbmatrix%7D%20%5Ctimes%20%5Cbegin%7Bbmatrix%7D0%20%26%201%5C%5C%200.25%20%26%200.75%5Cend%7Bbmatrix%7D%20%5Ctimes%20%5Cbegin%7Bbmatrix%7D0%20%26%201%5C%5C%200.25%20%26%200.75%5Cend%7Bbmatrix%7D)
= [43.75, 156.25]
Hence, 44 students will watch television for an hour or more in 2 days.
Now in 40 days,
![XP^40=\begin{bmatrix}100 & 100\end{bmatrix} \times \begin{bmatrix}0 & 1\\ 0.25 & 0.75\end{bmatrix}^{40}](https://tex.z-dn.net/?f=XP%5E40%3D%5Cbegin%7Bbmatrix%7D100%20%26%20100%5Cend%7Bbmatrix%7D%20%5Ctimes%20%5Cbegin%7Bbmatrix%7D0%20%26%201%5C%5C%200.25%20%26%200.75%5Cend%7Bbmatrix%7D%5E%7B40%7D)
But instead of multiplying the above matrix 40 times, we can we can find the long term division method.
Let
x = long term distribution of students watching television >1 hour
y = long term distribution of students watching television <1 hour
Therefore,
![\begin{bmatrix}x & y\end{bmatrix} \times \begin{bmatrix}0 & 1\\ 0.25 & 0.75\end{bmatrix} = \begin{bmatrix}x & y\end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7Dx%20%26%20y%5Cend%7Bbmatrix%7D%20%5Ctimes%20%5Cbegin%7Bbmatrix%7D0%20%26%201%5C%5C%200.25%20%26%200.75%5Cend%7Bbmatrix%7D%20%3D%20%5Cbegin%7Bbmatrix%7Dx%20%26%20y%5Cend%7Bbmatrix%7D)
⇒ 0.25 y = x
And we know that x + y = 200
∴ 0.25 y + y = 200
∴ y = 160
And x = 40 ( ∵ x + y = 200)
Thus 40 students will watch televisions in the 40 days for an hour or more.
Answer:
Step-by-step explanation:
<u>Given</u>
- Q(s) = -4s^3 + 7s^2 - 24;
- s = -4 and 1
<u>Verifying zeroes</u>
Q(-4) =
- -4(-4)^3 + 7(-4)^2 - 24 =
- 256 + 112 - 24 =
- 344
- Incorrect as 344 ≠ 0
Q(1) =
- -4(1)^3 + 7(1)^2 - 24 =
- -12 + 7 - 24 =
- -29
- Incorrect as -29 ≠ 0
Standard form for a is 1/2x - y = -3
the slope equation and standard form for b is x = 2 (i’m pretty sure it’s that hope this helps)
Answer:
11
Step-by-step explanation:
2x + 3
2(4) + 3 .......................replace x with 4
8 + 3
11
Answer:
i think it is y=-2/3x+8
Step-by-step explanation: