Answer:
<h2>=-7.1h+2k+1</h2>
Step-by-step explanation:
![-7.1h-(-2k-1)\\-\left(-2k-1\right):\quad 2k+1\\=-7.1h+2k+1](https://tex.z-dn.net/?f=-7.1h-%28-2k-1%29%5C%5C-%5Cleft%28-2k-1%5Cright%29%3A%5Cquad%202k%2B1%5C%5C%3D-7.1h%2B2k%2B1)
Answer:
<u>Step 1: Set x to 0
</u>
![-2(0) + y = 3](https://tex.z-dn.net/?f=-2%280%29%20%2B%20y%20%3D%203)
![y = 3](https://tex.z-dn.net/?f=y%20%3D%203)
(0, 3)
<u>Step 2: Set x to 1
</u>
![-2(1) + y = 3](https://tex.z-dn.net/?f=-2%281%29%20%2B%20y%20%3D%203)
![-2 + y + 2 = 3 + 2](https://tex.z-dn.net/?f=-2%20%2B%20y%20%2B%202%20%3D%203%20%2B%202)
![y = 5](https://tex.z-dn.net/?f=y%20%3D%205)
(1, 5)
<u>Step 3: Set x to 2
</u>
![-2(2) + y = 3](https://tex.z-dn.net/?f=-2%282%29%20%2B%20y%20%3D%203)
![-4 + y + 4 = 3 + 4](https://tex.z-dn.net/?f=-4%20%2B%20y%20%2B%204%20%3D%203%20%2B%204)
![y = 7](https://tex.z-dn.net/?f=y%20%3D%207)
(2, 7)
<u>Step 4: Set x to 3
</u>
![-2(3) + y = 3](https://tex.z-dn.net/?f=-2%283%29%20%2B%20y%20%3D%203)
![-6 + y + 6 = 3 + 6](https://tex.z-dn.net/?f=-6%20%2B%20y%20%2B%206%20%3D%203%20%2B%206)
![y = 9](https://tex.z-dn.net/?f=y%20%3D%209)
(3, 9)
Answer:
![x \approx 2.278863](https://tex.z-dn.net/?f=x%20%5Capprox%202.278863)
Step-by-step explanation:
Required
The positive root of ![3\sin(x) = x](https://tex.z-dn.net/?f=3%5Csin%28x%29%20%3D%20x)
Equate to 0
![0 = x -3\sin(x)](https://tex.z-dn.net/?f=0%20%3D%20x%20-3%5Csin%28x%29)
So, we have our function to be:
![h(x) = x -3\sin(x)](https://tex.z-dn.net/?f=h%28x%29%20%3D%20x%20-3%5Csin%28x%29)
Differentiate the above function:
![h'(x) = 1 -3\cos(x)](https://tex.z-dn.net/?f=h%27%28x%29%20%3D%201%20-3%5Ccos%28x%29)
Using Newton's method of approximation, we have:
![x_{n+1} = x_n - \frac{h(x_n)}{h'(x_n)}](https://tex.z-dn.net/?f=x_%7Bn%2B1%7D%20%3D%20x_n%20-%20%5Cfrac%7Bh%28x_n%29%7D%7Bh%27%28x_n%29%7D)
Plot the graph of
to get
--- see attachment for graph
From the attached graph, the first value of x is at 2.2; so:
![x_1 = 2.2](https://tex.z-dn.net/?f=x_1%20%3D%202.2)
So, we have:
![x_{n+1} = x_n - \frac{h(x_n)}{h'(x_n)}](https://tex.z-dn.net/?f=x_%7Bn%2B1%7D%20%3D%20x_n%20-%20%5Cfrac%7Bh%28x_n%29%7D%7Bh%27%28x_n%29%7D)
![x_{1+1} = x_1 - \frac{h(x_1)}{h'(x_1)}](https://tex.z-dn.net/?f=x_%7B1%2B1%7D%20%3D%20x_1%20-%20%5Cfrac%7Bh%28x_1%29%7D%7Bh%27%28x_1%29%7D)
![x_{2} = 2.2 - \frac{2.2 -3\sin(2.2)}{1 -3\cos(2.2)} = 2.28153641](https://tex.z-dn.net/?f=x_%7B2%7D%20%3D%202.2%20-%20%5Cfrac%7B2.2%20-3%5Csin%282.2%29%7D%7B1%20-3%5Ccos%282.2%29%7D%20%3D%202.28153641)
The process will be repeated until the digit in the 6th decimal place remains unchanged
![x_{3} = 2.28153641 - \frac{2.28153641 -3\sin(2.28153641)}{1 -3\cos(2.28153641)} = 2.2788654](https://tex.z-dn.net/?f=x_%7B3%7D%20%3D%202.28153641%20-%20%5Cfrac%7B2.28153641%20-3%5Csin%282.28153641%29%7D%7B1%20-3%5Ccos%282.28153641%29%7D%20%3D%202.2788654)
![x_{4} = 2.2788654 - \frac{2.2788654 -3\sin(2.2788654)}{1 -3\cos(2.2788654)} = 2.2788627](https://tex.z-dn.net/?f=x_%7B4%7D%20%3D%202.2788654%20-%20%5Cfrac%7B2.2788654%20-3%5Csin%282.2788654%29%7D%7B1%20-3%5Ccos%282.2788654%29%7D%20%3D%202.2788627)
![x_{5} = 2.2788627 - \frac{2.2788627-3\sin(2.2788627)}{1 -3\cos(2.2788627)} = 2.2788627](https://tex.z-dn.net/?f=x_%7B5%7D%20%3D%202.2788627%20-%20%5Cfrac%7B2.2788627-3%5Csin%282.2788627%29%7D%7B1%20-3%5Ccos%282.2788627%29%7D%20%3D%202.2788627)
Hence:
Answer:
A. Tickets sold
The table says nothing about the scariest movie, the favorite movie, or the cost of the tickets.
Answer:
33.33% probability that it takes Isabella more than 11 minutes to wait for the bus
Step-by-step explanation:
An uniform probability is a case of probability in which each outcome is equally as likely.
For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.
The probability that we find a value X lower than x is given by the following formula.
![P(X \leq x) = \frac{x - a}{b-a}](https://tex.z-dn.net/?f=P%28X%20%5Cleq%20x%29%20%3D%20%5Cfrac%7Bx%20-%20a%7D%7Bb-a%7D)
For this problem, we have that:
Uniformly distributed between 3 minutes and 15 minutes:
So ![a = 3, b = 15](https://tex.z-dn.net/?f=a%20%3D%203%2C%20b%20%3D%2015)
What is the probability that it takes Isabella more than 11 minutes to wait for the bus?
Either she has to wait 11 or less minutes for the bus, or she has to wait more than 11 minutes. The sum of these probabilities is 1. So
![P(X \leq 11) + P(X > 11) = 1](https://tex.z-dn.net/?f=P%28X%20%5Cleq%2011%29%20%2B%20P%28X%20%3E%2011%29%20%3D%201)
We want P(X > 11). So
![P(X > 11) = 1 - P(X \leq 11) = 1 - \frac{11 - 3}{15 - 3} = 0.3333](https://tex.z-dn.net/?f=P%28X%20%3E%2011%29%20%3D%201%20-%20P%28X%20%5Cleq%2011%29%20%3D%201%20-%20%5Cfrac%7B11%20-%203%7D%7B15%20-%203%7D%20%3D%200.3333)
33.33% probability that it takes Isabella more than 11 minutes to wait for the bus