Answer:
The required sequence is
. The average rate of change from n = 1 to n = 3 is -7.5.
Step-by-step explanation:
From the given graph it is clear that the sequence is a GP because the all terms are half of their previous terms.
Here, ![a_2=10,a_3=5,a_4=2.5,a_5=1.25](https://tex.z-dn.net/?f=a_2%3D10%2Ca_3%3D5%2Ca_4%3D2.5%2Ca_5%3D1.25)
![r=\frac{a_3}{a_2}=\frac{5}{10}=\frac{1}{2}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7Ba_3%7D%7Ba_2%7D%3D%5Cfrac%7B5%7D%7B10%7D%3D%5Cfrac%7B1%7D%7B2%7D)
The common ratio of GP is 1/2.
![r=\frac{a_2}{a_1}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7Ba_2%7D%7Ba_1%7D)
![\frac{1}{2}=\frac{10}{a_1}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%3D%5Cfrac%7B10%7D%7Ba_1%7D)
![a_1=20](https://tex.z-dn.net/?f=a_1%3D20)
The first term of the sequence is 20.
The formula for sequence is
![a_n=a(r)^{n-1}](https://tex.z-dn.net/?f=a_n%3Da%28r%29%5E%7Bn-1%7D)
Where a is first term and r is common difference.
The required sequence is
![a_n=20(\frac{1}{2})^{n-1}](https://tex.z-dn.net/?f=a_n%3D20%28%5Cfrac%7B1%7D%7B2%7D%29%5E%7Bn-1%7D)
The formula for rate of change is
![m=\frac{f(x_2)-f(x_1)}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7Bf%28x_2%29-f%28x_1%29%7D%7Bx_2-x_1%7D)
The average rate of change from n = 1 to n = 3 is
![m=\frac{f(3)-f(1)}{3-1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7Bf%283%29-f%281%29%7D%7B3-1%7D)
![m=\frac{5-20}{3-1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B5-20%7D%7B3-1%7D)
![m=\frac{-15}{2}=-7.5](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B-15%7D%7B2%7D%3D-7.5)
Therefore the required sequence is
. The average rate of change from n = 1 to n = 3 is -7.5.
The solution to the system of equation is (1, 4).
In order to find this, we can first just see where the graphs intersect each other. This will give us the solution set.
As for what it represents, the x value in the increase in temperature and the y value is the increase in customers.
Therefore, we know that we want the temperature to go up by 1 (although we don't know the units) and that would result in the amount of people coming, and staying longer by 4 (again, we don't know the units of measure).
Answer:
3n+2
Step-by-step explanation:
hope this helps :(
Can you support your question by uploading a drawing?
Answer: 27/36
Step-by-step explanation: It says there are 36 bikes (18 pairs), meaning that there are 2 bikes per pair because 18 multiplied by 2 is 36.
1 pair (2 bikes) are yellow.
3 pairs (6 bikes) are red.
For purple, add yellow and red together: 2 + 6 = 8. Subtract the total number of bikes from this: 36 - 8 = 28 purple bikes.
If you take out 1 purple bike, this leaves you with 27. The probability of choosing a purple bike out of the total (36), is 27/36.
Please let me know if this is correct or wrong.