Answer:
your sister is 43 and your are 18
Step-by-step explanation:
Answer:
9.9
Step-by-step explanation:
The table tells you numbers who "want" a job. The question asks you for numbers "looking for a job". Those may be different things. The question cannot be answered from the table, unless you make the assumption that those wanting a job are actually looking for a job.
total looking = (working and looking) + (not working and looking)
= 5.2 million + 4.7 million
= 9.9 million . . . . looking for a job
Answer:
23.8 pounds
Step-by-step explanation:
First we have to find how much she spend on coffee altogether, so our equation is:
141 - 83.16 = 57.84
Then we have to find how many times 2.43 goes into 57.84 so our equation is:
57.84 ÷ 2.43 = 23.8
So Sally bought 23.8 pounds of coffee
The linear equation representing the above said pair of points is "y=12x+9"
Step-by-step explanation:
The given set of points are
x Y
1 21
2 33
3 45
4 57
For finding the linear equation for the given sets of value
We must know the generic form of a linear equation is y=m*x + c
m= slope of the line where y= Δy/Δx
Δy= change in y value
Δx= change in x value
Thus slope ”m” = 33-21/2-1 = 12
we put slope “m” in the equation which becomes y=12x+c
Now we put any of the set value in the equation
33= 12*2+c ∴ c=9
Hence required linear equation is y=12x+9
Answer:
Arithmetic Sequence
---- Explicit
--- Recursive
Geometric Sequence
---- Explicit
---- Recursive
Step-by-step explanation:
Given
![180, 120,....](https://tex.z-dn.net/?f=180%2C%20120%2C....)
(a) Assume it is an arithmetic sequence
The explicit formula is calculated using:
![T_n = a + (n - 1)d](https://tex.z-dn.net/?f=T_n%20%3D%20a%20%2B%20%28n%20-%201%29d)
Where
![a = 180](https://tex.z-dn.net/?f=a%20%3D%20180)
![d = 120 - 180](https://tex.z-dn.net/?f=d%20%3D%20120%20-%20180)
![d = -60](https://tex.z-dn.net/?f=d%20%3D%20-60)
So, we have:
![T_n = 180 + (n - 1)*-60](https://tex.z-dn.net/?f=T_n%20%3D%20180%20%2B%20%28n%20-%201%29%2A-60)
![T_n = 180 -60n + 60](https://tex.z-dn.net/?f=T_n%20%3D%20180%20-60n%20%2B%2060)
Rewrite
![T_n = 180 + 60-60n](https://tex.z-dn.net/?f=T_n%20%3D%20180%20%2B%2060-60n)
![T_n = 240-60n](https://tex.z-dn.net/?f=T_n%20%3D%20240-60n)
The recursive function is calculated using:
![T_1 = 180](https://tex.z-dn.net/?f=T_1%20%3D%20180)
![T_2 = 120 = 180 - 60 = T_1 - 60](https://tex.z-dn.net/?f=T_2%20%3D%20120%20%3D%20180%20-%2060%20%3D%20T_1%20-%2060)
![T_3 = 60 = 120 - 60 = T_2 -60](https://tex.z-dn.net/?f=T_3%20%3D%2060%20%3D%20120%20-%2060%20%3D%20T_2%20-60)
-
![T_n = T_{n-1} - 60](https://tex.z-dn.net/?f=T_n%20%3D%20T_%7Bn-1%7D%20-%2060)
(b) Assume it is a geometric sequence
The explicit formula is calculated using:
![T_n = ar^{n-1}](https://tex.z-dn.net/?f=T_n%20%3D%20ar%5E%7Bn-1%7D)
Where
![a = 180](https://tex.z-dn.net/?f=a%20%3D%20180)
![r = \frac{120}{180}](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7B120%7D%7B180%7D)
![r = \frac{2}{3}](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7B2%7D%7B3%7D)
So, we have:
![T_n = 180 * (\frac{2}{3})^{n-1}](https://tex.z-dn.net/?f=T_n%20%3D%20180%20%2A%20%28%5Cfrac%7B2%7D%7B3%7D%29%5E%7Bn-1%7D)
Split
![T_n = 180 * (\frac{2}{3})^n \div (\frac{2}{3})^1](https://tex.z-dn.net/?f=T_n%20%3D%20180%20%2A%20%28%5Cfrac%7B2%7D%7B3%7D%29%5En%20%5Cdiv%20%28%5Cfrac%7B2%7D%7B3%7D%29%5E1)
![T_n = 180 * (\frac{2}{3})^n \div (\frac{2}{3})](https://tex.z-dn.net/?f=T_n%20%3D%20180%20%2A%20%28%5Cfrac%7B2%7D%7B3%7D%29%5En%20%5Cdiv%20%28%5Cfrac%7B2%7D%7B3%7D%29)
Rewrite as:
![T_n = 180 * (\frac{2}{3})^n * (\frac{3}{2})](https://tex.z-dn.net/?f=T_n%20%3D%20180%20%2A%20%28%5Cfrac%7B2%7D%7B3%7D%29%5En%20%2A%20%28%5Cfrac%7B3%7D%7B2%7D%29)
![T_n = 180 * (\frac{3}{2})* (\frac{2}{3})^n](https://tex.z-dn.net/?f=T_n%20%3D%20180%20%2A%20%28%5Cfrac%7B3%7D%7B2%7D%29%2A%20%28%5Cfrac%7B2%7D%7B3%7D%29%5En)
![T_n = 180 * \frac{3}{2}* (\frac{2}{3})^n](https://tex.z-dn.net/?f=T_n%20%3D%20180%20%2A%20%5Cfrac%7B3%7D%7B2%7D%2A%20%28%5Cfrac%7B2%7D%7B3%7D%29%5En)
![T_n = 90 * 3* (\frac{2}{3})^n](https://tex.z-dn.net/?f=T_n%20%3D%2090%20%2A%203%2A%20%28%5Cfrac%7B2%7D%7B3%7D%29%5En)
![T_n = 270* (\frac{2}{3})^n](https://tex.z-dn.net/?f=T_n%20%3D%20270%2A%20%28%5Cfrac%7B2%7D%7B3%7D%29%5En)
The recursive function is calculated using:
![T_1 = 180](https://tex.z-dn.net/?f=T_1%20%3D%20180)
![T_2 = 120 = 180 * \frac{2}{3} = T_1 * \frac{2}{3}](https://tex.z-dn.net/?f=T_2%20%3D%20120%20%3D%20180%20%2A%20%5Cfrac%7B2%7D%7B3%7D%20%3D%20T_1%20%2A%20%5Cfrac%7B2%7D%7B3%7D)
![T_3 = 80 = 120 * \frac{2}{3} = T_2 * \frac{2}{3}](https://tex.z-dn.net/?f=T_3%20%3D%2080%20%3D%20120%20%2A%20%5Cfrac%7B2%7D%7B3%7D%20%3D%20T_2%20%2A%20%5Cfrac%7B2%7D%7B3%7D)
-
![T_n = T_{n-1} * \frac{2}{3}](https://tex.z-dn.net/?f=T_n%20%3D%20T_%7Bn-1%7D%20%2A%20%5Cfrac%7B2%7D%7B3%7D)