Answer:
https://brainly.com/
Step-by-step explanation:
Option D:
are the coordinates of the point P
Explanation:
It is given that "A coordinate grid shown from negative 2 to positive 2 on x-axis and negative 2 to positive 2 on y-axis. There are 4 grid lines between a whole unit of the grid".
Thus, the value of each grid is ![0.2](https://tex.z-dn.net/?f=0.2)
It is also given that, "A point labeled P is shown at the intersection of 8 grid lines to the left of the y-axis and 4 grid lines above the x-axis".
Since the point P lies on the left of the y-axis and above the x-axis, the x-value will be negative and y-value will be positive.
Thus, the value of x-axis is given by
![8\times0.2=-1.6](https://tex.z-dn.net/?f=8%5Ctimes0.2%3D-1.6)
And the value of y-axis is given by
![4\times0.2=0.8](https://tex.z-dn.net/?f=4%5Ctimes0.2%3D0.8)
Thus, the coordinates of the point P is ![(-1.6,0.8)](https://tex.z-dn.net/?f=%28-1.6%2C0.8%29)
Hence, Option D is the correct answer.
Answer:
n+3 = 15 ; n = 12
3n -6 = 12; n=6
Step-by-step explanation:
more than means it comes after
a number
n
3 more than
n+3
is 15
n+3 = 15
Subtract 3 from each side
n+3-3 = 15-3
n = 12
Subtract from comes after
three times a number
3n
six subtracted from
3n -6
is 12 means equal to
3n -6 = 12
To solve add 6 to each side
3n -6+6 =12+6
3n = 18
Divide by 3
3n/3 =18/3
n =6
Answer:
future payment is $77056.92
total interest is paid after 45 year is $23056.42
Step-by-step explanation:
Given data
payment (P) = $100
No of installment (n) = 12
rate of interest ( r ) = 1.5 % i.e. = 0.015
time period (t) = 45 years
to find out
future payment and interest after 45 year
solution
we know future payment formula i.e. given below
future payment = payment × ![(1+\frac{r}{n})^{nt} - 1) / (r/n)](https://tex.z-dn.net/?f=%281%2B%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bnt%7D%20-%201%29%20%2F%20%28r%2Fn%29)
now put all these value in equation
future payment = $ 100 ×
future payment = $ 77056.92
payment paid in 45 year @ $100 total money is paid is 45 × 12 × $100 i.e. = $54000
total interest = future payment - money paid
total interest = $77056.42 - $54000
total interest = $23056.42
Answer:
![a_{3} = 405](https://tex.z-dn.net/?f=a_%7B3%7D%20%3D%20405)
Step-by-step explanation:
A geometric sequence is based on the following equation:
![a_{n+1} = ra_{n}](https://tex.z-dn.net/?f=a_%7Bn%2B1%7D%20%3D%20ra_%7Bn%7D)
In which r is the common ratio.
This can be expanded for the nth term in the following way:
![a_{n} = a_{1}r^{n-1}](https://tex.z-dn.net/?f=a_%7Bn%7D%20%3D%20a_%7B1%7Dr%5E%7Bn-1%7D)
In which
is the first term.
In this question:
![a_{1} = 3645, a_{6} = 15](https://tex.z-dn.net/?f=a_%7B1%7D%20%3D%203645%2C%20a_%7B6%7D%20%3D%2015)
Applying the equation:
![a_{6} = a_{1}r^{6-1}](https://tex.z-dn.net/?f=a_%7B6%7D%20%3D%20a_%7B1%7Dr%5E%7B6-1%7D)
![a_{6} = a_{1}r^{5}](https://tex.z-dn.net/?f=a_%7B6%7D%20%3D%20a_%7B1%7Dr%5E%7B5%7D)
![3645r^{5} = 15](https://tex.z-dn.net/?f=3645r%5E%7B5%7D%20%3D%2015)
![r^{5} = \frac{15}{3645}](https://tex.z-dn.net/?f=r%5E%7B5%7D%20%3D%20%5Cfrac%7B15%7D%7B3645%7D)
![r^{5} = \frac{1}{243}](https://tex.z-dn.net/?f=r%5E%7B5%7D%20%3D%20%5Cfrac%7B1%7D%7B243%7D)
![r = \sqrt[5]{\frac{1}{243}}](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%5B5%5D%7B%5Cfrac%7B1%7D%7B243%7D%7D)
![r = \frac{1}{3}](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7B1%7D%7B3%7D)
So
![a_{n} = 3645 \times (\frac{1}{3})^{n-1}](https://tex.z-dn.net/?f=a_%7Bn%7D%20%3D%203645%20%5Ctimes%20%28%5Cfrac%7B1%7D%7B3%7D%29%5E%7Bn-1%7D)
![a_{3} = 3645 \times (\frac{1}{3})^{3-1} = 405](https://tex.z-dn.net/?f=a_%7B3%7D%20%3D%203645%20%5Ctimes%20%28%5Cfrac%7B1%7D%7B3%7D%29%5E%7B3-1%7D%20%3D%20405)