The question is an annuity question with the present value of the annuity given.
The
present value of an annuity is given by PV = P(1 - (1 + r/t)^-nt) /
(r/t) where PV = $61,600; r = interest rate = 9.84% = 0.0984; t = number
of payments in a year = 6; n = number of years = 11 years and P is the
periodic payment.
61600 = P(1 - (1 + 0.0984/6)^-(11 x 6)) / (0.0984 / 6)
61600 = P(1 - (1 + 0.0164)^-66) / 0.0164
61600 x 0.0164 = P(1 - (1.0164)^-66)
1010.24 = P(1 - 0.341769) = 0.658231P
P = 1010.24 / 0.658231 = 1534.78
Thus, Niki pays $1,534.78 every two months for eleven years.
The total payment made by Niki = 11 x 6 x 1,534.78 = $101,295.48
Therefore, interest paid by Niki = $101,295.48 - $61,600 = $39,695.48
Answer:
8radical2
Step-by-step explanation:
8radical2 because the pyhthragehon theorem says the hypotenuse is radical 2 times the side lengths
Answer:
If my cousin gave me $16 ( my real cousins never did T_T) and I am left with $8 while buying a present. The present cost $8...
Wow, I thought I was bad at math
Answer:
12
Step-by-step explanation:
36/3
Answer:
--- Function A
--- Function B
--- Function C
Step-by-step explanation:
Solving (a): Equation of Function A
An exponential equation is represented as:
![y = ab^x](https://tex.z-dn.net/?f=y%20%3D%20ab%5Ex)
From the graph of function A,
![x = 0\ when\ y = 1](https://tex.z-dn.net/?f=x%20%3D%200%5C%20when%5C%20y%20%3D%201)
![x = 1\ when\ y = 3](https://tex.z-dn.net/?f=x%20%3D%201%5C%20when%5C%20y%20%3D%203)
For: ![x = 0\ when\ y = 1](https://tex.z-dn.net/?f=x%20%3D%200%5C%20when%5C%20y%20%3D%201)
becomes
![1 = ab^0](https://tex.z-dn.net/?f=1%20%3D%20ab%5E0)
![1 = a](https://tex.z-dn.net/?f=1%20%3D%20a)
![a =1](https://tex.z-dn.net/?f=a%20%3D1)
For: ![x = 1\ when\ y = 3](https://tex.z-dn.net/?f=x%20%3D%201%5C%20when%5C%20y%20%3D%203)
becomes
![3 = a*b^1](https://tex.z-dn.net/?f=3%20%3D%20a%2Ab%5E1)
![3 = a*b](https://tex.z-dn.net/?f=3%20%3D%20a%2Ab)
Substitute 1 for a
![3 = 1*b](https://tex.z-dn.net/?f=3%20%3D%201%2Ab)
![3 = b](https://tex.z-dn.net/?f=3%20%3D%20b)
![b = 3](https://tex.z-dn.net/?f=b%20%3D%203)
becomes
![y = 1*3^x](https://tex.z-dn.net/?f=y%20%3D%201%2A3%5Ex)
![y = 3^x](https://tex.z-dn.net/?f=y%20%3D%203%5Ex)
Replace y with f(x)
![f(x) = 3^x](https://tex.z-dn.net/?f=f%28x%29%20%3D%203%5Ex)
Solving (b): Equation of Function B
A quadratic equation is represented as:
![y = ax^2 + bx + c](https://tex.z-dn.net/?f=y%20%3D%20ax%5E2%20%2B%20bx%20%2B%20c)
From the table of function B,
![x = 3\ when\ y =4](https://tex.z-dn.net/?f=x%20%3D%203%5C%20when%5C%20y%20%3D4)
![x = 5\ when\ y =20](https://tex.z-dn.net/?f=x%20%3D%205%5C%20when%5C%20y%20%3D20)
![x = 6\ when\ y =31](https://tex.z-dn.net/?f=x%20%3D%206%5C%20when%5C%20y%20%3D31)
For: ![x = 3\ when\ y =4](https://tex.z-dn.net/?f=x%20%3D%203%5C%20when%5C%20y%20%3D4)
becomes
![4 = a*3^2 + b*3 + c](https://tex.z-dn.net/?f=4%20%3D%20a%2A3%5E2%20%2B%20b%2A3%20%2B%20c)
![4 = a*9 + 3b + c](https://tex.z-dn.net/?f=4%20%3D%20a%2A9%20%2B%203b%20%2B%20c)
![4 = 9a + 3b + c](https://tex.z-dn.net/?f=4%20%3D%209a%20%2B%203b%20%2B%20c)
For ![x = 5\ when\ y =20](https://tex.z-dn.net/?f=x%20%3D%205%5C%20when%5C%20y%20%3D20)
becomes
![20 = a*5^2 + b*5 + c](https://tex.z-dn.net/?f=20%20%3D%20a%2A5%5E2%20%2B%20b%2A5%20%2B%20c)
![20 = a*25 + b*5 + c](https://tex.z-dn.net/?f=20%20%3D%20a%2A25%20%2B%20b%2A5%20%2B%20c)
![20 = 25a + 5b + c](https://tex.z-dn.net/?f=20%20%3D%2025a%20%2B%205b%20%2B%20c)
For ![x = 6\ when\ y =31](https://tex.z-dn.net/?f=x%20%3D%206%5C%20when%5C%20y%20%3D31)
becomes
![31 = a*6^2 + b*6 + c](https://tex.z-dn.net/?f=31%20%3D%20a%2A6%5E2%20%2B%20b%2A6%20%2B%20c)
![31 = a*36 + b*6 + c](https://tex.z-dn.net/?f=31%20%3D%20a%2A36%20%2B%20b%2A6%20%2B%20c)
![31 = 36a + 6b + c](https://tex.z-dn.net/?f=31%20%3D%2036a%20%2B%206b%20%2B%20c)
So, we solve for a, b and c in:
![4 = 9a + 3b + c](https://tex.z-dn.net/?f=4%20%3D%209a%20%2B%203b%20%2B%20c)
![20 = 25a + 5b + c](https://tex.z-dn.net/?f=20%20%3D%2025a%20%2B%205b%20%2B%20c)
![31 = 36a + 6b + c](https://tex.z-dn.net/?f=31%20%3D%2036a%20%2B%206b%20%2B%20c)
Make c the subject in ![4 = 9a + 3b + c](https://tex.z-dn.net/?f=4%20%3D%209a%20%2B%203b%20%2B%20c)
![c = 4 - 9a - 3b](https://tex.z-dn.net/?f=c%20%3D%204%20-%209a%20-%203b)
Substitute
in
and ![31 = 36a + 6b + c](https://tex.z-dn.net/?f=31%20%3D%2036a%20%2B%206b%20%2B%20c)
becomes
![20 = 25a + 5b + 4-9a-3b](https://tex.z-dn.net/?f=20%20%3D%2025a%20%2B%205b%20%2B%204-9a-3b)
Collect Like Terms
![-4+20 = 25a -9a+ 5b -3b](https://tex.z-dn.net/?f=-4%2B20%20%3D%2025a%20-9a%2B%205b%20-3b)
![16 = 16a+ 2b](https://tex.z-dn.net/?f=16%20%3D%2016a%2B%202b)
Divide through by 2
![8 = 8a + b](https://tex.z-dn.net/?f=8%20%3D%208a%20%2B%20b)
![c = 4 - 9a - 3b](https://tex.z-dn.net/?f=c%20%3D%204%20-%209a%20-%203b)
becomes
![31 = 36a + 6b + 4 - 9a - 3b](https://tex.z-dn.net/?f=31%20%3D%2036a%20%2B%206b%20%2B%204%20-%209a%20-%203b)
Collect Like Terms
![-4+31 = 36a - 9a+ 6b - 3b](https://tex.z-dn.net/?f=-4%2B31%20%3D%2036a%20-%209a%2B%206b%20%20-%203b)
![27 = 27a+ 3b](https://tex.z-dn.net/?f=27%20%3D%2027a%2B%203b)
Divide through by 3
![9 = 9a + b](https://tex.z-dn.net/?f=9%20%3D%209a%20%2B%20b)
Solve for a and b in:
and ![9 = 9a + b](https://tex.z-dn.net/?f=9%20%3D%209a%20%2B%20b)
Subtract both equations:
![8 - 9 = 8a - 9a + b - b](https://tex.z-dn.net/?f=8%20-%209%20%3D%208a%20-%209a%20%2B%20b%20-%20b)
![8 - 9 = 8a - 9a](https://tex.z-dn.net/?f=8%20-%209%20%3D%208a%20-%209a)
![-1 = -a](https://tex.z-dn.net/?f=-1%20%3D%20-a)
Divide both sides by -1
![1 = a](https://tex.z-dn.net/?f=1%20%3D%20a)
![a = 1](https://tex.z-dn.net/?f=a%20%3D%201)
Substitute 1 for a in ![9 = 9a + b](https://tex.z-dn.net/?f=9%20%3D%209a%20%2B%20b)
![9 = 9*1 + b](https://tex.z-dn.net/?f=9%20%3D%209%2A1%20%2B%20b)
![9 = 9 +b](https://tex.z-dn.net/?f=9%20%3D%209%20%2Bb)
Subtract 9 from both sides
![9-9=9-9+b](https://tex.z-dn.net/?f=9-9%3D9-9%2Bb)
![0=b](https://tex.z-dn.net/?f=0%3Db)
![b = 0](https://tex.z-dn.net/?f=b%20%3D%200)
Substitute
and
in ![c = 4 - 9a - 3b](https://tex.z-dn.net/?f=c%20%3D%204%20-%209a%20-%203b)
![c = 4 - 9*1-3*0](https://tex.z-dn.net/?f=c%20%3D%204%20-%209%2A1-3%2A0)
![c = 4 - 9-0](https://tex.z-dn.net/?f=c%20%3D%204%20-%209-0)
![c = -5](https://tex.z-dn.net/?f=c%20%3D%20-5)
So, the equation is:
![y = ax^2 + bx + c](https://tex.z-dn.net/?f=y%20%3D%20ax%5E2%20%2B%20bx%20%2B%20c)
![y=1*x^2 +0*x-5](https://tex.z-dn.net/?f=y%3D1%2Ax%5E2%20%2B0%2Ax-5)
![y=x^2 -5](https://tex.z-dn.net/?f=y%3Dx%5E2%20-5)
Replace y with f(x)
![f(x) = x^2 - 5](https://tex.z-dn.net/?f=f%28x%29%20%3D%20x%5E2%20-%205)
Solving (c): Equation of Function C
This is calculated using:
![f(x) =a + (x -1)d](https://tex.z-dn.net/?f=f%28x%29%20%3Da%20%2B%20%28x%20-1%29d)
Where
-- the first term
d = the difference between successive terms
![d = 30 -12 = 48-30 = 66 -48](https://tex.z-dn.net/?f=d%20%3D%2030%20-12%20%3D%2048-30%20%3D%2066%20-48)
![d =18](https://tex.z-dn.net/?f=d%20%3D18)
So, we have:
![f(x) =a + (x -1)d](https://tex.z-dn.net/?f=f%28x%29%20%3Da%20%2B%20%28x%20-1%29d)
![f(x) = 12 + (x - 1)*18](https://tex.z-dn.net/?f=f%28x%29%20%3D%2012%20%2B%20%28x%20-%201%29%2A18)
Open bracket
![f(x) = 12 + 18x - 18](https://tex.z-dn.net/?f=f%28x%29%20%3D%2012%20%2B%2018x%20-%2018)
Collect Like Terms
![f(x) = 18x - 18+12](https://tex.z-dn.net/?f=f%28x%29%20%3D%2018x%20-%2018%2B12)
![f(x) = 18x -6](https://tex.z-dn.net/?f=f%28x%29%20%3D%2018x%20-6)