Answer:
the average of this new list of numbers is 94
Step-by-step explanation:
Hello!
To answer this question we will assign a letter to each number for the first list and the second list of numbers, remembering that the last number of the first list is 80 and the last number of the second list is 96
for the first list
for the new list
To solve this problem consider the following
1.X is the average value of the second list
2. We will assign a Y value to the sum of the numbers a, b, c.
a + b + c = Y to create two new equations
for the first list
solving for Y
Y=(90)(4)-80=280
Y=280=a+b+c
for the second list
the average of this new list of numbers is 94
Part 1:
After payment of $300, remaining balance = $2,348.62 - $300 = $2,048.62.
Interest accrued is given by:
Had it been $600 was paid, remaining balance = $2,348.62 - $600 = $1748.62. Interest accrued is given by:
Difference in interest accrued = $14.94 - $12.75 = $2.19
Part 2:
The present value of an annuity is given by:
![PV= \frac{P\left[1-\left(1+ \frac{r}{12} \right)^{-12n}\right]}{ \frac{r}{12} }](https://tex.z-dn.net/?f=PV%3D%20%5Cfrac%7BP%5Cleft%5B1-%5Cleft%281%2B%20%5Cfrac%7Br%7D%7B12%7D%20%5Cright%29%5E%7B-12n%7D%5Cright%5D%7D%7B%20%5Cfrac%7Br%7D%7B12%7D%20%7D)
Where PV is the amount to be repaid, P is the equal monthly payment, r is the annual interest rate and n is the number of years.
Thus,
![2348.62= \frac{600\left[1-\left(1+ \frac{0.0875}{12}\right)^{-12n}\right]}{\frac{0.0875}{12}} \\ \\ \Rightarrow 1-(1+0.007292)^{-12n}= \frac{2348.62\times0.0875}{12\times600} =0.028542 \\ \\ \Rightarrow(1.007292)^{-12n}=1-0.028542=0.971458 \\ \\ \Rightarrow \log(1.007292)^{-12n}=\log0.971458 \\ \\ \Rightarrow-12n\log1.007292=\log0.971458 \\ \\ \Rightarrow-12n= \frac{\log0.971458}{\log1.007292} =-3.985559 \\ \\ \Rightarrow n= \frac{-3.985559}{-12} =0.332130](https://tex.z-dn.net/?f=2348.62%3D%20%5Cfrac%7B600%5Cleft%5B1-%5Cleft%281%2B%20%5Cfrac%7B0.0875%7D%7B12%7D%5Cright%29%5E%7B-12n%7D%5Cright%5D%7D%7B%5Cfrac%7B0.0875%7D%7B12%7D%7D%20%20%5C%5C%20%20%5C%5C%20%5CRightarrow%201-%281%2B0.007292%29%5E%7B-12n%7D%3D%20%5Cfrac%7B2348.62%5Ctimes0.0875%7D%7B12%5Ctimes600%7D%20%3D0.028542%20%5C%5C%20%20%5C%5C%20%5CRightarrow%281.007292%29%5E%7B-12n%7D%3D1-0.028542%3D0.971458%20%5C%5C%20%20%5C%5C%20%5CRightarrow%20%5Clog%281.007292%29%5E%7B-12n%7D%3D%5Clog0.971458%20%5C%5C%20%20%5C%5C%20%5CRightarrow-12n%5Clog1.007292%3D%5Clog0.971458%20%5C%5C%20%20%5C%5C%20%5CRightarrow-12n%3D%20%5Cfrac%7B%5Clog0.971458%7D%7B%5Clog1.007292%7D%20%3D-3.985559%20%5C%5C%20%20%5C%5C%20%5CRightarrow%20n%3D%20%5Cfrac%7B-3.985559%7D%7B-12%7D%20%3D0.332130)
Therefore, the number of months it will take to pay of the debt is 3.99 months which is approximately 4 months.
Answer:
Catron's error is
"She did not follow order of operations"
Step-by-step explanation:
Catron evaluates the expression (negative 9) (2 and two-fifths)
That expression can be written as below
Catron's error is
"She did not follow order of operations"
The corrected steps are
Step1: Given expression is
Step2: Convert mixed fraction into improper fraction
Step3: Multiplying the terms
Therefore solution
Given: <span>f(x) = log3 (x + 1), look for f^-1 (2)
We are looking for the inverse of a function. The inverse of the function can be obtained by switching the variables and obtaining the values of the new function, before substituting f(2). Using a calculator:
</span><span>f^-1 (2) = 8</span>
