Answer:
8 correct, 6 wrong : 14 problems tried!
Step-by-step explanation:
If she gets 8 points by every question correctly answered and she got 13 points in total, she must have answered at least two questions (if she answers only 1 she gets at maximum 8 points, not reaching 13 never).
So lets try to find the solution.
If she answered 2 and mistaken 1 she would get:
2*8 - 1*5 = 16 - 5 = 11 -> So this is not correct.
If she answered 3 correct she would get 24 points, with 2 mistaken answers she would have:
8*3 - 5*2 = 24 -10 = 14
We need to see something important in this patterns:
As the wrong questions always subtract a multiple of 5, and we need a result of 13, we CAN'T have an even number of wrong questions, because this would imply a subtract of numbers like 10, 20, 30, etc; and as the correct answers only give us even numbers (8, 16, 32, 64, etc), the result of subtracting 2 even numbers would never be 13. And as we will be subtracting a number with a 5 in the units, the points for correct answers MUST have an 8 in the units, as 8-5=13.
So, lets go to the first posible number that ends in 8 and is multiple of 8 and greater than 16. This is 48. 48 = 6*8, this is, lets think about 6 correct answers that sum 48 points.
We now need to subtract a number to 48 that gives us 13. Which is?
48 - x = 13 <----> x = 35
So, we need a number of incorrect answers that sum 35. As every wrong answer sums 5 points, we need 7 wring answers (7*5 = 35):
8*6 - 5*7 = 48 - 35 = 13 points!!
There were 14 problems tried to solve
The steps to convert 23/4 to a decimal are shown below
Answer:
23/4 = 5.75
Step-by-step explanation:
HELP ASAP 100PTS PART A AND PART B
DONT COPY OTHERS I CAN TELL AND REPORT YOU
A scientist is studying the growth of a particular species of plant. He writes the following equation to show the height of the plant f(n), in cm, after n days:
f(n) = 10(1.02)n
Part A: When the scientist concluded his study, the height of the plant was approximately 11.04 cm. What is a reasonable domain to plot the growth function?
Part B: What is the average rate of change of the function f(n) from n = 1 to n = 5, and what does it represent?
Answer:
Part A) The reasonable domain to plot the growth function is the interval [0,5]
Part B) The average rate of change is [tex]0.21\ \frac{cm}{day}[/tex]
see the explanation
Step-by-step explanation:
Part A)
Let
f(n) -----> the height of the plant in cm
n ----> the number of days
we have
[tex]f(n)=10(1.02)^n[/tex]
This is a exponential function of the form
[tex]f(x)=a(b)^x[/tex]
where
a is the initial value
b is the base
r is the rate of growth
b=(1+r)
In this problem we have
[tex]a=10\ cm[/tex] ----> initial value or y-intercept
[tex]b=1.02\\r=b-1=1.02-1=0.02\\r=2\%[/tex]
For f(n)=11.04 cm
Find the value of n
substitute in the exponential function
[tex]11.04=10(1.02)^n\\11.04/10=(1.02)^n\\1.104=(1.02)^n[/tex]
Apply log both sides
[tex]log(1.104)=(n)log(1.02)\\n=log(1.104)/log(1.02)\\n=5\ days[/tex]
so
The reasonable domain to plot the growth function is the interval -----> [0,5]
[tex]0 \leq x \leq 5[/tex]
Part B) What is the average rate of change of the function f(n) from n = 1 to n = 5, and what does it represent?
the average rate of change is equal to
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
In this problem we have
[tex]f(a)=f(1)=10(1.02)^1=10.2\ cm f(b)=f(5)=10(1.02)^5=11.04\ cm\\a=1\\b=5\\[/tex]
Substitute
[tex]\frac{11.04-10.2}{5-1}=0.21\ \frac{cm}{day}[/tex]
The average rate of change is the change of the function values (output values) divided by the change of the input values.
That represent ----> The plant grew an average of 0.21 cm per day during that time interval
"Part A) The reasonable domain to plot the growth function is the interval [0,5]
Part B) The average rate of change is
see the explanation
Step-by-step explanation:
Part A)
Let
f(n) -----> the height of the plant in cm
n ----> the number of days
we have
This is a exponential function of the form
where
a is the initial value
b is the base
r is the rate of growth
b=(1+r)
In this problem we have
----> initial value or y-intercept
For f(n)=11.04 cm
Find the value of n
substitute in the exponential function
Apply log both sides
so
The reasonable domain to plot the growth function is the interval -----> [0,5]
Part B) What is the average rate of change of the function f(n) from n = 1 to n = 5, and what does it represent?
the average rate of change is equal to
In this problem we have
Substitute
The average rate of change is the change of the function values (output values) divided by the change of the input values.
That represent ----> The plant grew an average of 0.21 cm per day during that time interval"quoted from
"calculista"
y=x+5 y=3x solving systems by substitution
Answer:
x=5/2, y=15/2. (5/2, 15/2).
Step-by-step explanation:
y=x+5
y=3x
---------
x+5=3x
5=3x-x
5=2x
x=5/2
y=3(5/2)=15/2
Four times a number added to 8 times the number equals 48. Find the number
Answer:
4*6+8*6=48
Step-by-step explanation:
Answer:
The number is 4.
Step-by-step explanation:
4x+8x=48
12x=48
x=48/12
x=4
Question 15 (2.5 points)
Which ordered pair could replace the missing value and create a
function?
{(8,5), (2, 3), (1,6), (7,4), _?_}
O (3, 6)
(2,0)
(7,9)
(1,3)
(3, 6) can replace the missing value and create a function
Step-by-step explanation:
Given relation is:
{(8,5), (2, 3), (1,6), (7,4), _?_}
In order for a relation to be a function, the first condition is that there should be no repetition in domain of the function i.e. same input cannot map to multiple outputs.
In the form of ordered pairs, the first element of each ordered pair represents the elements of domain set
So,
From all the option given, only (3,6) is suitable to be put in the blank space as it will create no repetition in the domain while other ordered pairs will cause repetition.
Hence,
(3, 6) can replace the missing value and create a function
Keywords: Relations, functions
Learn more about functions at::
brainly.com/question/10940255brainly.com/question/10941043#LearnwithBrainly
Incline mats, or triangle mats, are offered with different levels of incline to help gymnasts learn basic moves. As the name may suggest, two sides of the mat are right triangles. If the height of the mat is 28 inches shorter than the length of the mat and the hypotenuse is 8 inches longer than the length of the mat, what is the length of the mat?
Answer:
The length of the mat is 60 in.
Step-by-step explanation:
Given :
Mats are inclined to form a triangle.
two sides of the mat are right triangles.
Hence the triangle formed is right angled triangle.
Let the length be x.
Now,The height of the mat is 28 inches shorter than the length of the mat.
Height of mat = x - 28
Also, the hypotenuse is 8 inches longer than the length of the mat.
Hypotenuse = x + 8
Hence by using Pythagoras theorem we get ,
[tex]Hypotenuse^2= lenght^2+height^2\\[/tex]
[tex]x^2+(x-28)^2=(x+8)^2\\x^2+x^2-56x+784=x^2+16x+64\\x^2-72x+720=0\\x^2-60x-12x+720 = 0\\x(x-60)-12(x-60)=0\\(x-12)(x-60) = 0\\x-12=0\\x=12\\x-60=0\\x=60[/tex]
Now we get 2 values of length 12 and 60.
But height is 28 in less than length.
And when we take length value as 12 the height will be negative hence it can't be true.
Hence the Length of mat = 60 in.
Garth has a summer job and earns $9.32 per hour. One week, he works
16 3/4 hours. He deposits $150 in a bank and decides to use the rest of the money to buy raffle tickets. Each raffle ticket costs $0.50. How many raffle tickets can Garth buy?
Answer:
12.22
Step-by-step explanation:
I don't know if 12.22 is an answer for you but if it's not I would round to 12. What you do is multiply 9.32 by 16 3/4 which gives you 156.11. Take 156.11 and subtract 150 since Garth is putting that in the bank which leaves you with 6.11. Lastly you will divide 6.11 by .5 which will give you 12.22. So Garth can buy 12 raffle tickets.
Answer:
Garth can buy 12 raffle tickets.
Step-by-step explanation:
This is because when you multiply 9.32 with 16, it is 149.12.
Then, each quarter an hour, or 15 minutes, he earns 2.33 dollars.
Multiply by 3 and you get 6.99.
Add 6.99 with 149.12 and you get 156.11
Get rid of 150$ and you have 6.11
Each dollar you can get 2 raffle tickets.
So 6 dollars or 6, multiplied by 2 is 12.
Hope this helps you!
P.S If I may, can I please have brainliest, I would greatly appreciate it.
Find the original price if the sale price of the cell phone is $205.50
Answer:
$293.6
Step-by-step explanation:
Here is the complete question: A cell phone is on sale for 30% off. Find the original price if the sale price of the cell phone is $205.50.
Given: Sale price of cell phone is $205.50
Discount= 30%
As 30% discount is given on original price or we can say 70% of original price is $205.50.
∴ Let the original price be x.
⇒ [tex]\frac{70}{100} \times x= 205.50[/tex]
Now, cross multiplying both side.
⇒ [tex]x= \frac{100}{70} \times 205.5[/tex]
∴ x= $293.6
The original price of cell phone is $293.6.
John wrote that 5 + 5 = 10. Then wrote that 5 + 5 + n = 10 + n. Are the equations John wrote equivalent? Explain.
Equation 5 + 5 = 10 and 5 + 5 + n = 10 + n are equivalent equation
Solution:Given that
John wrote that 5 + 5 = 10 ------ (1)
Then wrote that 5 + 5 + n = 10 + n ------ (2)
Need to determine are the equations written by John are equivalent.
First we need to keep in mind that whenever we apply same operation like addition, subtraction, multiplication and division on both the sides of equation that is left hand side and right hand side, we get the equivalent equation.
As in the second equation John added same value that is n on both sides of equation, we can say that equation with n is equivalent to the previous equation without n
Other way is let’s solve equation (2) and see if we can get equation (1)
5 + 5 + n = 10 + n
On subtracting both the sides with n we get,
5 + 5 + n – n = 10 + n – n
=> 5 + 5 = 10 which is same as equation (1)
Hence we can conclude that equation 5 + 5 = 10 and 5 + 5 + n = 10 + n are equivalent equation.
Final answer:
The equations 5 + 5 = 10 and 5 + 5 + n = 10 + n are equivalent because adding the same number 'n' to both sides of an equation does not change the original equality.
Explanation:
Yes, the equations that John wrote are equivalent. The first equation, 5 + 5 = 10, establishes that the sum of five plus five equals ten. The second equation, 5 + 5 + n = 10 + n, simply adds n to both sides of the first equation. This does not change the equality because, according to the properties of equality, if you add the same amount to both sides of an equal sign, the two sides remain equal. This can also be seen as an application of the commutative property of addition which states that numbers can be added in any order without changing the sum, as in A + B = B + A. Therefore, the original sum of 5 + 5 on the left side remains 10 when n is added to both sides, showing that 5 + 5 + n is indeed equal to 10 + n.
Determine whether the ratio are equivalent
18 trucks and 4 cars
21 trucks and 6 cars
These two ratios are not equivalent, as 18 trucks and 4 cars simplifies to a ratio of 9:2, while 21 trucks and 6cars simplifoes down to a ratio of 7:2. Obviously, there is a difference between 9:2 and 7:2, so they are not equivalent.
4. A local bakery sold 60 loaves of bread in one day. If 65%
of these were sold in the afternoon, how many loaves were
sold in the afternoon?
Answer: 39 loaves were sold in the afternoon
Step-by-step explanation: So basically what you do here is divide 60 by 100. That makes 0.6, 0.6 equals 1%. (60 equals 100% and that why you divide by 100) Now, you multiply 0.6 by 65. the answer is 39. 65% of the bread is 39 loaves. So 39 loaves were sold in the afternoon.
Have an amazing day! :)
Answer:
60 x 65% = 39
So 39 were sold in the afternoon
Step-by-step explanation:
Number sentence same sum as 50+6=56
Answer:
The sum of 50 and 6 is the total of 56
Answer:
Fifty plus six equals fifty-six.
Rewrite the expression using distributive property : 30x + 6
Answer:
This cannot be done, but it can be factored as: 6(5x + 1)
Step-by-step explanation:
This expression cannot be distributed any further.
The distributive property is used when multiplying polynomials (multiplying one or more terms by two or more terms). In which case, each term in multiplied by each of the terms in the bracket, for example: .
5(x + 2) = 5x + 10
We can factor this expression however to go the opposite direction:
30x + 6
Since 30 and 6 are both divisible by 6, we can factor it out of each term.
Divide 30x by 6 and divide 6 by 6.
6(5x + 1)
Shauna is 10 inches shorter than Ryan. Together their heights total 140 inches. How tall is each person?
Answer:
Ryan: 75
Shauna: 65
Step-by-step explanation:
x = ryan's height
x - 10 = shauna's height
x + (x - 10) = 140
2x - 10 = 140
2x = 150
x = 75
Shauna is 65 inches tall and Ryan is 75 inches tall.
Let the height of:
Shauna be represented with s
Ryan be represented with r.
Sum of their heights : s + r = 140
The equation that represents Shauna's height : r - 10
Substitute for Shauna's height in the first equation:
r - 10 + r = 140
Solve for r
2r = 150
r = 75 inches
Substitute for r in the first equation
75 + s = 140
s = 140 - 75
s = 65 inches
To learn more, please check: brainly.com/question/23589883
What symbol would you use to write an algebraic expression for "three divided by a number?"
A. +
B. −
C. ×
D. ÷
Answer:
D: is the answer
Step-by-step explanation:
A. + add
B. − subtract
C. × multiply
D. ÷ divide (can also be written with a "/") as in 3/2 vs 3÷ 2
The symbol used to write an algebraic expression for "three divided by a number" is the division symbol, ÷. We write this based off the description as '3 ÷ n' or '3/n' in fractional form.
Explanation:To write an algebraic expression for "three divided by a number," you would use the division symbol which is represented as ÷. So, if our unknown number is represented by the letter 'n', the algebraic expression would be written as "3 ÷ n" or "3/n" in fractional form.
In an algebraic expression, each symbol represents a specific mathematical action. The '+' symbol is for addition, '-' is for subtraction, 'x' is for multiplication, and '÷' is for division. In this case, since the problem specifies division, the correct symbol to use would be '÷'.
Learn more about Algebraic expressions here:https://brainly.com/question/34192827
#SPJ11
1+9i and 5-3i midpoint
Answer:6i-6
Step-by-step explanation:
9i-3i=6i
1+5=6
Chris's new car gets 42 miles per gallon. What is the equation that represents y, the total miles driven on x gallons of gas? x = 42 + y y = 42 + x y = 42x x = 42y
Answer:
y = 42x
Step-by-step explanation:
Answer:
The answer is y=42x
Helppp me pls I can’t figure this out
Answer:
A=F
Step-by-step explanation:
It's the congruency
The manager of a movie theater found that Saturdays sales were $3675. He knew that a total of 650 tickets were sold on saturday. Adult tickets cost $7.50, and children tickets cost $4.50. How many of each kind of ticket were sold?
Answer:
Adults= 250 tickets
Children= 400 tickets
Step-by-step explanation:
Answer
250 adult tickets were sold and 400 children tickets were sold
Step by Step Explanation:
Given
Saturday Sales: $3675
Total tickets: 650
Cost of adult tickets = $7.50
Cost of children tickets = $4.50
Let A represent the adult tickets and C represent the children tickets,
if there's a total of 650 tickets, then
A + C = 650
Also,
if an adult ticket cost $7.50 and a child ticket cost $4.50 then
7.5A + 4.5C = 3675
From these, we have a simultaneous equation
A + C = 650 ------- (1)
7.5A + 4.5C = 3675 ----------(2)
Make A the subject of formula in (1)
A + C = 650 becomes
A = 650 - C
Substitute 650 - C for A in (2), we have
7.5(650 - C) + 4.5C = 3675
Open the bracket
4875 - 7.5C + 4.5C = 3675
4875 - 3C = 3675
Collect like terms
-3C = 3675 - 4875
-3C = -1200
Divide through by -3
[tex]\frac{-3C}{-3} = \frac{-1200}{-3}[/tex]
C = 400
Recall that
A = 650 - C
So, A = 650 - 400
A = 250
Hence, 250 adult tickets were sold and 400 children tickets were sold
Find the values of x and y that make these triangles congruent by the HL Theorem.
Answer:
x = 2y
x + 4 = 3y + 1
2y + 4 = 3y + 1
y = 3, x = 6
a first number plus twice a second number is 7 twice the first number plus the second totals 29 find the numbers
Final answer:
The student's question involving a system of equations can be solved to find that the two numbers are 17 and -5. By setting up a system of equations based on the given conditions and solving it using the elimination method, we obtain the values for the two unknown numbers.
Explanation:
System of Equations to Find Two Numbers
Let's define the first number as x and the second number as y. The problem states that x plus twice y equals 7 and twice x plus y equals 29. These statements can be turned into a system of linear equations:
x + 2y = 7
2x + y = 29
Using the substitution or elimination method, we can solve these equations for x and y. First, multiply the first equation by 2 to align the coefficients of x:
(2)(x) + (2)(2y) = (2)(7)
The equations now become:
2x + 4y = 14
2x + y = 29
Subtracting the second equation from the first gives us:
3y = -15
Divide both sides of this new equation by 3 to get the value of y:
y = -5
Now that we have a value for y, substitute it back into one of the original equations to find x:
x + 2(-5) = 7
x - 10 = 7
x = 17
The two numbers that solve the system are x = 17 and y = -5.
Please answer this correctly
Is the answer
5:15pm
6:03am
2:15pm
7:03am
Answer:
2:15 PM
Step-by-step explanation:
When the plane arrives in Seattle, the time in eastern time period would be 5:15 PM. From eastern to pacific, the time goes back 3 hours. 5:15 - 3 hours is 2:15. Since the time is still in the afternoon, it is still PM.
Answer:
2:15pm
Step-by-step explanation:
1) Take 1:09pm and add 4 hours and 6 mins to the time
2) 1 hour and 9 minutes + 4 hours and 6 minutes = 5:15pm (in eastern time)
3) Subtract 3 hours from 5 hours and 15 minutes. This equals 2:15pm
This would be the answer because of the time zone change.
Cameron is making pumpkin bread. The recipe calls for 4 3/4 cups of flour. She has 2 2/3 cups. How much more flour does she need?
Answer:
25/12 or 2 1/12
Step-by-step explanation:
4 3/4=19/4
2 2/3=8/3
19/4-8/3=57/12-32/12=25/12
To convert the TUU UI
1
1.
What are numbers when Rs 880 is divided in to the ratio of 1 by 5 is to 1 by 6
Answer:
The ratio of 1 by 5 is to 1 by 6 is Rs 176 : Rs 146.67
Step-by-step explanation:
The given amount here = Rs 880
Now let us assume the 1 by 5 of Rs 880 = m
and assume 1 by 6 of the amount Rs 880 =n
To Find m : n
Now, [tex]\frac{1}{5} \times 880 = m\\\implies m =176[/tex]
or, 1 by 5 = 176
Similarly: [tex]\frac{1}{6} \times 880 = n\\\implies n =146.6666[/tex]
or, 1 by 6 = 146.67
⇒ m : n = 176 : 146.67
Hence, the ratio of 1 by 5 is to 1 by 6 = Rs 176 : Rs 146.67
Write an expression to describe the sequence below. Use n to represent the position of a term in the sequence, where n = 1 for the first term. 9, 10, 11, 12, ...
Answer:
[tex]T_n= 9+(n-1)[/tex]
Step-by-step explanation:
The Given sequence is 9, 10, 11, 12
We need to find the expression to describe the sequence.
Let [tex]T_n[/tex] be the [tex]n^{th}[/tex] term of the sequence.
Let n represent the position of the term.
Let a be the first term in the sequence.
and d be the common difference between the sequence
Hence the expression to find the above sequence is given below;
[tex]T_n= a+(n-1)d[/tex]
when n=1 d= 1 a = 9
[tex]T_1 = 9+(1-1)1 = 9 + 0 = 9[/tex]
when n=2 d= 1 a = 9
[tex]T_2 = 9+(2-1)1 = 9 + 1 = 10[/tex]
when n=3 d= 1 a = 9
[tex]T_3 = 9+(3-1)1 = 9 + 2 = 11[/tex]
when n=3 d= 1 a = 9
[tex]T_4 = 9+(4-1)1 = 9 + 3 = 12[/tex]
Hence the expression is [tex]T_n= 9+(n-1)[/tex]
The expression to describe the sequence 9, 10, 11, 12, ... is 8 + n, with n representing the position of the term in the sequence.
The sequence given is 9, 10, 11, 12, ..., which is an arithmetic sequence where each term increases by 1 from the previous term. To write an expression that represents the nth term of this sequence using n to represent the position of the term (with n = 1 for the first term), we need to find a formula that calculates the value of each term based on its position.
The first term of the sequence is 9 when n = 1. The second term is 9 + 1, and the third term is 9 + 2, and so on. Generalizing this, the nth term can be written as the first term value (9) plus the number of terms after the first one, which is (n - 1), since for the first term, n - 1 equals 0. Therefore, the final expression is:
9 + (n - 1)
We can simplify this expression as: 8 + n
This expression will give us the value of each term in the sequence based on its position n.
a flag pole is 30 feet tall a bug crawls 14 feet up the pole then it crawls another4 feet up the pole how much firther must the bug crawl to get to the top
Answer:
12 more feet
Step-by-step explanation:
Reason why is because if you add 14 and 4 you get 18 then you add 18 with 12 and you get 30. (hope this helps)
A number added to itself equals 5 less than the number
Answer:
The number is -5.
Step-by-step explanation:
x+x=x-5
2x=x-5
x-2x=5
-x=5
x=-5
Inverse for h(x)=2x-4/3
Answer:
[tex]y=\frac{x}{2}+\frac{2}{3}[/tex]
Step-by-step explanation:
The inverse function [tex]f^{-1}[/tex] of a function [tex]f[/tex] must meet that if [tex]f(a)=b[/tex], then [tex]f^{-1}(b)=a[/tex]. To find the inverse function one can clear out x from the initial equation, and once obtained an expression x=f(y), replace x by y, where y=f(x).In this case, [tex]y=h(x)=2x-\frac{4}{3}[/tex].To find the inverse function, we clear out x, as follows: [tex]y=2x-\frac{4}{3}[/tex]⇒[tex]y+\frac{4}{3} =2x[/tex]⇒[tex]x=\frac{y}{2}+\frac{2}{3}[/tex].Now that we have clear out the value of x as a function of y, we just have to replace x by y: [tex]y=\frac{x}{2}+\frac{2}{3}[/tex], which is the inverse function we have been looking for.To corroborate the function is correct, we can use the fact that [tex]f(a)=b[/tex], then [tex]f^{-1}(b)=a[/tex]. If we take x=1, in the first equation [tex]f(1)=2-\frac{4}{3} = \frac{2}{3}[/tex]. If now we replace b=2/3 in the inverse function we obtain [tex]f^{-1}(\frac{2}{3})=\frac{\frac{2}{3} }{2} +\frac{2}{3} =1[/tex]Delila has 4 coins. If Delila flips all the coins at once, how many outcomes are in the sample space?
Answer:0
Step-by-step explanation:
because once you flip all of them there all in the air and there flipped
Artemis took out a 30-year loan from her bank for $190,000 at an APR of
9.6%, compounded monthly. If her bank charges a prepayment fee of 6
months' interest on 80% of the balance, what prepayment fee would Artemis
be charged for paying off her loan 16 years early?
O
A. $5822.42
O
B. $7390.60
O C. $6182.58
O D. $7382.56
The prepayment fee of $6182.58 would be charged to Artemis for paying off her loan 16 years early.
Answer: Option C
Step-by-step explanation:
30 year loan at 9.6% interest yields.
Number of month = 30 (12) = 360 months
Annual percent interest of [tex]\frac{9.6 \%}{12}[/tex] = monthly percent interest of .8%
The formula for the present value of an ordinary annuity, as opposed to an annuity due, is as follows
[tex]P M T= \frac{P \times r}{1-(1+r)^{n}}[/tex]
With r and n adjusted for periodicity, where
P = the present value of an annuity stream
PMT = the dollar amount of each annuity payment
r = the interest rate (also known as the discount rate)
n = the number of periods in which payments will be made
[tex]P M T= \frac{190000 \times 0.008}{1-(1+0.008)^{-360}} = \frac{1520}{1-(1.008)^{-360}} = \frac{1520}{1-0.0567}=\frac{1520}{0.9432}[/tex]
PMT = $1611.50 per month
Her loan 16 year early. It means
[tex]\text { Worth of loan after } 14 \text { year } = 190000 \times(1.008)^{168} = 3.814 \times 190000=\$ 724641.16[/tex]
Worth of monthly payments for 14 year
[tex] = \frac{1611.50 \times\left\{(1.008)^{168}-1\right)}{0.008} = \frac{1611.50 \times(3.81-1)}{0.008} = \frac{4.534 .6}{0.008} = \$ 566825.15[/tex]
Amount still owed after 14 year = difference of the above two
=$724641.16 - $566825.18
=$157816.01
Prepayment fee = [tex](0.8 \times 157816.02) \times\left((1.008)^{6}-1\right)[/tex]
= 126252.82 (1.049-1) = 126252.82 (1.0489-1) = $6182.63