Answer:
A. The monthly payment is $202.85.
B. The total amount paid over the term of the loan is $36,513.60.
C. The percentage paid toward the principal is 54.77%, while the percentage paid for interest is 45.23%.
Step-by-step explanation:
A. Calculate the monthly payment.
This can be calculated using the formula for calculating the present value of an ordinary annuity as follows:
PV = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)
Where;
PV = Present value or principal or student loan = $20,000
P = Monthly payment = ?
r = Monthly rate = APR /12 = 9% / 12 = 0.09 / 12 = 0.0075
n = number of months = 15 * 12 = 180
Substituting the values into equation (1) and solve for P, we have:
$20,000 = P * ((1 - (1 / (1 + 0.0075))^180) / 0.0075)
$20,000 = P * 98.5934088350577
P = $20,000 / 98.5934088350577 = $202.85
Therefore, the monthly payment is $202.85.
B. Determine the total amount paid over the term of the loan.
Total amount paid = Monthly payment * Number of months = $202.85 * 180 = $36,513.60
Therefore, the total amount paid over the term of the loan is $36,513.60.
C. Of the total amount paid what percentage is paid toward the principal and what percentage is paid for interest.
Percentage paid toward the principal = Principal / Total amount paid = $20,000 / $36,513.60 = 0.5477, or 54.77%
Percentage paid for interest = 100% - Percentage paid toward the principal = 100% - 54.77% = 45.23%
Therefore, the percentage paid toward the principal is 54.77%, while the percentage paid for interest is 45.23%.
If the weight of 12 sheets of thick paper is 40 grams, how many sheets of the same paper would weigh 2500 grams
Answer:
750 is the answer..
Step-by-step explanation:
(12/40)*2500
Two complementary angles have measures 4x and x + 50. Find x.
Answer:
x =17
Step-by-step explanation:
Complementary angles add to 90
4x+ x+5 = 90
Combine like terms
5x+5 = 90
Subtract 5 from each side
5x+5-5 = 90-5
5x = 85
Divide by 5
5x/5 = 85/5
x =17
Answer my question please!! i will give brainlest!
Answer:
hello u so cool i admire you <3
What is
4/11
as a decimal?
2.75
0.364
0.4
0.36
Maybe y’all don’t find the -
answer i got u guys its 0.36
Answer:
0.36
Step-by-step explanation:
Convert the fraction to a decimal by dividing the numerator by the denominator.
Hope it is helpful...Answer:
Yes, you are correct! 0.36363636... is the answer. 0.364 would be closest.
Happy learning!
--Applepi101
The mean sustained wind velocity, v, can be determined by the equation v = 6.3 StartRoot 1013 minus p EndRoot, where p is the air pressure, in millibars, at the center of the hurricane. What is the approximate air pressure at the center of a hurricane when the mean sustained wind velocity is 64 meters per second? 103 millibars 194 millibars 363 millibars 910 millibars
Answer:
910 millibars
Step-by-step explanation:
According to the Question,
Given That, The mean sustained wind velocity equation [tex]v=6.3*\sqrt{1013-p}[/tex] And The mean sustained wind velocity is 64m/s (v=64) . where, p is the air pressure(in millibars).Now, the air pressure at the center of a hurricane when the mean sustained wind velocity is 64 m/s is
[tex]64=6.3*\sqrt{1013-p}\\\frac{64}{6.3} = \sqrt{1013-p}\\[/tex]
on squaring both sides we get,
(10.1587)² = 1012 - p ⇒ p = 908.80≈910millibar
p = 910millibars air pressure .
Answer: 910
Step-by-step explanation: Did the review and got it right
Any help on this please ?
Answer:
x=35
Step-by-step explanation:
because the angles are next to each other they are supplementary, which makes the total of the angle 180 degrees.
the equation would be:
180=x+14 +4x -9
add the like terms
180=5x =5
then subtract 5 from both sides
175=5x
then divide five from both sides
x=35
select the right answer
Answer:
Blurry po
Step-by-step explanation:
Pwede kunan nyu ulit
What is the height of the pyramid ???
Answers:
A: 7cm
B: 5cm
C: 14 cm
D: 10 cm
Given:
[tex]m\angle ACD=45^\circ[/tex]
Point B is the center of the base.
Each side of the base = 10 cm
To find:
The height of the pyramid.
Solution:
It is given that the measure of each side of the base is 10 cm. It means the base is square. The length of the diagonal of a square is:
[tex]d=a\sqrt{2}[/tex]
Where, a is the side length of the square.
Putting [tex]a=10[/tex] in the above formula, we get
[tex]d=10\sqrt{2}[/tex]
It is given that point B is the center of the base. It means point B bisect each diagonal of a base. So,
[tex]BC=\dfrac{d}{2}[/tex]
[tex]BC=\dfrac{10\sqrt{2}}{2}[/tex]
[tex]BC=5\sqrt{2}[/tex]
In a right angle triangle,
[tex]\tan \theta=\dfrac{Perpendicular}{Base}[/tex]
In triangle ABC,
[tex]\tan (45^\circ)=\dfrac{AB}{BC}[/tex]
[tex]1=\dfrac{h}{5\sqrt{2}}[/tex]
[tex]5\sqrt{2}=h[/tex]
[tex]7.0710678=h[/tex]
Round the value to the nearest integer.
[tex]h\approx 7[/tex]
The height of the pyramid is about 7 cm. Therefore, the correct option is A.
Determine the value of x in the diagram,
108°
72
1080
Answer:
72
Step-by-step explanation:
parallel sides= same angle.
also alternate angles theorem shows that if angles that alternate are the same. 72,108,72,108
Which is the most convenient placement of an isosceles triangle in the coordinate plane for finding the side lengths?
Answer:
The bottom left
Step-by-step explanation:
Find the value of f(-4)?
Answer:
Step-by-step explanation:
This question is asking you to find the value of y when x = -4. If you locate the x value of -4, y = -10 here. Therefore, f(-4) = -10 and in coordinate form, (-4, -10).
$690 is invested in an account earning 7% interest (APR),
compounded quarterly. Write a function showing the value of the
account after t years, where the annual growth rate can be found from
a constant in the function. Round all coefficients in the function to four
decimal places. Also, determine the percentage of growth per year
(APY), to the nearest hundredth of a percent.
Answer:
a
567 is the answer because of the 7percent
Help me plz I’m stuck!!! If a line passes through the points (2,2) and (4,5), the equation of the line is
Step-by-step explanation:
the answer is in the above image
Which word describes the slope of the line?
O Positive
O Negative
O Zero
O Undefined
Answer:
Option (1)
Step-by-step explanation:
Slope of a line is defined by the rule,
Slope = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]
Here, Rise and Run of the line are positive.
Therefore, sign of the slope of the line will be positive.
Option (1) will be the correct option.
What is the inverse fraction of f(x)=x/x-2
Answer:
[tex]inverse \ of \ f(x) : \frac{2x}{x-1}[/tex]
Step-by-step explanation:
[tex]y = \frac{x}{x-2}\\\\swap\ x\ and \ y\\\\x = \frac{y}{y-2}\\\\x(y -2) = y\\\\xy - 2x = y\\\\xy - y = 2x\\\\y(x-1)= 2x\\\\y = \frac{2x}{(x-1)}[/tex]
Step-by-step explanation:
Given two one-to-one functions f(x)f(x) and g(x)g(x) if
(f∘g)(x)=xAND(g∘f)(x)=x(f∘g)(x)=xAND(g∘f)(x)=x
then we say that f(x)f(x) and g(x)g(x) are inverses of each other. More specifically we will say that g(x)g(x) is the inverse of f(x)f(x) and
denote it by
g(x)=f−1(x)g(x)=f−1(x)
Likewise, we could also say that f(x)f(x) is the inverse of g(x)g(x) and denote it by
f(x)=g−1(x)
Given the function f(x)f(x) we want to find the inverse function, f−1(x)f−1(x).
First, replace f(x)f(x) with yy. This is done to make the rest of the process easier.
Replace every xx with a yy and replace every yy with an xx.
Solve the equation from Step 2 for yy. This is the step where mistakes are most often made so be careful with this step.
Replace yy with f−1(x)f−1(x). In other words, we’ve managed to find the inverse at this point!
Verify your work by checking that (f∘f−1)(x)=x(f∘f−1)(x)=x and (f−1∘f)(x)=x(f−1∘f)(x)=x are both true. This work can sometimes be messy making it easy to make mistakes so again be careful.
Explanation:
Setting y=f(x)
y=xx−2
this may be rearranged (intermediate steps shown) as follows
y(x−2)=x
x⋅y−2y=x
x⋅y−x=2y
x(y−1)=2y
x=2yy−1
This expression shows x in terms of y.
That is,
f−1(x)=2xx−1
Setting y=f(x)
y=xx−2
this may be rearranged (intermediate steps shown) as follows
y(x−2)=x
x⋅y−2y=x
x⋅y−x=2y
x(y−1)=2y
x=2yy−1
This expression shows x in terms of y.
That is, it is the inverse of function f(x).
That is,
f−1(x)=2xx−1
as required.
more help im dum lol
Answer:
32780
Step-by-step explanation:
Answer:
32,780
Step-by-step explanation:
It should be 30,000
PLEASE HELP!!! If the quadratic equation has the form y = ax 2and y = ax 2+ c, then their axis of symmetry must always be?
Answer:
axis of symmetry , x = 0
Step-by-step explanation:
For the quadratic equation of the form [tex]ax^2 + bx + c[/tex],
the axis of symmetry is the straight line [tex]x =- \frac{b}{2a}[/tex]
( i) Given equation y = ax² + 0x + 0
b = 0, therefore axis of symmetry is x = 0
( ii ) Second equation y = ax² + 0x + c
b = 0, therefore axis of symmetry is x = 0
can someone please help me with this i dont have much time left
Answer:
Step-by-step explanation:
sin A = opposite/hypotenuse
=5/13
cos A =adjacent/hypotenuse
=12/13
tan A =opposite/adjacent
=5/12
cosec A = hypotenuse/opposite
=13/5
sec A = hypotenuse/adjacent
=12/5
cot A = adjacent/opposite
=12/5
can i get the answer for this question would be verrryy much appreciated:)
Answer
The answer is EH= 50
Como se encuentra la mediana?
Answer:
Para encontrar la mediana: Organice los puntos de datos de menor a mayor. Si el número de puntos de datos es impar, la mediana es el punto de datos intermedio de la lista. Si el número de puntos de datos es par, la mediana es el promedio de los dos puntos de datos intermedios de la lista.
Step-by-step explanation:
que tenga un lindo día
A boy spends 3/8 of his journey in playing games on his mobile.Then 4/5 of the remaining time talking to his sister.If he has 5 min to complete his journey,what is the total time of the journey
Answer:
40 mins
Step-by-step explanation:
time spent talking to his sister = (1 - 3/8) x 4/5 =
5/8 x 4/5 = 1/2
total fraction of time spent playing games and talking to his sister :
[tex]\frac{3}{8} + \frac{1}{2}[/tex]
[tex]\frac{ 3 + 4}{8}[/tex] = [tex]\frac{7}{8}[/tex]
fraction of time remaining to complete the journey = 1 - 7/8 = 1/8
let t = total journey time
1/8 x t = 5
multiply both sides of the equation by 8
t = 5 x 8 = 40 minutes
Solve for xx. Round to the nearest tenth of a degree, if necessary.
Answer:
50.8Step-by-step explanation:
sin x = 6.2/8
sin x = 0.775
x = 50. 8
Bye , have a nice day ! :-)
Applying the sine ratio, sin ∅ = opposite/hypotenuse, the value of x, to the nearest tenth of a degree, is: 50.8°.
Hpw to Use the Sine Ratio?When solving a right triangle involving the opposite side and hypotenuse, the sine ratio can be used which is, sin ∅ = opposite/hypotenuse.
Apply the sine ratio to find x
sin x = opp/hyp = 6.2/8
x = sin^(-1)(6.2/8)
x = 50.8°
Learn more about the sine ratio on:
https://brainly.com/question/2920412
#SPJ2
A line has a slope of -4/5. Which ordered pairs could be points on a line that is perpendicular to this line?
Answer:
(5,4) & (8,-10)
Step-by-step explanation:
First step:
[tex]y=mx+b[/tex]
You can use any number you want for b (I used 4)
[tex]y=-\frac{4}{5} x+4[/tex]
Make x=0
[tex]y=-\frac{4}{5} (0)+4[/tex]
[tex]y=4[/tex]
Make y=0
[tex]0=-\frac{4}{5} x+4[/tex]
Subtract 4 from both sides
[tex]-4=-\frac{4}{5} x[/tex]
Divide both sides by [tex]-\frac{4}{5}[/tex]
[tex]x=5[/tex]
Second step:
In order to make a line perpendicular to another the slope of the second line will be the negative inverse of the first line. So [tex]m=-\frac{4}{5}[/tex] will be [tex]m=\frac{5}{4}[/tex] for the second line.
Then you just need to repeat the process in first step to get the intercepts. (Again I used a random number like -10 for b)
What is the y-intercept of the function f(x) = -4.2^x
Answer:
[tex](0,-1)[/tex]
Step-by-step explanation:
The y-intercept always occurs when [tex]x=0[/tex]. To find the y-value of the y-intercept, substitute [tex]x=0[/tex] into your equation:
Given [tex]f(x)=-4.2^x[/tex], when [tex]x=0[/tex]:
[tex]f(x)=-4.2^0,\\f(x)=-(1)=-1[/tex]
Recall that [tex]n^0=1[/tex] for [tex]n\in \mathbb{R}[/tex]Therefore, the y-intercept of this function is [tex](0, -1)[/tex].
I need help with angles in a triangle to find x
I need help with these. please :(
Answer:
[tex]a. \: \: x = {60}^{o} [/tex]
[tex]b. \: \: x = {24}^{o} [/tex]
Step-by-step explanation:
Hint :Sum of angles = 180°
Simplify :[tex]a. \: \: {x}^{o} + {40}^{o} + {80}^{o} = {180}^{o} [/tex]
[tex] {x}^{o} + {120}^{o} = {180}^{o} [/tex]
[tex] {x}^{o} = {180}^{o} - {120}^{o} [/tex]
[tex] {x}^{o} = {60}^{o} [/tex]
[tex]b. \: 96+(x+12)+2x=180[/tex]
[tex]x+108+2x=180[/tex]
[tex]3x+108=180[/tex]
[tex]3x=180−108[/tex]
[tex]3x=72[/tex]
[tex]x = \frac{72}{3} [/tex][tex]x = 24[/tex]
Hope it is helpful...A bag has 3 red marbles and 12 blue marbles. Half of the blue marbles are made of plastic. A marble is selected at random from the bag. What is the probability that it is a blue, plastic marble?
Answer: 2/5
Step-by-step explanation:
There are 15 total marbles in the bag. 12 are blue, with only 6 made from plastic. 6/15 reduced is 2/5
NEED HELP ASAP AS SOON AS POSSIBLE, WILL GIVE 69 POINTS
A city park commission received a donation of playground equipment from a parents' organization. The area of the playground needs to be 256 square yards for the children to use it safely. The playground will be rectangular.
The city will also put a fence around the playground. The perimeter, P, of the fence includes the gates. To save money, the city wants the least perimeter of fencing for the area of 256 square yards.
Jovana was trying to find a formula for that perimeter with one side 8 yards longer than the other side using the area. In which step did she make a mistake?
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
Step 6:
Step 7:
Explain her mistake. What is the correct formula?
Which of the following is equivalent to (2x^3)(7x^4)?
Answer:
A: (2 times 7)x^3 plus 4
Step-by-step explanation:
2 times 7 is 14 so 14 in the parentheses and then add 3 plus 4 equals 7.
14x^7.
make x the subject of n = jx + h
I'M SORRY GUYS I RLLY HATE MATHS
Answer:
x = (n-h)/j
Step-by-step explanation:
n = jx + h
Subtract h from each side
n-h = jx+h-h
n-h = jx
Divide by j
(n-h)/j = jx/j
(n-h)/j = x
Answer:
x = [tex]\frac{n-h}{j}[/tex]
Step-by-step explanation:
Given
n = jx + h ( subtract h from both sides )
n - h = jx ( isolate x by dividing both sides by j )
[tex]\frac{n-h}{j}[/tex] = x
Someone please ill mark you the brainliest! No cheating or else i’ll report you.
Answer:
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