Complete Question
Laura and martin obtain a 25 year 120,000 conventional mortgage at 8.5% on a house selling for 140,000 their monthly mortgage payment including principal and interest is 966 dollars
a) Determine the total amount they will pay for their house
b) How much of the cost will be interest?
c) How much of the first payment on the mortgage is applied to the principal?
Answer:
a) [tex]X=\$289800[/tex]
b) [tex]I=\$169800[/tex]
c) [tex]Y=\$116[/tex]
Step-by-step explanation:
From the question we are told that:
Time [tex]T=25years =>300 months[/tex]
Initial Mortgage [tex]N=140,000[/tex]
Mortgage [tex]N'=120,000[/tex]
Rate [tex]r=8.5\%=>0.085[/tex]
Monthly Mortgage payment P=\%966
a)
The total amount Payable X is mathematically given as
[tex]X=Monthly\ Mortgage\ payment*Number\ of\ months[/tex]
[tex]X=966*300[/tex]
[tex]X=\$289800[/tex]
b)
Generally the equation for Interest I is mathematically given by
[tex]Interest= Total\ amount\ Payable -Mortgage N'[/tex]
[tex]I=289800-120000[/tex]
[tex]I=\$169800[/tex]
c)
Generally the equation for Interest I is mathematically given by
[tex]I=Ptr[/tex]
Where
[tex]t= Month +.1month=>1/12[/tex]
Therefore
[tex]I=120000*1/12*0.085[/tex]
[tex]I=850[/tex]
Therefore the first payment on the mortgage is applied to the principal is
[tex]Y=\$966-850[/tex]
[tex]Y=\$116[/tex]
please find the result !
Answer:
[tex] \displaystyle - \frac{1}{2} [/tex]
Step-by-step explanation:
we would like to compute the following limit:
[tex] \displaystyle \lim _{x \to 0} \left( \frac{1}{ \ln(x + \sqrt{ {x}^{2} + 1} ) } - \frac{1}{ \ln(x + 1) } \right) [/tex]
if we substitute 0 directly we would end up with:
[tex] \displaystyle\frac{1}{0} - \frac{1}{0} [/tex]
which is an indeterminate form! therefore we need an alternate way to compute the limit to do so simplify the expression and that yields:
[tex] \displaystyle \lim _{x \to 0} \left( \frac{ \ln(x + 1) - \ln(x + \sqrt{ {x}^{2} + 1 } }{ \ln(x + \sqrt{ {x}^{2} + 1} ) \ln(x + 1) } \right) [/tex]
now notice that after simplifying we ended up with a rational expression in that case to compute the limit we can consider using L'hopital rule which states that
[tex] \rm \displaystyle \lim _{x \to c} \left( \frac{f(x)}{g(x)} \right) = \lim _{x \to c} \left( \frac{f'(x)}{g'(x)} \right) [/tex]
thus apply L'hopital rule which yields:
[tex] \displaystyle \lim _{x \to 0} \left( \frac{ \dfrac{d}{dx} \ln(x + 1) - \ln(x + \sqrt{ {x}^{2} + 1 } }{ \dfrac{d}{dx} \ln(x + \sqrt{ {x}^{2} + 1} ) \ln(x + 1) } \right) [/tex]
use difference and Product derivation rule to differentiate the numerator and the denominator respectively which yields:
[tex] \displaystyle \lim _{x \to 0} \left( \frac{ \frac{1}{x + 1} - \frac{1}{ \sqrt{x + 1} } }{ \frac{ \ln(x + 1)}{ \sqrt{ {x}^{2} + 1 } } + \frac{ \ln(x + \sqrt{x ^{2} + 1 } }{x + 1} } \right) [/tex]
simplify which yields:
[tex] \displaystyle \lim _{x \to 0} \left( \frac{ \sqrt{ {x}^{2} + 1 } - x - 1 }{ (x + 1)\ln(x + 1 ) + \sqrt{ {x}^{2} + 1} \ln( x + \sqrt{ {x }^{2} + 1} ) } \right) [/tex]
unfortunately! it's still an indeterminate form if we substitute 0 for x therefore apply L'hopital rule once again which yields:
[tex] \displaystyle \lim _{x \to 0} \left( \frac{ \dfrac{d}{dx} \sqrt{ {x}^{2} + 1 } - x - 1 }{ \dfrac{d}{dx} (x + 1)\ln(x + 1 ) + \sqrt{ {x}^{2} + 1} \ln( x + \sqrt{ {x }^{2} + 1} ) } \right) [/tex]
use difference and sum derivation rule to differentiate the numerator and the denominator respectively and that is yields:
[tex] \displaystyle \lim _{x \to 0} \left( \frac{ \frac{x}{ \sqrt{ {x}^{2} + 1 } } - 1}{ \ln(x + 1) + 2 + \frac{x \ln(x + \sqrt{ {x}^{2} + 1 } ) }{ \sqrt{ {x}^{2} + 1 } } } \right) [/tex]
thank god! now it's not an indeterminate form if we substitute 0 for x thus do so which yields:
[tex] \displaystyle \frac{ \frac{0}{ \sqrt{ {0}^{2} + 1 } } - 1}{ \ln(0 + 1) + 2 + \frac{0 \ln(0 + \sqrt{ {0}^{2} + 1 } ) }{ \sqrt{ {0}^{2} + 1 } } } [/tex]
simplify which yields:
[tex] \displaystyle - \frac{1}{2} [/tex]
finally, we are done!
9514 1404 393
Answer:
-1/2
Step-by-step explanation:
Evaluating the expression directly at x=0 gives ...
[tex]\dfrac{1}{\ln(\sqrt{1})}-\dfrac{1}{\ln(1)}=\dfrac{1}{0}-\dfrac{1}{0}\qquad\text{an indeterminate form}[/tex]
Using the linear approximations of the log and root functions, we can put this in a form that can be evaluated at x=0.
The approximations of interest are ...
[tex]\ln(x+1)\approx x\quad\text{for x near 0}\\\\\sqrt{x+1}\approx \dfrac{x}{2}+1\quad\text{for x near 0}[/tex]
__
Then as x nears zero, the limit we seek is reasonably approximated by the limit ...
[tex]\displaystyle\lim_{x\to0}\left(\dfrac{1}{x+\dfrac{x^2}{2}}-\dfrac{1}{x}\right)=\lim_{x\to0}\left(\dfrac{x-(x+\dfrac{x^2}{2})}{x(x+\dfrac{x^2}{2})}\right)\\\\=\lim_{x\to0}\dfrac{-\dfrac{x^2}{2}}{x^2(1+\dfrac{x}{2})}=\lim_{x\to0}\dfrac{-1}{2+x}=\boxed{-\dfrac{1}{2}}[/tex]
_____
I find a graphing calculator can often give a good clue as to the limit of a function.
PLEASE HELP FAST WILL MARK BRAINLIEST!!!!!!!!
9.
Chelsey puts twelve colored pieces of chocolate candy in a bag. Three pieces are green,
four pleces are yellow, two pieces are purple, and three pieces are red. She draws one
piece of candy from the bag at a time and eats it.
a What is the probability that Chelsey will draw out three pieces of candy in this
order: red, green, yellow? (3 points)
b.
What is the probability that Chelsey will draw out three pieces of candy in this
order: green, yellow, red? (3 points)
c.
What is the probability that Chelsey will draw out three pieces of candy in this
order: yellow, red, green? (3 points)
d.
Make a conclusion about how the order in which she draws out the red, green,
and yellow pieces affects the probability. (3 points)
Answer:
The chances of her pulling the candy out in that exact order for all of them is extremley low
Step-by-step explanation:
I cannot figure out D though sorry
Answer:
Your welcome
Step-by-step explanation:
Last question, so please help me out ASAP!
Answer:
5/18
Step-by-step explanation:
conditional probability formula:
A|B (a given b) = (A∩B)/(B)
so
Moderate|college (moderate given college)= (moderate∩college)/college
moderate∩college= 15
college= 11+15+28= 54
15/54= 5/18
Which angles are supplementary? You can just give 1 example so I get the idea
Answer
supplementary angles sum to 180
1 & 2
1 & 4
1 & 8
1 & 6
2 & 3
2 & 7
2 & 5
3 & 4
3 & 8
3 & 6
4 & 5
4 & 7
5 & 6
5 & 8
6 & 7
8 & 7
find the value of a²+b
if...
a=-2 and b=5
Answer:
9
Step-by-step explanation:
a^2 +b
Let a = -2 and b = 5
(-2)^2 +5
Exponents first
4 +5
Then add
9
Answer:
9
Step-by-step explanation:
Here, we have to observe that a^2 = a×a =-2 × -2 = 4
hence, a^2 + b = 4 + 5 = 9.
Solve 3x + 8 = 2x + 21
What the hcf of 24 and 180
Answer:
12
Step-by-step explanation:
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 180: 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
change from improper fraction to mix number 51/7
Answer:
7 3/7
Step-by-step explanation:
Which operation properly transforms matrix I to matrix II?
11
1
2
1
1
5
1
2
1
5
5
5
0
1 2
→ 0 1
2
5
2 7
825
0 36
15
Answer:
D
Step-by-step explanation:
Replace R1 with 1 and R3 with 0 you have -2(1)+0 which equals 0 and that matches matrix II. Repeat the process with the other numbers in R1 and R3 and they all come out equal therefor the answer is D.
help asap ------------------------------
Answer:
(0,-41)
Step-by-step explanation:
Let see if this table of values are proportional.
All x values decrease by -9.All y values decrease by -19.This mean that the function is proportional. This also gives us the slope which is 19/9.
This tell us that this function will be a linear function since we are trying to find the y intercept we would use this equation
We know the slope and we know a point so let use point slope form to find the intercept.
[tex]y - y _1= m(x - x _1)[/tex]
Let use points (-18,-79) and let m =19/9.
[tex]y + 79 = \frac{19}{9} (x + 18)[/tex]
[tex]y + 79 = \frac{19}{9} x + 38[/tex]
[tex]y = \frac{19}{9} x - 41[/tex]
This is in slope intercept form so the y intercept is
[tex] - 41[/tex]
The answer is -41.
What would x be in the image above?
Answer:
x= -7
Step-by-step explanation:
the labeled angles are alternate-interior angles which are congruent
we can solve for 'x' by creating this equation:
x+139 = 132
x = -7
What is the measure of _X in degrees?
O A. Cannot be determined
O B. 20°
O C. 40°
O D. 70°
Graph the image of AUVW after a translation 11 units left and 3 units down.
randy is a car salesman who earns a base pay of $39,800 and is a paid commission of 18% for each car he sells. if x represents total sales in dollars, which equation best represents randys total pay in dollars
Answer:
39,800+x0.18= his total pay
Your Welcome
Biffy Out!!!
what is the scale factor from figure a to figure b
Scale factor from figure a to figure b = DIVIDE BY 3
{Check:- 33/3 = 11 & 15/3 = 5}
hope this helps :)
Answer:
1/3
Step-by-step explanation:
These two quadrilaterals are similar because figure A's sides are 3 times figure B's sides. Figure A's bottom is 15, while figure B's bottom is 5. To get from 15 to 5, we multiply by 1/3. This is the scale factor. All the other sides of figure A are also 3 times bigger than figure B's.
Jay has a car worth $36,001. It is depreciating at a rate of 16% per year. How much will
it be worth in 3 years?
Answer:
$18,720.5
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Depreciation Formula: A = P(1 - rt)
P is principle amountr is ratet is timeStep-by-step explanation:
Step 1: Define
Identify variables
P = 36001
r = 16% = 0.16
t = 3
Step 2: Find Cost
Substitute in variables [Depreciation Formula]: A = 36001(1 - 0.16 · 3)(Parenthesis) Multiply: A = 36001(1 - 0.48)(Parenthesis) Subtract: A = 36001(0.52)Multiply: A = 18720.5A credit card has a nominal annual interest rate of 18%, and interest is compounded monthly. The cardholder uses the card to make a $30 purchase.
Which expression represents the balance on the card after 5 years, in dollars, assuming no further charges or payments are made?
Answer:
30 [tex](1 + \frac{.18}{12})^{5*12}[/tex]
Step-by-step explanation:
graph:y-10=-2(x-10)grgrgrgrggrgrgrgrgrgrrgrrggr
Answer: 14
Step-by-step explanation:
y -1 0 = -6
Ans -2 (x-10) = 14
Hope I could help :)
Which equation shows the distributive property? (a) 6 x 3 + 6 x 8 = 6 x (3 + 8) (b) 5 + (22 + 19) = (5 + 22) + 19 (c) 20 x 10 = 10 x 20 (d) 45 + 7 = 7 + 45
help me please
Parallel Lines
PLEASE HELP I NEED ASAP!
Answer:
B
Step-by-step explanation:
The triangles do have equal angles and proportional sides, because they are bot right triangles formed on parallel lines.
:)ur welcome
Answer: Choice B
Yes. Right triangles formed on parallel lines have proportional side lengths and congruent angles.
====================================================
Explanation:
Parallel lines always have equal slopes, but different y intercepts.
Recall that slope = rise/run.
The "rise" is the vertical portion of the triangle, while the "run" is the horizontal portion.
So let's say we had a slope of rise/run = 2/3. This means rise = 2 and run = 3.
If we had something like rise/run = 4/6, then that reduces to 2/3, showing that 4/6 = 2/3. They are the same slope.
We can use the SAS similarity theorem to prove the triangles formed in the diagram are congruent based on what is discussed above.
Because the triangles are similar, this means the corresponding angles are congruent. One such pair is the pair of right angles shown.
-3x+20+7x=80 what is x? and how do I get it?
Answer:
x = 15
Step-by-step explanation:
-3x+20+7x=80
Combine like terms
4x+20 = 80
Subtract 20 from each side
4x+20 -20 = 80-20
4x = 60
Divide by 4
4x/4 = 60/4
x = 15
A triangle has vertices (-1, 2), (3, 1), and (7.2). What is the approximate perimeter of the triangle? Round your answer to the nearest hundredth
Answer
16.25
Step-by-step explanation: To The Nearest Hundredth
(-1, 2), (3, 1)
√17
(3, 1), (7, 2)
√17
(3, 1), (7, 2)
√8
So our answer is =
8 + √17 + √17 = 16.25
hope it works for you!
help plzzzzzzzzzzzzzzzzzzzzz
Put these numbers in order from least to greatest.
0.36,7/10, and 0.44
Answer:
0.36,0.44,7/10
Step-by-step explanation:
Answer:
0.36, 0.44, 7/10
Step-by-step explanation:
7/10=0.7=0.70
can someone help me in this problem
Answer:
8a³b
Step-by-step explanation:
help pls i need this asap
Answer:
I got 45 degrees
Step-by-step explanation:
knowing that where T is is 90 degrees and a triangle always= 180 degrees I just split 90 in half and got 45. I could be wrong but I hope this helps :)
1 Select the correct answer. Kalid simplified a polynomial expression as shown. (6x3 + 8x2 − 7x) − (2x2 + 3)(x − 8) step 1 (6x3 + 8x2 − 7x) − (2x3 − 16x2 + 3x − 24) step 2 6x3 + 8x2 − 7x − 2x3 − 16x2 + 3x − 24 step 3
Answer:
So, the step1 is correct.
Step-by-step explanation:
The expression is
[tex](6 x^3 + 8 x^2 - 7 x)-(2x^2 + 3)(x- 8)\\\\(6 x^3 + 8 x^2 - 7 x) - (2x^3 - 16 x^2 + 3 x - 24)\\\\6 x^3 + 8 x^2 - 7 x - 2 x^3 - 16 x^2 + 3 x - 24\\\\4 x^3 - 8 x^2 - 4 x - 24[/tex]
So, the step 1 is correct.
PLEASE HELP ASAP!!!!
Jackson is testing different types of planting soil to determine which type is most effective for growing strawberry bushes. He purchases two different brands of planting soil from a local store. Jackson applies brand A to an area of the yard that receives full sunlight and brand B to another area of the yard that is in partial sunlight. He waters the area with brand B daily; he waters the area with brand A every other day. At the end of the study, Jackson concludes brand A is more effective in growing strawberry bushes. Is Jackson's conclusion valid? Explain why or why not.
Answer:
It is not valid since there is more than one variable being changed at one.
Step-by-step explanation:
Jackson changed the brand of soil, but he also changes the amount of water, and the amount of sunlight the plants are receiving, so his conclusion that the soil was more effective is not valid.
Answer:
No, Jackson did not take into account alternate theories.
Jackson's findings could have been influenced by the watering schedule and the amount of sunlight. Without adjusting for these variables, the experiment is inconclusive.
what is the perimeter of semicircle with radius of 3cm
Answer:
198/7
Step-by-step explanation:
perimeter of semi circle= (pi) x r + d
= 22/7 x 3 + 6
= 198 cm
Answer:
15.42 cm
Step-by-step explanation:
perimeter of semicircle = πr + 2r
=3.14*3 + 2*3
=9.42 + 6
=15.42
What is the perimeter of the shape?
4 cm
3 cm
3 cm
4 cm
Answer:
14cm
Step-by-step explanation:
The shape is a rectangle.
The formula for perimeter of a rectangle= 2(lenght + breadth)
lenght = 4cm
width = 3cm
2(4+3)
2 × 7
= 14cm