The full workings for the house purchase you made on a mortgage are as follows:
1. Price of House = $499,000 (given)
2. Down Payment = $99,800 ($499,000 x 20%)
3. Amount Financed (Mortgage principal) = $399,200 ($499,000 - $99,800).
4. Monthly Payment = $2,522.94 (given)
5. Number of monthly payments = 360 months (30 x 12)
6. Total Payback = $908,258.40 ($2,522.94 x 360)
7. Total Interest = $509,058.40 ($908,258.40 - $399,200)
8. Assessed Valuation = $199,600 ($499,000 x 40%)
9. Real Estate Taxes (annual) = $6,047.88 ($199,600 x $3.03/$100)
10. Escrow Payment Per month (taxes & insurance) = $628.99 ($6,047.88 + $1,500)/12
11. Monthly Payment to lender (escrow + mortgage) = $3,151.93 ($628.99 + $2,522.94)
What is a mortgage?A mortgage is a loan arrangement that allows a borrower to buy some property, usually a house, without paying for the full cost immediately.
The borrower then makes a monthly payment, which includes the principal and its interest.
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Question 5 of 25
Which graph shows a system with an infinite number of solutions?
A. Graph A
B. Graph C
C. Graph B
Answer:
The answer is Graph C.
Step-by-step explanation:
Both the equation of each other are the same in Graph C..
Answer:
B. Graph C
The lines are together, so every point they pass is a solution
Find the value of x given the EXTERIOR angle measures in a convex pentagon are x, 77, 72, 64, and 80.
Answer:
x = 67°
Step-by-step explanation:
The sum of the exterior angles of a convex pentagon is 360°.
Hence, by adding the given angle measures, we can find x.
⇒ x + 77 + 72 + 64 + 80 = 360
⇒ x + 149 + 144 = 360
⇒ x + 293 = 360
⇒ x = 67°
Answer:
The value of x is 67°Step-by-step explanation:
We know that exterior angles of any polygon sum to 360°.
Use the given angle measures to find the sum
x + 77 + 72 + 64 + 80 = 360Solve it for x
x + 293 = 360x = 360 - 293x = 67Is 2/3 < 3/4 , or is 3/4 < 2/3 ? Explain how you know.
Answer:2/3 < 3/4
Step-by-step explanation: 3/4 is greater than 2/3.
.. Discuss the nature of the root of equation x2 + 2x + 3 = 0
Answer:
No real rootsStep-by-step explanation:
Given equation:
x² + 2x + 3 = 0On comparing the equation by ax² + bx + x = 0, We get: a = 1, b = 2 and c = 3
To Find the nature of the roots of the equation firstly we need to find the discriminant of the equation. The expression b²- 4ac is called the discriminant.
[tex]~[/tex]
Two Distinct real roots, if b² - 4ac > 0Two equal real roots, if b² - 4ac = 0No real roots, if b² - 4ac < 0[tex] \\ \: \: \dashrightarrow \: \: \: \sf {b}^{2} - 4ac = 0 \\ \\ \\\: \: \dashrightarrow \: \: \: \sf (2)² - 4 \times 1 \times 3 = 0 \\ \\ \\ \: \: \dashrightarrow \: \: \: \sf 4 - 4 \times 1 \times 3 = 0 \\ \\ \\ \: \: \dashrightarrow \: \: \: \sf 4 - 12 = 0 \\ \\ \\ \: \: \dashrightarrow \: \: \: \sf {\underline{\boxed{\sf{\purple{ -8 > 0}}}}} \\ \\ [/tex]
The discriminant is smaller than 0.
Hence, Equation has no real roots (no solution)Determine whether the function x2 = –y – 2 is quadratic or not. Explain.
Answer:
Yes, it is.
Step-by-step explanation:
A quadratic function always has [tex]x^{2}[/tex] [tex]x[/tex]≠0The function x² = -y - 2 is a quadratic function.
What is a Function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences. The German mathematician Peter Dirichlet initially offered the contemporary definition of function in 1837: A variable y is said to be a function of the independent variable x if there is a relationship between them such that whenever a numerical value is assigned to x, there is a rule that determines a specific value of y.
As per the given data:
The function is x² = -y - 2
Rearranging the function:
y = x² - 2
A quadratic function is always of the form:
y = ax² + bx + c, where a, b and c are real numbers with a not equal to 0.
We can write y = x² - 2 as:
y = x² + 0(x) - 2, here a = 1, b = 0, c = -2
Hence, the function x² = -y - 2 is a quadratic function.
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Suppose your friend's parents invest $ 10,000 in an account paying 5% compounded annually. What will the balance be after 8 years?
Answer:
A = $14,745.544
Step-by-step explanation:
The equation for compound interest is
A = P (1+i)t
A = final value
P = amount invested (principal) (10000)
i = interest rate, expressed as a decimal (.05)
t = number of years invested (8)
This formula assumes annual compounding.
Plugging in what we know.
A = 10000(1.05)^8
A = 10000 (1.47745544)
A = $14,745.544
All of the following countries were impacted by Chernobyl EXCEPT...
A. Great Britain
B. Brazil
C. Norway
Answer:
B: Brazil
Step-by-step explanation:
The Chernobyl impacted Belarus, Russia, and Ukraine as well as many other European countries. And Brazil isnt a European country.
( I hoped this helped)
Serika has hired Tom to build her a dollhouse. The dollhouse will be a scale model of her home, and the scale will be 2 inches :
3 feet.
The living room in Serika’s house is 18 feet by 12 feet and has wall-to-wall beige carpeting. How many square inches of
carpeting will Tom need for the living room in Serika’s dollhouse?
Answer:
96 square inches
Step-by-step explanation:
The scale is 2 inches : 3 feet
Thus for 18 feet in Serika's real house, the model is 18 * (2"/3') = 12 inches
For 12 feet in Serika's real house, the model is 12 * (2"/3') = 8 inches
Area of carpeting needed in Serika's dollhouse = 12" * 8" = 96 square inches
You accidentally dropped a coin from the top of 12 stairs. What is the probability that it will land on the fifth step heads up?
This is a probability question! I need help ASAP
Answer:
The answer is 1/24
Step-by-step explanation:
1stepout of the 12 is the 5th so 1/12 and divid by 2 because you want it to land on heads.
Find p write your answer in simplest radical form
Answer:
[tex]p =[/tex] [tex]7\sqrt{2}[/tex]
Step-by-step explanation:
The side length ratio for a 45-45-90 angle triangle is [tex]1:1:\sqrt{2}[/tex]
The length of the bottom adjacent side of the 90-degree angle is 7, so p would be [tex]7\sqrt{2}[/tex]
What type of expenses are mortgages, taxes, and property insurance?
Answer:
Typical household fixed expenses are mortgage or car payments, rent payments, real estate taxes and insurance premiums.
Mortgages, taxes, and property insurance are housing expense.
What are expenses?An expense is a cost that businesses incur in running their operations. Expenses include wages, salaries, maintenance, rent, and depreciation.
Given that, What type of expenses are mortgages, taxes, and property insurance.
They come under housing expenses.
Total housing expense adds up all the relevant ongoing costs needed to maintain homeownership. This will include monthly bills, insurance costs, taxes, and homeowners association dues in addition to mortgage interest and principal.
Hence, Mortgages, taxes, and property insurance are a housing expense.
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Help. Please and thanks
Step-by-step explanation:
24.
AC = 12 = cos(angle) × AB = cos(angle) × 13
imagine a circle with center in A and radius 13.
that is why we can say AC = cos(angle) × radius, and BC = sin(angle) × radius.
cos(angle) = 12/13 = 0.923076923...
angle = 22.61986495...°
so, B is the right answer.
25.
we have a right-angled triangle.
from the point in the ground, where the ladder starts, to the point on the wall, where the ladder ends, and the point on the ground right under the wall point.
at this ground point there is the right angle.
at the ladder ground point we have 70°.
so, the angle at ladder/wall point is
180 - 90 - 70 = 20°.
remember, the sum of all angles in a triangle is always 180°.
the ladder itself (20 ft) is the Hypotenuse (the baseline opposite of the 90° angle).
the height of the ladder/wall point is one leg (and what we need to calculate), and the ground distance from the ladder/ground point to the point right under the ladder/wall point is the second leg.
we can use the law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
with the sides being always opposite of the associated angles.
so, we have
20/sin(90) = 20/1 = 20 = height/sin(70)
height = 20×sin(70) = 18.79385242... ft
so, D is the right answer.
Given that A, O & B lie on a straight line segment, evaluate obtuse ∠AOC.
The diagram is not drawn to scale.
∠AOC=
Answer:
AOC = 124°
Step-by-step explanation:
Angle on a straight line is 180°, therefore, the sum of the three angles shown is 180;
This can be written like so:
(3x + 94) + (x + 30) + (2x - 4) = 180
This equation can be solved to find x:
6x + 120 = 180
6x = 180 - 120
6x = 60
x = 10
AOC = 3(10) + 94
= 30 + 94
= 124
Answer:
angle AOC = 124
Step-by-step explanation:
3x + 94 + x + 30 + 2x - 4 = 180 ( ^'s on a STR line)
6x = 180 - 120
6x = 60
x = 10
sub x into 3x + 94
3(10) + 94 = 124
I don't understand. Help please.
Answer:
the H stands for hours. the E stands for money. because it says 10h that means she gets $10 per hour. that answers the first question. I don't understand the second part though. hope you get it!
The Dow Jones Travel Index reported what business travelers pay for hotel rooms per night in major U.S. cities (The Wall Street Journal, January 16, 2004). The average hotel room rates for 20 cities are as follows: Atlanta $163 Minneapolis $125 Boston 177 New Orleans 167 Chicago 166 New York 245 Cleveland 126 Orlando 146 Dallas 123 Phoenix 139 Denver 120 Pittsburgh 134 Detroit 144 San Francisco 167 Houston 173 Seattle 162 Los Angeles 160 St. Louis 145 Miami 192 Washington, D.C. 207
The mean hotel room rate based on the reported room rates paid by business travelers in 2003 by the Dow Jones Travel Index is $159.05.
What is the mean?The mean is the average of a set of data or numbers.
It is a typical value that averagely represents the dataset.
The mean can be computed by dividing the total by the number of data values.
Data and Calculations:Atlanta $163
Minneapolis $125
Boston 177
New Orleans 167
Chicago 166
New York 245
Cleveland 126
Orlando 146
Dallas 123
Phoenix 139
Denver 120
Pittsburgh 134
Detroit 144
San Francisco 167
Houston 173
Seattle 162
Los Angeles 160
St. Louis 145
Miami 192
Washington, D.C. 207
Total = $3,181
Mean = $159.05 ($3,181/20)
Question Completion:What is the mean hotel room rate?
Thus, the mean hotel room rate based on the reported room rates paid by business travelers in 2003 by the Dow Jones Travel Index is $159.05.
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Mr. Clinton chose 10 different test scores out of 50, and they are shown below. For the following set of data, find the mean test score, rounding to the nearest tenth (i.e. one decimal place)
{48, 36, 23, 19, 50, 50, 49, 47, 38, 20}
Answer:
38.0
Step-by-step explanation:
'Mean' is just the average of the 10 scores ....
add them all together and divide by 10
380 / 10 = 38
You wish to test the following claim (
H
a
) at a significance level of
α
=
0.002
.
H
o
:
μ
=
63.5
H
a
:
μ
<
63.5
You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size
n
=
62
with mean
M
=
56.3
and a standard deviation of
S
D
=
13.2
.
What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =
What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =
Using the t-distribution, it is found that the desired measures are given as follows:
The test statistic is t = -4.29.The p-value is of 0.What are the hypotheses tested?At the null hypotheses, it is tested if the mean is of 63.5, that is:
[tex]H_0: \mu = 63.5[/tex]
At the alternative hypotheses, it is tested if the mean is less than 63.5, that is:
[tex]H_1: \mu < 63.5[/tex]
What is the test statistic?The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.The values of the parameters are given as follows:
[tex]\overline{x} = 56.3, \mu = 63.5, s = 13.2, n = 62[/tex]
Hence, the test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{56.3 - 63.5}{\frac{13.2}{\sqrt{62}}}[/tex]
t = -4.29.
What is the p-value?We have a left-tailed test, as we are testing if the mean is less than a value, with 62 - 1 = 61 df and t = -4.29. Hence, using a t-distribution calculator, the p-value is of 0.
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Jared wants to paint his room. The dimensions of the room are 12 feet by 15 feet, and the walls are 9 feet tall. There are two windows, each with dimensions 6 feet by 5 feet. There are two doors, each with dimensions 30 inches by 6 feet. If a gallon of paint covers about 350 square feet, how many gallons of paint will he need to put two coats of paint on the wall? List the steps to solve the problem and solve.
Answer:
1 ft = 12 in
1 in = (1/12) ft
30 in = (30/12) ft
30 in = 5/6 ft
The area of the surface that Jared needs to paint is:
2(12*9 + 15*9) - 2(5*6 + (5/6)*6) = 416 ft^2
Step-by-step explanation:
Answer:
3 gallons of paint
Step-by-step explanation:
Steps you have to take,
identifying the area of the 4 walls subtracting the windows and doors from the area.finding out how many gallons of paint it will take to cover the total area twiceFormula:
[tex](A = lw)(2) + (A = lw)(2) - (A = lw)(2) - (A = lw)(2)[/tex]
[tex](wall 1)(2) + (wall 3)(2) - (window)(2) - (door)(2)[/tex] ↑
door = 30in by 6ft
30in to feet = 2.5 feet
Lets start solving.[tex](A = 12(9))2 + (A = 15(9))2 - (A = 6(5))2 - (A =2.5(6))2[/tex]
[tex](A = 108)2 + (A = 135)2 - (A = 30)2 - (A = 15)2[/tex]
[tex](A = 216) + (A = 270) - (A = 60) - (A = 30)[/tex]
[tex]combine\\(A = 486) - (A= 90)\\(A = 396)[/tex]
two coats = A(2)396(2) =
792sq ft
We know that one gallon covers 350sq ft
792/350 =
2.26 gallons
(can't have .26 of a gallon so we round up)
it takes 3 gallons of paint Jared's room3) A customer in a bookstore is interested in eleven books on sale.
How many ways can she select three books to buy?
Find any 2 irrational no. Between 0.1 and 0.12
0.10100100010000 and 0.110100100010000 are two irrational numbers between 0.1 and 0.12.
Step-by-step explanation:
Any two irrational Numbers between 0.1 and 0.12 will be those numbers which will be=> greater than 0.1 and smaller than 0.12
And those numbers are = 0.10100100010000 and 0.110100100010000.You can also choose any other numbers too.
___________________Irrational Number :
Irrational numbers are non terminatingNon recurring / repeatingOn a number line 1.77 would be located where?
Step-by-step explanation:
1.77 would be closer to 2
Help the pic has questions
Answer:
a) [tex]x = 9[/tex]
b) [tex]m \angle 1 = m \angle 2 = 54^\circ[/tex]
Step-by-step explanation:
Since [tex]r\ ||\ s[/tex], through the Alternate Angle Theorem, [tex]m \angle 1 = m \angle 2[/tex]. We can solve for x by setting up an equation where both angles are equal to each other:
[tex]m \angle 1 = m \angle 2\\63-x = 72-2x\\63 +x = 72\\x = 9[/tex]
Now plug in x for both of the formulas to get their angles:
[tex]m \angle 1 = (63 - x)^\circ = (63-9)^\circ = 54^\circ[/tex][tex]m \angle 2 = (72-2x)^\circ = (72-2(9))^\circ = (72-18)^\circ = 54^\circ[/tex]
3.2 × 10^7
write in expanded form
Answer:
32000000
Step-by-step explanation:
3.2 x 10 = 32
you will have 10^6 left
32 x 10^6 = 32000000
just add 6 zeroes
Answer:
32, 000, 000.
Step-by-step explanation:
3.2 x 10^7 <======= move the decimal 7 places to the right
32,000,000.
The length and width of a rectangle are consecutive even integers. The perimeter is 92 meters. Find the length and width!
Answer:
w represents the width
w + 2 represents the length
2(w + w +2) = 76 formula for perimeter
w + w + 2 = 38 divide both sides by 2
2w + 2 = 38 combine like terms
2w = 36 subtract 2 from both sides
w = 18 divide both sides by 2
Write the equation of the line that passes through the points (4,-5)(4,−5) and (4,-7)(4,−7). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
well, it's a vertical line, so, Check the picture below.
To the nearest tenth, what is the area of a circle whose diameter is 21 inches?
Use 3.14 for PI
Enter your answer in the box.
____in2
Please show work and thank you
Answer: [tex]4\sqrt{7}[/tex]
Step-by-step explanation:
If [tex]AC=16, DC=7[/tex], then this means [tex]AD=9[/tex].
So, by the geometric mean theorem, [tex]DB=\sqrt{(9)(7)}=\sqrt{63}[/tex].
This means that by the Pythagorean theorem, [tex]BC=\sqrt{\left(\sqrt{63} \right)^{2}+7^{2}}=\boxed{4\sqrt{7}}[/tex]
i need help with this math
Answer:
(-0.6, 8.4)
Step-by-step explanation:
so first, we have to find out what x is. because y is equal to itself, we can substitute to get
[tex]x+9=-4x-6\\5x+9=6\\5x=-3\\x=-\frac{3}{5}[/tex]
now we can plug in the value of x to find y
[tex]y=-\frac{3}{5} +9\\y=8\frac{2}{5}=8.4[/tex]
your answer is written in the form (x,y) so the answer is (-0.6, 8.4)
Answer: Heyaa! ~
Your Answers are... (-0.6, 8.4)
Step-by-step explanation:
Hopefully this helps you!
~ Lets solve:
Use one equation to find an expression for one of the variables in terms of the other variable. Then substitute that expression in place of that variable in the second equation. You can then solve this equation as it will now have only one variable.
Help me plsssssssssssss
Answer:
3/1/4
That's the expression represents Lena's speed in miles per hour
given that (3x+2) is a factor of 3x^3+bx^2-3x-2. find the value of b?
Answer:
[tex]b = 2[/tex].
Step-by-step explanation:
By the factor theorem, if a monomial of the form [tex](x - a)[/tex] is a factor of the polynomial [tex](3\, x^{3} + b\, x^{2} - 3\, x - 2)[/tex], then substituting in [tex]x = a[/tex] would set this polynomial to [tex]0[/tex].
Notice that in the factor theorem, the coefficient of [tex]x[/tex] in [tex](x - a)[/tex] is [tex]1[/tex], and the sign in front of the constant [tex]a[/tex] is a minus sign. Rewrite the given factor [tex](3\, x + 2)[/tex] in this form to find the value of [tex]a\![/tex]:
[tex]\begin{aligned}& (3\, x + 2) \\ =\; & 3\, (x + (2/3)) \\ =\; & 3\, (x - \underbrace{(-2/3)}_{a}) \end{aligned}[/tex].
Thus, [tex]x = (-2/3)[/tex] should set the polynomial [tex](3\, x^{3} + b\, x^{2} - 3\, x - 2)[/tex] to [tex]0[/tex]:
[tex]\begin{aligned} & (3\, x^{3} + b\, x^{2} - 3\, x - 2) \\ =\; & 3\times (-2/3)^{3} + b\times (-2/3)^{2} - 3 \times (-2/3) - 2 \\ =\; & -3\times (2/3)^{3} + b\times (2/3)^{2} + 3 \times (2/3) - 2 \\ =\; & -\frac{8}{9} + \frac{4\, b}{9} + 2 - 2 \\ =\; & \frac{-8 + 4\, b}{9}\end{aligned}[/tex].
Set this expression to [tex]0[/tex] and solve for [tex]b[/tex]:
[tex]\displaystyle \frac{-8 + 4\, b}{9} = 0[/tex].
[tex]b = 2[/tex].