Using a spreadsheet program, create an amortization schedule for a 30-year mortgage of $500,000 at an annual interest rate of 4.23%.
(a)
In which month does the amount of principal in a monthly payment first exceed the amount of interest?
(b)
How much interest is repaid for the term of the loan? (Round your answer to the nearest cent.)
$
(c)
If the loan amount was $750,000 instead of $500,000, would the month in which the amount of principal in a monthly payment first exceeded the amount of interest change?
Yes
No

Answer:

[tex]2x+5y=41[/tex]

Step-by-step explanation:

Median of a triangle:  A line segment that connects a vertex of a triangle to the midpoint of the opposite side.

Vertex:  The point where any two sides of a triangle meet.

Given vertices of a triangle:

Find the midpoint of BC (Point D) by using the Midpoint formula.

Midpoint between two points

[tex]\textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\quad \textsf{where}\:(x_1,y_1)\:\textsf{and}\:(x_2,y_2)\:\textsf{are the endpoints}}\right)[/tex]

Define the endpoints:

Substitute the defined endpoints into the formula:

[tex]\textsf{Midpoint of BC}=\left(\dfrac{-21-33}{2},\dfrac{25+13}{2}\right)=(-27,19)[/tex]

Therefore, D = (-27, 19).

Find the slope of the median (line AD) using the Slope formula.

Define the points:

Substitute the defined points into the Slope formula:

[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{19-9}{-27-(-2)}=-\dfrac{2}{5}[/tex]

Therefore, the slope of the median is -²/₅.

Substitute the found slope and one of the points into the Point-slope formula to create an equation for the median.

[tex]\implies y-y_1=m(x-x_1)[/tex]

[tex]\implies y-9=-\dfrac{2}{5}(x-(-2))[/tex]

Simplify and rearrange the equation so it is in standard form Ax+By=C:

[tex]\implies 5(y-9)=-2(x+2)[/tex]

[tex]\implies 5y-45=-2x-4[/tex]

[tex]\implies 2x+5y-45=-4[/tex]

[tex]\implies 2x+5y=41[/tex]

Therefore, the equation of the median is:  

2x + 5y = 41

Answer:

(a - b)(a + b)(a² + b²)([tex]a^{4}[/tex] + [tex]b^{4}[/tex] )

Step-by-step explanation:

by repeated use of the difference of squares factorising method, that is

a² - b² = (a - b)(a + b)

given

[tex]a^{8}[/tex] - [tex]b^{8}[/tex]

= ([tex]a^{4}[/tex] )² - ([tex]b^{4}[/tex] )²

= ([tex]a^{4}[/tex] - [tex]b^{4}[/tex] )([tex]a^{4}[/tex] + [tex]b^{4}[/tex] ) ← factor left parenthesis using difference of squares

= ( a² - b²)(a² + b²)([tex]a^{4}[/tex] + [tex]b^{4}[/tex] ) ← factor left parenthesis by difference of squares

= (a - b)(a + b)(a² + b² )([tex]a^{4}[/tex] + [tex]b^{4}[/tex] )

Yes, the mean is 26.4 and the standard deviation is 3

We are given;

n = 40, p = 66% = 0.66, and  q = 1 – 0.66 = 0.34

If np ≥ 5 and np ≥ 5, then the binomial random variable, x is approximately normally distributed, then;

Mean; µ = np

Standard deviation; σ = √npq

where;

n is the sample size.

p is the population proportion.

q = 1 – p.

Calculating np and nq gives;

np = (40)(0.66) = 26.4

nq = (40)(0.34) = 13.6

Both np and nq are greater than 5, the normal distribution can be used to approximate the binomial distribution.

Thus, µ = np

µ = 40(0.66) = 26.4

Standard deviation;

σ = √(40 * 0.66 * 0.34)

σ = 3

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a.

Solution Given:

Slope of the line passing through the point is

m= [tex] \frac{y_2-y_1}{x_2-x_1}=\frac{3-(-5)}{-2-2}=\frac{8}{-4}=-2[/tex]

slope=-2

b.

Solution given:

equation is

2x-5y=-10

2x+10=5y

y=2x/5 +10/5

y=2/5 x +3

comparing above equation with y=mx+c

we get

m=2/5

slope=2/5

c.

Slope of the line passing through the point is

m=[tex] \frac{y_2-y_1}{x_2-x_1}[/tex]

-4=[tex] \frac{1-(-9)}{0-x}[/tex]

-4=10/-x

doing criss cross multiplication

-4*-x=10

4x=10

x=10/4

x=5/2

slope=5/2

d.

we have

equation of line passing through the one point is

[tex] y-y_1=m(x-x_1)[/tex]

y-5=-7(x-(-1))

y=-7(x+1)+5

y=-7x-7+5

y=-7x-2 is a required equation:

Hello and Good Morning/Afternoon:

Let's take this problem step-by-step:

When we expand a function, everything must be multiplied out evenly.

      [tex](x+6)*(x+6)\\=x*x +x*6+6*x+6*6\\=x^2 + 6x + 6x+36\\x^2 +12x+36[/tex]

Answer: x² + 12x + 36

Hope that helps!

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Polynomials are mathematical expressions made up of many terms.

To simplify the polynomial to the maximum, all like terms must be grouped together and rearranged from highest to lowest power.

Distribute

Combining like terms.

Trabajando con porcentajes, concluimos que la pérdida es de $4800.

Sabemos que la inversión inicial es de $60000, y de esta cantidad, se pierde un 8%.

Entonces la pérdida va a ser el 8% de $60000.

Podemos escribir las relaciones:

$60000 = 100%

x = 8%

Queremos resolver esto para x, tomando el cociente entre esas relaciones y resolviendo para x obtenemos:

x = $60000*(8%/100%) = $60000*0.08 = $4800

Así, concluimos que la pérdida es de $4800.

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Given the measure of angle B, side b and side, the measure of angle C to the nearest whole number is 43 degrees.

From the Rule of Sine;

sinA/a = sinB/b = sinC/c

Where A,B and C are the angles of the triangle and a, b and c are the corresponding opposing sides.

Given that;

Using the rule of sine.

sinB/b = sinC/c

We substitute the given values into the equation

sin( 18° )/9 = sinC/20

We solve for C.

sin( 18° ) × 20 = sinC × 9

0.309016994 × 20 = sinC × 9

6.18033988 = sinC × 9

Divide both sides by 9

6.18033988/9 = (sinC × 9)/9

sinC = 0.686704431

C = sin⁻¹( 0.686704431 )

C = 43.3697°

C = 43°

Given the measure of angle B, side b and side, the measure of angle C to the nearest whole number is 43 degrees.

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Answer: B. All real numbers

Step-by-step explanation:

See attached image.

Answer:

A = $11; C = $7 tickets

Step-by-step explanation:

Using the given info, we can create a system of equations to find the price of adult and children tickets.

Thus, we have 5A + 7C = 104 and 7A + 3C = 98

The easiest method to solve would be elimination:

Answer:

Step-by-step explanation:

The sales on the two days can be expressed using equations that can be solved for ticket prices.

Let x and y represent the prices of adult and children's tickets, respectively. Then the sales revenue for the two days can be expressed in the equations ...

One of the easiest solution methods is to use a graphing calculator. The first attachment shows the prices are $11 for an adult ticket; $7 for children tickets.

Using the matrix functions of a calculator, the augmented matrix of the equation coefficients can be reduced to row-echelon form. This, too, shows the solution to be (adult price, children price) = ($11, $7). See the second attachment. (The solution is the right-most column of the reduced matrix.)

Yet another solution method can use the coefficients from the equations written in general form:

In this form, we define three products of "cross multiplication":

  Δ1 = (5)(3) -(7)(7) = -34

  Δ2 = (7)(-98) -(3)(-104) = -374

  Δ3 = (-104)(7) -(-98)(5) = -238

Using those, we find the variable values to be ...

  x = Δ2/Δ1 = -374/-34 = 11

  y = Δ3/Δ1 = -238/-34 = 7

(adult price, children price) = ($11, $7)

__

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\cos (\tan \left( -1\right) (\frac{x}{2}))

c

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(

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Simplify

1

Combine multiplied terms into a single fraction

\cos (\tan \left( -1\right) \cdot \frac{x}{2})

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(

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⋅

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\cos (\frac{\tan \left( -1\right) x}{2})

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Solution

\cos \left( \frac{\tan \left( -1\right) x}{2}\right)

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Answer:

Step-by-step explanation:

[tex]cos(tan^{-1}(\frac{x}{2} ))\\put~tan^{-1}(\frac{x}{2} )=t\\\frac{x}{2} =tan~t\\sec^2t-tan^2t=1\\sec^2t=1+tan^2t=1+(\frac{x}{2} )^2=\frac{x^2+4}{4} \\sec~t=\pm\frac{\sqrt{x^2+4}}{2} \\cos ~t=\pm\frac{2}{\sqrt{x^2+4}} \\hence~cos(tan^{-1}(\frac{x}{2} ))=cos~t=\pm\frac{2}{\sqrt{x^2+4}}[/tex]

The sum of the two rational equations is equal to (3 · n² + 5 · n - 10) / (3 · n³ - 6 · n²).

In this question we must use algebra definitions and theorems to simplify the addition of two rational equations into a single rational equation. Now we proceed to show the procedure of solution in detail:

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Answer:

Step-by-step explanation:

Use your 45-45-90 special triangle with side lengths 1, 1, sqrt(2).

The given triangle has legs length 8 (given) which is 8 times the size of our special 1-1-sqrt(2) triangle.

Therefore the length of the hypotenuse is 8 times the length of the hypotenuse in our special triangle

= 8 sqrt(2)

Answer:

.00476

Step-by-step explanation:

The surface area of the Spheres is 104.19 cm².

According to the statement

we have given that the

there is a cube with side 10 cm and convert into ten spheres and we have to find the surface area of a sphere.

So,

we know that the cube has a  6 sides, each one 10 x 10 cm

So,

A cube with sides of 10 cm will have a surface area of 600 cm².

And The volume of the cube will be 1,000 cm³  ( = 10 x 10 x 10).

If you melt it down to form ten identical spheres, each of them will have a volume of:

1,000 cm³ / 10  =  100 cm³

And the volume of a sphere is:

[tex]V = 4/3 (pi)r ^{2}[/tex]

So you can calculate the radius of the spheres:

r³ =  3V / 4pi  =  (300) / (12.5664)  =  23.8732 cm³

r  =  2.8794 cm

Now, you can use the radius to find the surface area of the spheres:

As  =  4pi*r² =  (12.5664)(2.8794)^2  =  104.19 cm²

So, The surface area of the Spheres is 104.19 cm².

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Answer:W ^10

Step-by-step explanation:

The solution is in the

Answer:

4days atlases in the week

Quantity             day

  25------------------1

 1000---------------x

We solve

                  [tex]\boldsymbol{\sf{x=\dfrac{1000\times1}{25}=\dfrac{1000}{25}=40 }}[/tex]

Answer: To spend $1,000 it will take 40 days.

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[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

The general equation of ellipse is :

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {x}^{2} }{ {a}^{2} } + \cfrac{ {y}^{2} }{ {b}^{2} } = 1[/tex]

[ because it's a horizontal ellipse with centre at origin ]

so, let's equate given equation with the standard equation ~

[tex]\qquad \sf  \dashrightarrow \: \cfrac{ {x}^{2} }{64} + \cfrac{ {y}^{2} }{36} = 1[/tex]

se get :

As we know, length of minor axis is : 2b = 2 × 6 = 12 units

and, the smaller circle has diameter = 2b = 12 units

so, it's radius = 6 units ~

Now, let's write the equation of circle with origin as centre and radius = 6 units

[tex]\qquad \sf  \dashrightarrow \: {(x - h)}^{2} + (y - k) {}^{2} = {r}^{2} [/tex]

[ h = 0, k = 0, since circle has centre at origin ]

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} + {y}^{2} = 36[/tex]

Answer:

[tex]x^2+y^2=36[/tex]

Step-by-step explanation:

Equation of the red eclipse (taken from your previously posted question):

[tex]\dfrac{x^2}{64}+\dfrac{y^2}{36}=1[/tex]

General equation of an ellipse

[tex]\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1[/tex]

where:

As the center of the red ellipse is (0, 0) ⇒ h = 0, k = 0.

[tex]\implies a^2=64 \implies a=\sqrt{64}=\pm8[/tex]

[tex]\implies b^2=36 \implies a=\sqrt{36}=\pm6[/tex]

The Major Axis is the longest diameter of an ellipse.

Therefore, using the formula for the vertices, the vertices of the major axis of the red ellipse are (8, 0) and (-8, 0).

The Minor Axis is the shortest diameter of an ellipse.

Therefore, using the formula for the vertices, the vertices of the minor axis of the red ellipse  (0, 6) and (0, -6).

Therefore, the radius of the larger circle is 8 units and the radius of the smaller circle is 6 units (half the respective axis, since the radius of a circle is half its diameter).

Equation of a circle

[tex](x-a)^2+(y-b)^2=r^2[/tex]

(where (a, b) is the center and r is the radius)

Given:

The equation of the smaller circle is:

[tex]\implies (x-0)^2+(y-0)^2=6^2[/tex]

[tex]\implies x^2+y^2=36[/tex]

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Answer: 470.4 N

Step-by-step explanation:

Concept:

1 kg on Earth = 9.8 N

Given information:

Mass = 48 kg

Find the weight on Earth

1 kg = 9.8 N

48 kg = 48 * 9.8 = [tex]\Large\boxed{470.4N\\}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The algebraic expression that represents the number of hours Anna and Tamara traveled the first two days is (2x - 1) hours.

We are told that;

On the first day, Anna and Tamara stop for sightseeing and lost 2 hours of travel time.

On the second day, they did not stop for lunch and gained 1 hour.

Now, we are told that x is the number of hours driven per day. Thus, for two days, number of hours driven is expressed as 2x.

Now, since they lost 2 hours on the first day, then total hours travelled is;

2x - 2 hours

On the second day, they gained 1 hour. Thus;

Final total number of hours traveled = 2x - 2 + 1

Final total number of hours traveled = (2x - 1) hours

Thus, we can conclude that the algebraic expression that represents how many hours Anna and Tamara traveled the first two days is (2x - 1) hours.

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Answer:

18 miles

Step-by-step explanation:

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Answer:

25, 26, and 27 are the three consecutive integers.

Step-by-step explanation:

Let the numbers be represented as x, x + 1 and x + 2.

We can write the equation:

[tex]x+(x+1)+ (x+2)=78[/tex]

Opening the brackets and simplifying:

[tex]x+x+1+x+2=78[/tex]

[tex]3x+3=78[/tex]

Subtract 3 from both sides.

[tex]3x=75[/tex]

Divide both sides by 3.

[tex]x=25[/tex]

Since the three consecutive integers are x, x + 1 and x + 2, replace x with 25.

∴ 25, 26 and 27 are the three consecutive integers.

Answer:

25 , 26 and 27

Step-by-step explanation:

Answer:

205

Step-by-step explanation:

We start with 235, this will be our y-intercept.

6 Is deducted from our value every visit, making our slope -6.

Put the two into slope intercept form:

[tex]y=235-6x[/tex]

To find the value after 5 visits substitute x for 5:

[tex]y=235-6(5)[/tex]

Solve

[tex]y=235-6(5)\\y=235-30\\y=205[/tex]

Therefore you have 205 left in your account after 5 visits.

The statements which are correct about the equation of circle [tex]x^{2} +y^{2}-2x-8=0[/tex] are 1) The radius of the circle is 3 units,2) The center of the circle lies on the x axis,5) The radius of this circle is the same the radius of the circle whose equation is [tex]x^{2} +y^{2} =9[/tex].

Given the equation of circle be [tex]x^{2} +y^{2}-2x-8=0[/tex].

We are required to find the appropriate statements related to the equation [tex]x^{2} +y^{2}-2x-8=0[/tex].

[tex]x^{2} +y^{2}-2x-8=0[/tex] can be written as under:

[tex]x^{2} +y^{2} -2x+1-9=0[/tex]

[tex]x^{2} +1^{2}-2x+y^{2} -9=0[/tex]

[tex](x-1)^{2}+y^{2}[/tex]-9=0

[tex](x-1)^{2} +y^{2} =9[/tex]

[tex](x-1)^{2}+y^{2} =3^{2}[/tex]

Equation of a circle usually in the form [tex]x^{2} +y^{2} =a^{2}[/tex] in which a is radius.

From the comparison of both the equations we get that radius is 3 units.

From the equation point will be (1,0). It is on the x axis.

Hence the statements which are correct about the equation of circle [tex]x^{2} +y^{2}-2x-8=0[/tex] are 1) The radius of the circle is 3 units,2) The center of the circle lies on the x axis,5) The radius of this circle is the same the radius of the circle whose equation is [tex]x^{2} +y^{2} =9[/tex].

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Answer: 1,2,5 on edge

Step-by-step explanation:
see above ans for work

Samuel is incorrect because he didn't subtract the power of the numbers.

The number of rod and cone cells in the human eye is written in scientific notation. Scientific notation is used in expressing large numbers in smaller numbers. To write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10. For example, 1 x 10² is equivalent to 100

(9.1 x 10^7) - (4.5 x 10^6)

= (9.1 - 4.5) x 10^(7 - 6)

4.6 x 10 = 46

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Answer:

  understand the meaning of m > 0 and c > 0.

Step-by-step explanation:

The slope-intercept form of the equation of a line tells you its slope and its y-intercept.

  y = mx +c . . . . line with slope m and y-intercept c

The slope is the rate of increase moving from left to right. It is positive (m>0) when the line slants upward to the right. It is negative (m<0) when the line slants down to the right.

The y-intercept is where the line crosses the (vertical) y-axis. It is positive (c>0) when the line crosses above the x-axis, where y-values are positive. It is negative (c<0) when the line crosses below the x-axis. If the line passes through the origin, then c=0.

Answer:

The original price was $30

Step-by-step explanation:

40% = 40/100 = 0.4

[tex]\frac{12}{0.4} =30[/tex]

Hope this helps

The value of x when the richter scale rating scale is 8.4 is 251188643.151

A richter scale is a numerical scale that is used for expressing the magnitude of an earthquake in a geographical area

The richter scale takes the amplitude of the earthquake's largest seismic as an input and calculate (and display) the magnitude of an earthquake in the geographical area using a logarithmic function

The formula of a richter scale is expressed as:

log(x) = n

Where n represents the scale rating of the scale

In this case, n = 8.4.

So, we have:

log(x) = 8.4

Express as an exponent

x = 10^8.4

Evaluate the exponent

x = 251188643.151

Hence, the value of x when the richter scale rating scale is 8.4 is 251188643.151

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The inference is that the author suggest that looking at birds is silly A. to create a sense of doubt in the reader.

It should be noted that that an inference simply means the conclusion that can be deduced based on the information given in a story.

In this case, A Big Year" is a year in which a person attempts to see as many different species of birds as possible within a particular region. For most in North America who participate in a "Big Year," this region is the lower 48 American states, plus Alaska, Canada, and a couple of French islands off the Canadian coast.

The inference is that the author suggest that looking at birds is silly is to create a sense of doubt in the reader. Therefore, the correct option is A.

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The amount of the mortgage on this house is given as $300000, while the 1.5 points on the house is given as 3000 dollars

The data from the questions says that the cost of the house = $245000

The down payment amount amount is 45000

Given that they already paid 45000 from the cost of the house, the mortgage would be 245000 - 45000

= $200000

The cost of 1.5 points is the same as the cost of 1.5% of the mortgage of this house.

This is calculated as 0.015 x 200000

= $3000

The conclusion is that the amount of the mortgage on this house is given as $300000, while the 1.5 points on the house is given as 3000 dollars

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