A company applies for a €170,000 mortgage loan to be repaid with fixed monthly installments at a 2,25% annual nominal interest rate compounded over 25 years. Please, find the amounts that would correspond to the following items:

a) The amount of the monthly installments, the total amount paid, and the interest to be paid over those 30 years.
b) The principal pending at the end of year 10 and the amount of interest paid in those 10 years.
c) The amounts corresponding to the first 4 years of the loan amortization schedule.

Answer:

One pair of vertical angles is a and c.

Step-by-step explanation:

This is basically an inscribed angle in a circle which encompasses twice as many degrees of arc (246) as the angle measure : angle 3 = 123 degrees

The numeric value of the function at x = 4 is given as follows:

f(4) = 0.

The expression for the numeric value of the function in this problem is given as follows:

f(4).

This means that the input is given as follows:

x = 4.

Passing a vertical line through x = 4 the value of y in which the vertical line crosses the graph is given as follows:

y = 0.

Hence the numeric value is given as follows:

f(4) = 0.

The graph is given by the image presented at the end of the answer.

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There are 5,245,786 possible winning number combinations in a 6/42 lottery, and for every ticket purchased, there is a 1 in 5,245,786 chance of winning the jackpot prize.

What is the combinations?

Combinations refer to the different ways of selecting a subset of items from a larger set without regard to the order in which the items are selected. In other words, combinations are the different ways of choosing a group of items without taking into account their arrangement or order.

In a 6/42 lottery, there are 6 numbers drawn from a pool of 42 numbers. To determine the number of possible winning number combinations, we can use the formula for combinations:

C(n,r) = n! / (r! * (n-r)!)

where n is the total number of items in the set and r is the number of items being chosen.

In this case, we have 42 numbers in the pool and we need to choose 6 numbers, so the formula becomes:

C(42,6) = 42! / (6! * (42-6)!)

which simplifies to:

C(42,6) = 5,245,786

Therefore, there are 5,245,786 possible winning number combinations in a 6/42 lottery.

To calculate the probability of winning the jackpot prize, we need to divide the number of ways to win by the total number of possible outcomes. Since there is only one winning combination, the probability of winning the jackpot is:

1 / 5,245,786

which simplifies to approximately:

0.000019% or 1 in 5,245,786.

This means that for every ticket purchased, there is a 1 in 5,245,786 chance of winning the jackpot prize.

hence,  there are 5,245,786 possible winning number combinations in a 6/42 lottery, and for every ticket purchased, there is a 1 in 5,245,786 chance of winning the jackpot prize.

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The value of m + n for the given quadratic equation is 8.

What is a quadratic equation?

A quadratic equation is a polynomial equation of the form:

[tex]ax^{2} +bx+c=0[/tex]

where x is the unknown variable, and a,b and c are constants. The highest power of the variable x in a quadratic equation is 2, hence the term "quadratic". The constants a,b and c are known as the coefficients of the quadratic equation.

According to the given information:

Let's denote the roots of the quadratic equation [tex]2x^{2} -mx+n=0[/tex] as r1 and r2, with r1 and r2 being the roots of the equation.

Given that the sum of the roots is 6 and the product of the roots is 10. This gives us the following equations:

r1 + r2 = 6 ------ (1)

r1*r2 = 10 ------- (2)

We can use these equations to solve for the values of m and n.

The sum of the roots r1 + r2 is also equal to [tex]\frac{-m}{2}[/tex] by Vieta's formulas, which state that the sum of the roots of a quadratic equation [tex]ax^{2} +bx+c=0[/tex] is given by [tex]\frac{-b}{a}[/tex]. Therefore, we can write:

[tex]\frac{-m}{2}[/tex] = 6

Solving for m, we get:

m = -2*6 = -12  ----------(3)

The product of the roots r1*r2 is also equal to n/2 by Vieta's formulas, which states that the product of the roots of a quadratic equation [tex]ax^{2} +bx+c=0\\[/tex] is given by [tex]\frac{c}{a}[/tex]. Therefore, we can write:

n/2 = 10

Solving for n, we get:

n = 2 * 10 = 20  ------------(4)

Now, we can find the value of m+n by substituting the values of m and n from equations (3) and (4) respectively:

m + n = -12 + 20 = 8

So, the value of m+n is 8.

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the area of the trapezoidal base of the first prism is 9 square units, and the area of the trapezoidal base of the second prism is 16 square units.

What is Volume of both the trapezoidal prisms?

volume = area of cross section of object*  height of object (A)

V = (1/2) * h * (b1 + b2) * H

For the first trapezoid prism, we have:

24 = (1/2) * 6 * (b1 + b2) * 8

Simplifying this equation, we get:

3 = (b1 + b2)

For the second trapezoid prism, we have:

24 = (1/2) * 8 * (b1' + b2') * 6

Simplifying this equation, we get:

4 = (b1' + b2')

A = (1/2) * h * (b1 + b2)

For the first trapezoidal prism:

A = (1/2) * 6 * 3

A = 9 square units

For the second trapezoidal prism:

A = (1/2) * 8 * 4

A = 16 square units

Therefore, the area of the trapezoidal base of the first prism is 9 square units, and the area of the trapezoidal base of the second prism is 16 square units.

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The correct option- C: 75T + 70S + 160, represent their combined earnings of Terry and Susan  for the week.

Every feature, number, or amount that can be gauged or quantified is referred to as a variable. An amount that can fluctuate depending on the mathematical issue is referred to as a variable. The generic letters x, y, and z are frequently employed in mathematical expressions and equations. A variable, then, is a symbol denoting a number whose value is unknown.

Given data:

T - number of cars detailed by Terry (T)

S - number of cars detailed by Susan (S).

Terry's charge - $75 for each car .

Total Terry's charge for T number of cars - 75T

Additional tip - $65

Susan's charge - $70 for each car.

Total Susan's charge for S number of cars - 70T

Additional tip - $95

Combined earnings = 75T + 65 + 70T + 95

Combined earnings = 75T + 70T + 160

Thus,  75T + 70S + 160, represent their combined earnings of Terry and Susan  for the week.

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Complete question:

Terry and Susan both detail cars. Terry chargers $75 for each car and Susan charges $70 for each car. This week Terry made an additional $65 in tips and Susan made an additional $95 in tips. Given that T and S represent the number of cars detailed by Terry (T) and Susan (S), which expression can be used to represent their combined earnings for the week?​

A: 145(T+S) + 160

B: 65T + 70S + 160

C: 75T + 70S + 160

D: 145TS + 160

Answer:

I'm sorry, but there seems to be an error in the formula you provided. The correct formula for finding the volume (V) of a rectangular prism is V = l x w x h, where l, w, and h are the length, width, and height of the prism, respectively.

The cost of capital for the second option, issuing new preferred stock, is 0.00356, or 0.356%. This means that for every dollar of capital raised through issuing preferred stock, the company will need to pay 0.356 cents in annual interest or dividend payments.

To calculate the cost of capital for the second option, we need to first calculate the cost of the preferred stock. The cost of preferred stock is the dividend yield, or the annual dividend divided by the market price of the stock. In this case, the annual dividend is $5.00 and the market price is $56,000.

Cost of preferred stock = Annual dividend / Market price of stock

Cost of preferred stock = $5.00 / $56,000

Cost of preferred stock = 0.000089

To calculate the cost of capital, we need to weight the cost of preferred stock with the proportion of capital that is financed by preferred stock. Let's assume that the preferred stock will finance 40% of the total capital.

Cost of capital = Cost of preferred stock * Proportion of capital financed by preferred stock

Cost of capital = 0.000089 * 0.40

Cost of capital = 0.0000356

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Answer:

Step-by-step explanation:

Para despejar "a" de la ecuación 2as = vf^2 - vo^2, podemos seguir los siguientes pasos:

2as + vo^2 = vf^2

a = (vf^2 - vo^2) / 2s

Por lo tanto, la fórmula para calcular "a" a partir de la distancia de desplazamiento "s", la velocidad final "vf" y la velocidad inicial "vo" es:

a = (vf^2 - vo^2) / 2s

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[tex]\begin{align}\colorbox{black}{\textcolor{white}{\underline{\underline{\sf{Please\: mark\: as\: brillinest !}}}}}\end{align}[/tex]

[tex]\textcolor{blue}{\small\texttt{If you have any further questions,}}[/tex] [tex]\textcolor{blue}{\small{\texttt{feel free to ask!}}}[/tex]

♥️ [tex]{\underline{\underline{\texttt{\large{\color{hotpink}{Sumit\:\:Roy\:\:(:\:\:}}}}}}\\[/tex]

The answers to Q11 to 14 with the figure representing angles with protractor are as follows:

11.Acute angle= JEH & measure=25°

12.Obtuse angle=JEK & measure=75°

13.One right angle=DEJ

14.One straight angle=DEF

What is protractor ?

With the aid of the scale on it, it serves as a tool for measuring angles. Protractors often feature two sets of numbers that face each other. A protractor is a tool having a semicircular shape and markings from 0° to 180° on both its inner and outer scales. Angles come in many different shapes and sizes in geometry, including obtuse (>90), acute (90), right (90), reflex (180–270), complete (360), and straight (>90).(180).

11)Acute angles:

HEJ=25

JEK=50

KEF=40

HED=65

12)Obtuse angles:

KED=140

JEK=75

13)right angles:

JEF

JED

14)straight lines

DEF

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All the values are,

Compound interest = $1280.2

Future value = $1280.2 + $x

Given that;

P = $865

r = 4%

T = 10 years

Formula is,

Compound Interest = P(1 + r)^t

Where, Principal = P, Interest rate = r, Number of compounds = n, Interest time = t

Plug, p = 865, r = 0.04, t = 10

Compound Interest = 865 (1 + 0.04)¹⁰

Compound Interest = 865 (1.04)¹⁰

Compound Interest = 865 x 1.48

Compound Interest = 1280.2

Hence, We get;

Future value = Compound Interest + Principal

Future value = $1280.2 + $x

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Answer:

3/8

Explanation:

I just know :) (;

1) The opposite face of the black circle is, Plus +.

2) The volume of the sliced cylinder is 96π cubic cm.

We have to given that;

Three different views of identical cubes are shown at right.

Now, From first and third dice,

Star is just opposite to symbol ~.

Hence, From second and third dice,

The opposite face of the black circle is, +

2) For the volume of the sliced cylinder, we need to first find the volume of the full cylinder and then subtract the volume of the smaller cylinder that's left after the slice is made.

Hence, The volume of the full cylinder is given by:

V = πr²h

Where r is the radius of the base and h is the height of the full cylinder.

Using the given values, we can find:

V = π(4²)(18)

V = 288π cubic cm

Now, let's find the volume of the smaller cylinder. The shorter height of 12 cm tells us that the slice removed 6 cm from the top of the cylinder. So the height of the smaller cylinder is,

18 - 6 = 12 cm.

The radius remains the same at 4 cm.

Thus, the volume of the smaller cylinder is:

V = π(4²)(12)

V = 192π cubic cm

Finally, we can find the volume of the sliced cylinder by subtracting the volume of the smaller cylinder from the volume of the full cylinder;

⇒ V = (288π) - (192π)

⇒ V = 96π cubic cm

Therefore, the volume of the sliced cylinder is 96π cubic cm.

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Answer:

To compare the texting rates of Student A and Student B, we need to calculate their respective rates of change.

For Student A, we can use the formula for the slope of a line:

slope = (change in y) / (change in x)

In this case, the "y" variable represents the number of texts sent, and the "x" variable represents the number of tests sent. Looking at the table, we can see that Student A sent 10.5 texts after sending 1 test, and 10 texts after sending 2 tests. So the change in y is -0.5 (10.5 - 10), and the change in x is 1. Therefore:

slope = (-0.5) / 1 = -0.5

So Student A's texting rate is -0.5 texts per test.

For Student B, we can look at the graph and find the slope of the line connecting any two points. Let's choose the points (2, 15) and (5, 23) because they are easy to read off the graph. The change in y is 8 (23 - 15), and the change in x is 3 (5 - 2). Therefore:

slope = 8 / 3 = 2.67

So Student B's texting rate is 2.67 texts per minute.

To find the difference in their texting rates, we simply subtract:

difference = Student B's rate - Student A's rate

difference = 2.67 - (-0.5) = 3.17

So the difference in their texting rates is 3.17 texts per test.

Step-by-step explanation:

We are given the graph of

y = h(x)

If the graph of y = h(x-3) is drawn on the same set of axes as the graph above, then the two graphs intersect at one point. What is that point?

We begin by identifying two points on the graph of h(x).

These are;

P1(-2,3), P2(1,3)

next, we are told that the graph of y = h(x - 3) is drawn on the same axis, which means the graph of the function has been shifted 3 units to the right.

Therefore, the points identified above will now be;

P 1 Rightarrow (- 2 + 3, 3)

P_{1}' = (1, 3)

P 2 Rightarrow (1 + 3, 3)

P_{2}' = (4, 3)

In summary,

The point is

The height of the Zeta Tower as a percentage of the height of the Delta tower is the 94.72%

Here we know that:

The epsilon tower is 23% taller than the delta one, then the height is:

H = 55m*(1 + 0.23) = 67.65 m

And we know that the Zeta tower is 23 short than the epsilon one, then the height of this twoer is.

H' = 67.65m*(1 - 0.23) = 52.0905 m

The height of the delta tower is 55m, this is our 100%.

Then the height of the zeta tower written as a percentage will be:

(52.0905 m/55m)*100% = 94.72%

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The standard form based on the information given will be:

a) 2.35 x 10^-3 = 0.00235 (in standard form)

b) 2.35 x 10^3 = 2350 (in standard form)

It should be noted that in mathematics and computer science, a normal, or standard form of a mathematical object is a standard way of presenting that object as a mathematical expression.

Often, it is one which provides the simplest representation of an object and allows it to be identified in a unique way

he standard form for linear equations in two variables is Ax+By=C. For example, 2x+3y=5 is a linear equation in standard form.

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If each person drove at a constant rate, the person who drove the fastest (in miles per hour) is: C. Nathan.

In Mathematics and Science, speed is the distance covered by a physical object per unit of time. This ultimately implies that, speed can be measured by using the following unit of measurement;

In Mathematics and Science, the speed of any a physical object can be calculated by using this formula;

Speed = distance/time

For Hank, we have:

Speed = 176/3.2 = 55 miles per hour.

For Laura, we have:

Speed = 150/2.5 = 60 miles per hour.

For Nathan, we have:

Speed = 112.5/2.25 = 50 miles per hour (Fastest).

For Raquel, we have:

Speed = 286/4.4 = 65 miles per hour.

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The number line where we plotted -1 1/6 and 7/3 is added as an attachment

From the question, we have the following parameters that can be used in our computation:

-1 1/6 and 7/3

To start with, we convert both numbers to the same form

i.e. decimal or fraction

When converted to fractions, we have

-7/6 and 7/3

Rewrite the denominators of the fractions

So, we have

-7/6 and 14/6

This means that we can plot -7/6 at -7 and 7/3 at point 14 where the difference in each interval is 1/6

Using the above as a guide, we have the following:

The number line is attached

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The value of x, y, and z in the rhombus below x = 20, y = -7, z = -11

Recall that a  rhombus is an equilateral parallelogram with both pairs of opposite sides parallel and all sides the same length.

Sum of interior angles of a rhombus = 360°

The opposite angles of a rhombus are equal to each other.

The adjacent angles are supplementary (add up to 180°)

Therefore,

66 + (6x - 6) = 180

⇒ 66 + 6x - 6 = 180

⇒ 6x = 180 - 66 + 6

⇒ 6x = 120

⇒ x = 120 ÷ 6

⇒ x = 20

66 + (-10z + 4) = 180

⇒ 66 - 10z + 4 = 180

⇒ -10z= 180 - 66 - 4

⇒ -10z = 110

⇒ z = 110 ÷ -10

⇒ z = -11

(6x - 6) + (-10y - 4) = 180

⇒ 6x - 6 - 10y - 4 = 180

⇒ 120 - 6 - 10y - 4 = 180

⇒ -10y = 180 - 120 + 6 + 4

⇒ -10y = 70

⇒ y = 70 ÷ -10

⇒ y = -7

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All the arcs are derived as given below.

5)

∡LO = 180°

so

∡KL = ∡ON = 180-90-67

∡KL = ∡ON = 23°
∡OM = 90 + 23 = 113°
∡ NL = 67 + 90 = 157°


7)

Where

(9x + 23) + 31 = 180
9x + 54 = 180
9x = 180-54

9x = 126
x = 126/9
x = 14

9.

(21x-9) = 90+27
21x - 9 = 117
21x = 117 + 9
x = 126/21
x = 6

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Answer:

Step-by-step explanation:

To solve the differential equation:

y′′′ + y = 3(y′ − 1)

we first find the characteristic equation:

r^3 + 1 = 0

The roots of this equation are:

r = -1, 0 ± i

So, the general solution of the homogeneous equation (y′′′ + y = 0) is:

y_h(t) = c1 e^(-t) + c2 cos(t) + c3 sin(t)

To find a particular solution of the non-homogeneous equation (3(y′ − 1)), we assume a solution of the form:

y_p(t) = a t + b

Taking the first, second and third derivatives of y_p(t), we get:

y′_p(t) = a

y′′_p(t) = 0

y′′′_p(t) = 0

Substituting these into the differential equation, we get:

0 + (a t + b) = 3(a - 1)

Solving for a and b, we get:

a = 1

b = 2

Therefore, the particular solution of the non-homogeneous equation is:

y_p(t) = t + 2

So, the general solution of the non-homogeneous equation is:

y(t) = y_h(t) + y_p(t) = c1 e^(-t) + c2 cos(t) + c3 sin(t) + t + 2

To find the values of c1, c2 and c3, we use the initial conditions:

y(0) = c1 + c2 + 2 = 1

y′(0) = -c1 + c2 + c3 = 0

y′′(0) = c1 - c2 = 0

Solving these equations simultaneously, we get:

c1 = c2 = 1/2

c3 = -1/2

So, the solution of the differential equation with initial conditions (0) = 1, ′(0) = 0, ′′(0) = 0 is:

y(t) = 1/2 e^(-t) + 1/2 cos(t) - 1/2 sin(t) + t + 2

Answer:

The probability that a randomly chosen college student does not take statistics is 0.76.

Step-by-step explanation:

The probability of an event happening and the probability of its complement (the event not happening) must add up to 1. Therefore, if the probability that a randomly chosen college student takes statistics is 0.24, then the probability that they do not take statistics is:

1 - 0.24 = 0.76

So the probability that a randomly chosen college student does not take statistics is 0.76 or 76%.