Diego’s family car holds 14 gallons of fuel. Each day the car uses 0.6 gallons of fuel. A warning light comes on when the remaining fuel is 1.5 gallons or less. Starting from a full tank, can Diego’s family drive the car for 25 days without the warning light coming on? Explain or show your reasoning.

After solving the given equation In [tex]e^{lnx} +[/tex] in [tex]e ^{lnx2}[/tex] = 2 in 8, we know that the value of x is (B) 4.

The equals sign is a mathematical symbol that indicates that two expressions in a formula are equal.

A mathematical statement known as an equation is one that uses the word "equal to" between two expressions with the same value.

As in 3x + 5 = 15, for example.

Equations can be of many different types, such as linear, quadratic, cubic, and others.

So, we have the equation:

[tex]Ine^{inx} + Ine^{Inx2}[/tex] [tex]= 2In8,[/tex]

Now, solve the following equation as follows:

[tex]Inx * Ine +Inx^2 * Ine = 2In8[/tex]

[tex]e^{Inx}+Ine^{Inx2} = 2in8[/tex]

[tex]Inx+Inx^2 = In8^2[/tex]

[tex]In* (x*x^2) In64[/tex]

[tex]x^2 = 64 =4^3[/tex]

[tex]x=4[/tex]

Therefore, after solving the given equation In [tex]e^{lnx }[/tex] + in[tex]e ^{lnx2}[/tex] = 2in8, we know that the value of x is (B) 4.

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Correct question:

What is the true solution to the equation below? In [tex]e^{lnx}[/tex]+ in [tex]e ^{lnx2}[/tex] = 2 in 8

a x = 2

b x = 4

c x = 8

d x = 64

If more than 400 sheets are duplicated, this equation will provide us with the overall expense, t.

A method that describes how two lines along both side of a sign connect each other. It typically contains an equal symbol and one variable. Similarly, 2x - 4 = 2. The variable x is present in the particular circumstance.

The equation that could be used to calculate the total cost, t, to copy p pages when p is greater than 400 is:

t = $5,000 + ($0.01 × (p - 400))

The base cost for copying the first 400 pages is $5,000. For each additional page above 400, the customer is charged $0.01 per page. Therefore, to calculate the total cost for copying p pages, we need to subtract 400 from p to determine the number of pages that are being charged at the additional rate, and then multiply that by $0.01 to determine the additional cost. This gives us:

Additional cost = $0.01 × (p - 400)

The total cost is then the sum of the base cost and the additional cost:

t = $5,000 + ($0.01 × (p - 400))

This equation will give us the total cost, t, for any number of pages greater than 400 that are copied.

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Answer:

I believe the answer you are looking for is [tex]6b^{4}[/tex] -  [tex]8b^{2}[/tex]

Step-by-step explanation:

Hope it helps

Sorry if I'm wrong

All the real solutions of the equation are x=3, x=1, and x=-2. The rational root theorem states that any rational root of the equation x³-2x²-5x+6=0 can be written in the form p/q, where p is a factor of the constant term (6) and q is a factor of the leading coefficient (1). Therefore, the possible rational roots of the equation are: ±1, ±2, ±3, ±6

We can use synthetic division to test each of these possible roots until we find one that gives a remainder of 0.

1 | 1 -2 -5 6
 |   1 -1 4
 |_____________
 | 1 -1 -6 10

The remainder is not 0, so 1 is not a root of the equation.

-1 | 1 -2 -5 6
  |  -1  3 2
  |_____________
  | 1 -3 -2 8

The remainder is not 0, so -1 is not a root of the equation.

2 | 1 -2 -5 6
 |   2  0 10
 |_____________
 | 1  0 -5 16

The remainder is not 0, so 2 is not a root of the equation.

-2 | 1 -2 -5 6
  |  -2  8 14
  |_____________
  | 1 -4  3 20

The remainder is not 0, so -2 is not a root of the equation.

3 | 1 -2 -5 6
 |   3  3 0
 |_____________
 | 1  1 -2 6

The remainder is 0, so 3 is a root of the equation. We can use the quotient (1x²+1x-2) to find the remaining roots of the equation.

1x²+1x-2=0

Using the quadratic formula, we can find the remaining roots:

x = (-1 ± √(1²-4(1)(-2)))/(2(1))

x = (-1 ± √(1+8))/2

x = (-1 ± √9)/2

x = (-1 ± 3)/2

x = 1 or x = -2

Therefore, the real solutions using rational root theorem and quadratic formula are of the equation are x=3, x=1, and x=-2.

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Answer:

21.6 feet?

Step-by-step explanation:

8 percent of 3 is 0.24

0.24 x 90 is 21.6

The new points after the translation are (0, -4), (0, 0), (5, -5) and (5, 0) and the image is added as attachment

Translation is the movement of a point either up, left, right or down on the coordinate plane.

If a point A(x, y) is translated a units left and b units down, the new point is A'(x - a, y - b)

From the question, the vertices of the rectangle are (2, 3), (2, 7), (7, 2) and (7, 7).

The translation T<-2, -7>; is a translation of 2 units left and 7 units down.

This means that

The new points are (0, -4), (0, 0), (5, -5) and (5, 0).

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The probability of rolling a sum greater than 5 is 13/18.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes

There are six different possible outcomes for a dice, the set (S) of all the outcomes can be listed as follows:

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

a) The probability of rolling a sum of even number

Number of favorable outcomes = 9

Total number of outcomes = 36

Now, probability = 9/36

= 1/4

b) The probability of rolling a sum of odd numbers

Number of favorable outcomes = 9

Total number of outcomes = 36

Now, probability = 9/36

= 1/4

c) The probability of rolling a sum of greater than 5

Number of favorable outcomes = 26

Total number of outcomes = 36

Now, probability = 26/36

= 13/18

Therefore, the probability of rolling a sum greater than 5 is 13/18.

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[tex] \: [/tex]

_________

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \small{\star \boxed{ \tt \color{blue} volume \: of \: cone \: = \frac{1}{3}h\pi {r}^{2} }}[/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

━━━━━━━━━━━━━━━━━━━━━━━━━

hope it helps! :)

The graph of the functions are added as an attachment

The graphs are sinusoidal functions such that they are mathematical functions that exhibit a repetitive pattern over time or space

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

y = 4cot(4x)

y = -1/2cot(2x - π/4)

To plot y = 4cot(4x) using two periods, we make use of the domain

{0 < x < π/2}

To plot y = 4cot(4x) using two periods, we make use of the domain

{0 < x < π}

See attachement for the graphs of the functions

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There will be 22 blue signs at the end of the event.

The probability of an event can be determined by dividing the number of favorable outcomes by the total number of possible outcomes. For example, the probability of rolling a six on a standard six-sided die is 1/6, as there is only one favorable outcome (rolling a six) out of six possible outcomes (rolling a one, two, three, four, five, or six).

To solve this problem, we need to consider the factors that determine whether a house's sign will be flipped or not. A sign will only be flipped if the number of residents can divide the house number. For example, the sign on house number 12 will be flipped by the residents of that house because 12 is divisible by 2, 3, 4, and 6 (the factors of 12).

At the beginning, all signs are red, which means that none of the houses have had their sign flipped yet. Let's start with house number 1 and consider which houses will flip its sign.

For house number 1, its sign will not be flipped because 1 is only divisible by 1.

For house number 2, its sign will be flipped because 2 is divisible by 2.

For house number 3, its sign will not be flipped because 3 is only divisible by 1 and 3.

For house number 4, its sign will be flipped because 4 is divisible by 2 and 4.

For house number 5, its sign will not be flipped because 5 is only divisible by 1 and 5.

And so on, continuing this process for all 500 houses.

We can see that the signs on the houses with numbers that have an odd number of factors will end up blue, and the signs on the houses with numbers that have an even number of factors will end up red. This is because a factor always comes in pairs, except when the number is a perfect square, in which case the factor pair is identical (e.g. 4 has factors 1, 2, and 4, which is an odd number of factors).

So we need to count the number of integers from 1 to 500 that have an odd number of factors. These are the perfect squares, which are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, and 484.

Therefore, there will be 22 blue signs at the end of the event.

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We deduced the following from the given phrase:

1) The supplied expression is a sum with the four terms a, b, l, and c.

2) 2c is the result of the factors 2 and c on its own.

A function is a relationship between a number of inputs and outputs. Simply described, a function is an association between inputs in which each input is coupled to exactly one output. For each function, there is a corresponding range, codomain, and domain.

What follows is:

A + (b+1) + 2c is the function that has been discovered and written in the question.

As we can see, three distinct terms—a, b+1, and 2c—have been demonstrated to be a part of this function.

As a result, we deduced the following from the above formula:

1) With the four terms a, b, 1 and 2c, the complete equation is a sum.

2) 2c is the result of the factors 2 and c on its own.

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The complete question is:

On its own 2c is a product with

Answer:

θ = 78.69°

Step-by-step explanation:

As this is a right angle triangle we use trigonometric ratios/

The perpendicular i.e the height of the mast = 50 ft

The base i.e the shadow = 10 ft

tanθ = perpendicular / base

tanθ = 50/10

θ = [tex]tan^{-1}[/tex] (50/10)

θ = 78.69°

We can write tanz in terms of secz using the Pythagorean Identity as:
tanz = -sqrt(sec^2z - 1)

Part 1 of 2:
The Pythagorean Identity states that sin^2z + cos^2z = 1. We can use this identity to write tan^2z in terms of sec^2z.

First, let's rearrange the Pythagorean Identity to isolate cos^2z:
cos^2z = 1 - sin^2z

Next, we can divide both sides of the equation by cos^2z to get:
1 = sec^2z - (sin^2z)/(cos^2z)

Since tan^2z = (sin^2z)/(cos^2z), we can substitute this into the equation:
1 = sec^2z - tan^2z

Finally, we can rearrange the equation to isolate tan^2z:
tan^2z = sec^2z - 1

Now, let's consider the case when z is in Quadrant II. In this quadrant, tanz is negative and secz is negative. Therefore, we can write:
tanz = -sqrt(sec^2z - 1)

Part 2 of 2:
In the case when z is in Quadrant IV, tanz is negative and secz is positive. Therefore, we can write:
tanz = -sqrt(sec^2z - 1)

So, in both cases, we can write tanz in terms of secz using the Pythagorean Identity as:
tanz = -sqrt(sec^2z - 1)

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Answer:

perfect square therefore rational

non perfect square therefore irrational

cuberoot

5

Step-by-step explanation:

the topic is about perfect squares and rationality of numbers

Option (c) has the same equation as above after simplification, so the answer is (c):y-8=-0.2(x+10).

Simplification involves reducing an expression, equation, or problem to a simpler form. This can involve performing operations such as combining like terms, factoring, or canceling out common factors.

Point-slope form is a way of writing the equation of a straight line in two-dimensional space, using a given point on the line and the line's slope.

The point-slope form equation for a line passing through a point (x1, y1) with slope m is:y - y1 = m(x - x1).

In the given question,

To write the equation of a line in point-slope form, we need to use the formula:

y - y1 = m(x - x1)

where m is the slope of the line and (x1, y1) is any point on the line.

We are given two points on the line: (-10, 8) and (10, 4). We can use these points to find the slope of the line:

m = (y2 - y1) / (x2 - x1)

= (4 - 8) / (10 - (-10))

= -0.15

Now we can use the point-slope form with the point (-10, 8) and slope -0.15:

y - 8 = -0.15(x - (-10))

Simplifying this equation, we get:

y - 8 = -0.15(x + 10)

Option (c) has the same equation as above after simplification, so the answer is (c):

y-8=-0.2(x+10).

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The solutions to this problem are y = 5 and y = -1/3.

Sure! The quadratic formula is a useful tool for solving equations of the form ax^2 + bx + c = 0. In this problem, we need to rearrange the equation so that it fits this form before we can use the quadratic formula.

First, let's multiply both sides of the equation by y to get rid of the fraction:

y^2 + 1 = 13y/6

Next, let's rearrange the equation so that it equals zero:

y^2 - 13y/6 - 1 = 0

Now we can use the quadratic formula to solve for y. The quadratic formula is:

y = (-b ± √(b^2 - 4ac))/(2a)

In this problem, a = 1, b = -13/6, and c = -1. Plugging these values into the quadratic formula gives us:

y = (-(-13/6) ± √((-13/6)^2 - 4(1)(-1)))/(2(1))

Simplifying the equation gives us:

y = (13/6 ± √(169/36 + 4))/2

Finally, we can solve for y by simplifying the square root and dividing by 2:

y = (13/6 ± √(289/36))/2

y = (13/6 ± 17/6)/2

y = (30/6)/2 or y = (-4/6)/2

y = 5 or y = -1/3

So the solutions to this problem are y = 5 and y = -1/3. I hope this helps! Let me know if you have any further questions.

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An equation that best represents the relationship between x and y in the graph is: A. y = -3x/4 - 3.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

At point (-4, 0), an equation of this line can be calculated by using the point-slope form:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 0 = (-3 - 0)/(0 + 4)(x + 4)

y - 0 = -3/4(x + 4)

y = -3x/4 - 3.

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Step-by-step explanation:

Since the new poison kills half the population every 2 months, we can say that the remaining half will survive for another 2 months. Therefore, after 2 months, the rodent population will be half of 1,000,000, which is 500,000.

After another 2 months, the remaining half of the 500,000 will survive, which is 250,000.

After another 2 months, the remaining half of the 250,000 will survive, which is 125,000.

After 6 months, the rodent population will be 125,000.

Since 12 months is six 2-month periods, we can repeat this process again. After another 2 months, the rodent population will be 62,500.

After another 2 months, the rodent population will be 31,250.

After another 2 months, the rodent population will be 15,625.

Therefore, after 12 months, the rodent population will be 15,625.

Answer:

$81

Step-by-step explanation:

36/4 = 9

We can deduce that each shirt costs $9 so...

9x9 = 81

To simplify the expression (5 + 3i)(7 – 4i), two important processes to remember are to use the distributive property to multiply the real parts and imaginary parts separately and simplify the resulting expression by combining any like terms.

Use the distributive property:

For the expression (5 + 3i)(7 – 4i),

(5 + 3i)(7 – 4i) = 5(7) + 5(-4i) + 3i(7) + 3i(-4i)

= 35 - 20i + 21i - 12i^2

Note that i^2 = -1,

35 + i(21 - 20) - 12(-1) = 47 + i(41)

Simplify the resulting expression:

After using the distributive property to expand the expression, we can simplify the resulting expression by combining any like terms. In this case, there are no like terms to combine, so our final answer is:

(5 + 3i)(7 – 4i) = 47 + 41i

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The length of MN, to the nearest tenth of a unit is equal to: C. 14.4 units.

In order to determine the missing side length of a geometric figure with the adjacent and hypotenuse side lengths given, you should apply the law of cosine:

C² = A² + B² - 2(A)(B)cosθ

Where:

A, B, and C is the length of side of a given triangle.

By substituting the given side lengths and angle into the law of cosine formula, we have the following;

MN² = LM² + LN² - 2(LM)(LN)cosθ

MN² = 12² + 10² - 2(12)(10)cos(52)

MN² = 144 + 100 - 147.76

MN = √96.24

MN = 9.8 units.

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The scale factor of dilation is 3.

What is Dilation of a circle?

Dilation is the process of altering an object's or shape's size by reducing or enlarging its dimensions by a certain amount of scale. A circle with a radius of 10 units, for instance, is reduced to a circle with a radius of 5 units. This technique is applied in art and craft, photography, and logo design, among other fields.

Given : Radius of original circle A = 3

            Radius of Dilation circle B = 9

We know that, Scale factor of dilation =

Dimension of Dilation shape / Dimension of original shape

So, Scale factor of given dilation = Radius of Circle B / Radius of Circle A

                                                      = 9/3

                                                      = 3.

Hence, Scale factor of dilation of circle B on Circle A is 3.

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11. The area of the floor is 24. 62 m²

12. The area of the enclosed string is 3, 853. 09cm²

13. The circumference of the circular mat is  4.39m

The formula for the area of a circle is expressed with the equation;

A = πr²

Where;

Also, circumference of a circle is 2πr

For a circumference of 17. 6m, we have

17. 6 = 2×3.14r

r = 2. 80

Substitute the value

Area = 3.14 × (2. 80)²

Area = 24. 62 m²

For the string, circumference = 220cm

220 = 2× 31.4r

r = 35. 03 cm

Area of the enclosed string = 3.14 × (35. 03)²

Area = 3, 853. 09cm²

For the circular mat

1.54 = 3.14r²

r² = 0. 49

Take the square root

r = 0. 7m

Circumference = 2× 3.14 × 0. 7 = 4.39m

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You should invest $26,100 in Stock Boll and $12,900 in Stock Coff to maximize your annual interest earned, and the maximum annual interest is $2,337.

To maximize your annual interest earned, you should invest as much money as possible in the stock with the higher interest rate, which is Stock Coff. However, there are two constraints that you need to consider: the buying limit on Stock Coff and the requirement to spend at least twice as much money on Stock Boll as Stock Coff.

Let's use algebra to solve this problem. Let x be the amount of money you invest in Stock Boll and y be the amount of money you invest in Stock Coff. Then we have the following equations:

x + y = $39,000 (the total amount of money you have to invest)
y <= $12,900 (the buying limit on Stock Coff)
x >= 2y (the requirement to spend at least twice as much money on Stock Boll as Stock Coff)

To maximize your annual interest earned, you want to maximize the expression 0.05x + 0.08y (the sum of the interest earned from Stock Boll and Stock Coff).

If you invest the maximum amount of money in Stock Coff ($12,900), then you have $39,000 - $12,900 = $26,100 left to invest in Stock Boll. This satisfies the requirement to spend at least twice as much money on Stock Boll as Stock Coff ($26,100 >= 2 * $12,900).

So the optimal solution is to invest $26,100 in Stock Boll and $12,900 in Stock Coff. The maximum annual interest earned is 0.05 * $26,100 + 0.08 * $12,900 = $1,305 + $1,032 = $2,337.

Therefore, you should invest $26,100 in Stock Boll and $12,900 in Stock Coff to maximize your annual interest earned, and the maximum annual interest is $2,337.

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The 7th term of the geometric sequence is 5,103.

To find the 7th term of a geometric sequence with a first term of 7 and a common ratio of -3, we can use the formula:

an = a1 × [tex]r^(n-1)[/tex]

where an is the nth term of the sequence, a1 is the first term of the sequence, r is the common ratio, and n is the number of the term we want to find.

Substituting the given values, we get:

a7 = 7 × [tex](-3)^(7-1)[/tex]

Simplifying the exponent, we get:

a7 = 7 × [tex](-3)^6[/tex]

Evaluating the exponent, we get:

a7 = 7 × 729

Multiplying, we get:

a7 = 5,103

Therefore, the 7th term of the geometric sequence is 5,103.

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A labour economist aims to estimate the variance of unemployed workers' mathematic test scores. Assume that a random sample of 18 scores had a sample standard deviation of 10.4. To form a 90% confidence interval for the population varianceis The confidence interval is exactly between 46.64 and 202.07. The correct answer is option (a)



Find the degrees of freedom (df) by subtracting 1 from the sample size:
df = n - 1 = 18 - 1 = 17

Find the chi-square values for the 90% confidence interval using a chi-square table or calculator. The lower value corresponds to the 5th percentile (0.05) and the upper value corresponds to the 95th percentile (0.95):
χ² lower = 27.488
χ² upper = 8.672

Calculate the lower and upper limits of the confidence interval using the formula:
CI lower = (df * s²) / χ²_upper
CI upper = (df * s²) / χ²_lower

Where s² is the sample variance (the square of the sample standard deviation):
s² = 10.4² = 108.16

Plugging in the values:
CI lower = (17 * 108.16) / 27.488 = 46.64
CI upper = (17 * 108.16) / 8.672 = 202.07

The 90% confidence interval for the population variance is between the lower and upper limits:
CI = (46.64, 202.07)

Therefore, the correct answer is option (a) The confidence interval is exactly between 46.64 and 202.07.

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Answer:

56%, 4/5, 1.07, 5/4

Step-by-step explanation:

5/4=1.25

56%=0.56

1.07

4/5=0.8

so the order is

56%, 4/5, 1.07, 5/4

As one loaf of bread weighs about 1 pound, the metric measures that are less than 1 pound are:

The pound means the unit of measurement used in the U. S. customary system and the British imperial system to measure weight. One familiar use of pounds is measuring how much a person weighs.

A pound is approximately 0.4535 kilogrammes, so 453.5 grammes. With this information, we can determine that answers 450 grammes and 100 grammes are the only correct ones because they are lesser than 453.5 grammes.

Full question "A loaf of bread weighs about 1pound. Chose all of the metric measures that are less than 1pound. 1kg 0.5kg 500g 450g 100g"

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By solving the given equation, we can plot these two points on a coordinate plane, and then connect the points with a line. The formed line is the graph of the linear equation 3y=2x-7.

The coordinate plane is made up of two perpendicular lines called the x-axis and the y-axis. The x-axis, which is horizontal, is used to measure the distance of a point from the left and right side of the plane. The y-axis, which is vertical, is used to measure the distance of a point from the top and bottom of the plane.

To graph the equation 3y=2x-7, we first need to identify two points that satisfy the equation. We can do this by plugging in different values for x and solving for y. For example, when x=0, the equation becomes 3y=-7. Thus, one point that satisfies the equation is (0,-7). We can find a second point by plugging in a different value for x. For example, when x=2, the equation becomes 3y=-3. Thus, the second point that satisfies the equation is (2,-3).

Now, we can plot these two points on a coordinate plane, and then connect the points with a line. The formed line is the graph of the linear equation 3y=2x-7.

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The first monthly charge has about $78.78 allotted in the direction of reducing the principal.

The total buy charge of the house is $96,400 and the Spinoses made a 25% down payment, because of this they paid $96,400 x 0.25 = $24,100 in advance.

Therefore, the final quantity that they financed is $96,400 - $24,100 = $72,300.

They financed this amount at 5.50% for 30 years, which gives us the following method for calculating the monthly payment (P):

P = (r * PV) / (1 - (1 + r)^(-n))

in which:

Substituting the values, we get:

P = (0.00458 * 72,300) / (1 - (1 + 0.00458)^(-360))

P ≈ $410.66

We recognise that the monthly payment is $410.66 and we will calculate the interest portion of the primary monthly price as follows:

interest = balance * monthly interest price

interest = $72,300 * (5.50% / 12) ≈ $331.88

To calculate the amount of the primary monthly charge this is used to lessen the fundamental, we subtract the interest component from the total monthly payment:

$410.66 - $331.88 ≈ $78.78

Thus, the first monthly charge has about $78.78 allotted in the direction of reducing the principal.

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