If a family borrows $12,843 for an addition to their home, and the loan is to be paid off in monthly payments over a period of 5 years, how much should each payment be? (Interest has been included in the total amount borrowed.)

Answer:

Below

Step-by-step explanation:

See diagram

.158384 = height/x      <======   x = height/.15838

.061162 = height /(11+x)    <====sub in x from above into here

.061162 = height /(11+height/.158384)      solve for height

.672789 + .386163 height = height

height = 1.1 mi high

Answer:

Fred spent $3.18 on brownies.

The value of the given expression, -50 + 5/13p, when p = -26 is -60

From the question, we are to evaluate the given expression for the given value of p

The given expression is

-50 + 5/13p

and

The given value of p is p = - 26

Substitute the given value of p into the given expression

That is,

-50 + 5/13p

When p = -26, the expression becomes

-50 + 5/13(-26)

Simplify

-50 + 5(-2)

-50 - 10

= - 60

Hence, the value of the expression is -60

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31/6 or 5.167 feet of lumber was left.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Given,  Peter cut a piece of lumber 9 5/6 feet long from a piece that was 15 feet long.

Since the total length of wood is 15 feet

Thus,

The remaining wood = 15 - (9 5/6)

The remaining wood = 6 - 5/6

The remaining wood = 31/6

therefore, 31/6 or 5.167 feet of the lumber was left.

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Answer:

121

Step-by-step explanation:

The formula for calculating the sum of interior angles is ( n − 2 ) × 180

so you have 5 sides n=5

so total is 3*180 = 540

there are 3 right angles = 3/90 = 270

so 540-270 = 270 = angle B+ angle C

so 6x+1 +8x-11 =270

14x-10 = 270

14 x =280

x=20

B =6x+1 =121

Two lines that are perpendicular to one another have a slope product that is negative one. If m1 and m2 are the slopes of the two lines, then m1.m2 = -1.

As a result, we may state that m1 = 4, which is the slope of this line.

As a result, m2 = -1/4 is the slope of the line perpendicular to this line.

Now, the 2nd line's general equation can be expressed as

y = (-1/4)x + c —— 1)

Since point (-12,4) is located on this line, we may solve for c by substituting y = -12 and x = 4 in the equation above.

We may finish the equation for the line perpendicular to the line y = 4x+3 once we know the value of c.

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The solution of the inequality 3x < 13 is x < 4.33.

None of the given option is correct.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

An inequality,

3x < 13.

Simplifying,

x < 4.33

The graph is given in the attached image.

Therefore, the solution is x < 4.33.

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Answer:

Step-by-step explanation:

If 3<y<7 then,

0 < 14-2y < 8

14 - 2(3) = 8

14 - 2(7) = 0

The eigen values of matrix A  [tex]\left[\begin{array}{ccc}1&2&1\\0&2&1\\0&0&3\end{array}\right][/tex] are respectively, 1, 2, 3

In mathematics, the eigen values are characteristic roots of the equation

| A - λI |,

where,  A is matrix and λ is eigen value of the matrix

Properties of matrix,

1.  Sum of diagonal elements = Sum of eigen values

2. Determinant of matrix  = Product of eigen values

Given that,

Matrix A =    [tex]\left[\begin{array}{ccc}1&2&1\\0&2&1\\0&0&3\end{array}\right][/tex]

The eigen values of A = ?

It is known that,

For the upper and lower triangular matrix, eigen values of the matrix are diagonal elements,

given matrix is, upper triangular,

Diagonal elements are  1, 2, 3

So, The eigen values will be 1, 2, 3

Thus, the eigen values are  1, 2, 3

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The system of equations are solved and the number of performers for the show A is 10,034

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as T

Now , the value of T is

The total number of performers in the two shows T = 16,756

A + B = 16,756

The number of performers in show A = 3312 + number of performers in show B

Substituting the values in the equation , we get

A = B + 3,312

On simplifying the equation , we get

A + A - 3,312 = 16,756

Subtracting 3,312 on both sides of the equation , we get

2A = 16,756 + 3,312

2A = 20,068

A = 10,034

Hence , the equation is A = 10,034

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The solution for the One-Variable Addition Equations is,

1: d = 0.6,  2:  k = 11,  and 3: y = 3.

When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."

There are both one-variable and two-variable linear equations.

Given 1: d  + 3.2 = 6.3 - 2.5

subtract 3.2 from both sides

d = 6.3 - 2.5 - 3.2

d = 0.6

2: 25 + k + 4(1/4) = 37

divide 4/4 = 1

25 + k + 1 = 37

k = 37 - 26

k = 11

3: 4(1/2) + y = 10(1/2)

so 4/2 = 2 and 10/2 = 5

2 + y = 5

y = 3

Hence d  = 0.6, k = 11,  and y = 3.

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Answer:

a) C(n) = 0.74 * min(n, 100) + 0.69 * max(n - 100, 0)
b) 39.22
c)  143.69

Step-by-step explanation:

(a) We can write a piecewise function to describe the cost C(n) of n CDs purchased:

C(n) = 0.74 * min(n, 100) + 0.69 * max(n - 100, 0)

(b) The cost of 53 CDs is:

C(53) = 0.74 * min(53, 100) + 0.69 * max(53 - 100, 0) = 0.74 * 53 = 39.22

(c) The cost for 201 CDs is:

C(201) = 0.74 * min(201, 100) + 0.69 * max(201 - 100, 0) = 0.74 * 100 + 0.69 * 101 = 74 + 69.69 = 143.69

Answer:

The range of acceptable length is between 35.28 inches and 36.72 inches.

To calculate the range of acceptable length:

Lower bound: 36 in. - (36 in. x 0.05) = 35.28 in.

Upper bound: 36 in. + (36 in. x 0.05) = 36.72 in.

The domain is the second option:

(2, 8]

For a function y = f(x), we define the domain as the set of the possible inputs for the function.

Here we have a piecewise function that is defined in the 3 regions:

2 < x  ≤ 4

4 < x < 8

x ≥ 8

So the domain is the set of any value larger than 2, and we can write that as:

(2, 8]

We end it at "8" becase is the last defined value and that is the only option that makes sense.

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The equation of line is y = -2x + 9 , where the slope is m = -2

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

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

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the point be represented as P ( 1 , 7 )

Let the slope of the line be m = -2

And , equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

Substituting the values in the equation , we get

y - 7 = -2 ( x - 1 )

On simplifying the equation , we get

y - 7 = -2x + 2

Adding 7 on both sides of the equation , we get

y = -2x + 9

Hence , the equation of line is y = -2x + 9

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Answer: 1

               _

               32

Step-by-step explanation: because the are skip count and adding the number every single time .

Step-by-step explanation:

To solve the inequality |2x + 5| < 2 - x, we need to split it into two cases:

When 2x + 5 > 0:

In this case, the absolute value is positive, so we can simplify the inequality as follows:

2x + 5 < 2 - x

Expanding the left side:

3x + 5 < 2

Subtracting 5 from both sides:

3x < -3

Dividing both sides by 3:

x < -1

So the solution for this case is x < -1.

When 2x + 5 < 0:

In this case, the absolute value is negative, so we can simplify the inequality as follows:

(2x + 5) < 2 - x

Expanding the left side:

-2x - 5 < 2 - x

Adding x to both sides:

-2x - 5 + x < 2

Combining like terms:

-x - 5 < 2

Adding 5 to both sides:

-x < 7

Dividing both sides by -1:

x > -7

So the solution for this case is x > -7.

Taking the union of the two solutions, we get:

-7 < x < -1.

This means that x is between -7 and -1, excluding -7 and -1.

The equation which models the product is, A = 6 x 8

The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the components that are multiplied are referred to as the factors.

Given that,

A area model,

which has 6  box in column arrangement and 8  box in row arrangement,

Suppose, each box has 1 unit square area

Now, area of a model can be written as,

Area = Number of box in column x Number of box in row

Number of box in column  = 6

Number of box in row = 8

Each box has 1 unit square area,

So,

A = 6 x 8

   = 48 unit square

Hence, it can be represented as, A = 6 x 8

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From the audio, what is inferred from the fairy's action is that she was appreciative. The Option A is correct.

A fairy tale is a story, typically intended for children, that features fantastic and wondrous characters such as elves, goblins, wizards, and even, but not always, fairies. The term "fairy" tale appears to refer to a story's fantastic and magical setting or magical influences, rather than the presence of a fairy character within that story.

Fairy tales are frequently traditional; many were passed down from storyteller to storyteller before being written down in books. Examples of Fairy Tale includes Snow White, Cinderella, Rip Van Winkle, The Twelve Dancing Princesses, Rumpelstiltskin, Thumbelina

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Answer: She was vengeful

Step-by-step explanation:

The audio states that the other fairies were giving the princess positive spells while a fairy that wasn't invited to the party casted an evil spell on the princess, making her sleep for a 100 years. (It's based on the sleeping beauty story)

The Canal's price/earnings ratio is 2.92.

To calculate Canal's price/earnings ratio, we need to find the earnings per share (EPS) first. The EPS can be calculated by dividing the net income by the weighted average number of common shares outstanding.

The weighted average number of common shares outstanding can be calculated as follows:

Weighted average number of common shares outstanding = Total number of common shares - Weighted average number of treasury shares

Weighted average number of common shares outstanding = 24,200 - 4,200 = 20,000

EPS = Net income / Weighted average number of common shares outstanding

EPS = $260,000 / 20,000 = $13

Finally, the price/earnings ratio can be calculated by dividing the market price per share by the EPS:

Price/earnings ratio = Market price per share / EPS

Price/earnings ratio = $38 / $13 = 2.92

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Answer:

Step-by-step explanation:  https://flexbooks.ck12.org/cbook/ck-12-middle-school-math-concepts-grade-6/section/6.15/primary/lesson/elapsed-time-msm6/

Answer:

There are two solutions:

[tex]\boxed{v = \dfrac{4}{3} \text { and }v = \dfrac{3}{2}}\\\\or\\\\\boxed{v = 1.3333.... \text{ and }v= 1.5}\\[/tex]

Step-by-step explanation:

The given equation is  :

[tex]\dfrac{2}{v-2}=-6\:+\:\dfrac {1}{v-1}\\\\[/tex]

Find the LCM of the denominators:

LCM = [tex]\left(v-2\right)\left(v-1\right)[/tex]

Multiply by LCM:
[tex]\dfrac{2}{v-2}\left(v-2\right)\left(v-1\right)=-6\left(v-2\right)\left(v-1\right)+\dfrac{1}{v-1}\left(v-2\right)\left(v-1\right)[/tex]

Simplify

[tex]\dfrac{2}{v-2}\left(v-2\right)\left(v-1\right):\quad 2\left(v-1\right)[/tex]

[tex]\dfrac{1}{v-1}\left(v-2\right)\left(v-1\right):\quad v-2[/tex]

So the equality becomes
[tex]2\left(v-1\right)=-6\left(v-2\right)\left(v-1\right)+v-2[/tex]

Expand the brackets:
[tex]2\left(v-1\right):\quad 2v-2[/tex]

[tex]\text {Right side becomes: }\\-6\left(v-2\right)\left(v-1\right)+v-2\\Expand \; \left(v-2\right)\left(v-1\right):\quad v^2-3v+2\\\\\text {Right side becomes}\\-6\left(v^2-3v+2\right) + v -2\\= -6v^2+6\cdot \:3v-6\cdot \:2 + v - 2\\\\\\= -6v^2+18v-12+v-2\\\\\text{Simplify}\\= -6v^2+19v-14\\\\\text{Left side}2(v-1= 2v-2\\\\\text{Finally we get}\\2v - 2 = 6v^2+19v-14\\\\[/tex]

Switch sides:
[tex]-6v^2+19v-14=2v-2[/tex]

Move 2 from right to left(sign changes)
[tex]-6v^2+19v-14 + 2 =2v\\\rightarrow -6v^2+19v-12=2v\\\\[/tex]

Move 2v to left side(sign changes)

[tex]-6v^2+19v-12-2v = 0\\\\\rightarrow -6v^2+17v-12=0\\\\[/tex]

This is a quadratic equation which can be solved with a quadratic equation calculator. I used a calculator to solve this:

The solutions are:
[tex]v = \dfrac{4}{3} \text { and }v = \dfrac{3}{2}\\\\\\\text{In decimal these would be}\\\\v = 1.3333.... \text{ and v}= 1.5\\[/tex]

The cost of the book in Naira is N 24.99  

Mr. Awolowo needs to pay N 4165 at the post office.  

An exchange rate determines the value of one unit of currency in relation to another type of money. Which means exchanging the price from one currency to another currency.

People use the exchange rates when they want to travel abroad and It is necessary to convert cash into local currency in order to do purchases locally.

Here we have

The book costs £3. If the rate of exchange is £ 1 = N 8.33  

Cost of the book in Naira = 3 × N 8.33  

= N 24.99  

Mr Awolowo wants to send £500 to his brother in the United Kingdom  

As we know the rate of exchange, is £ 1 = N 8.33    

=>  £500 = 500 × 8.33  = N 4165  

Therefore,

The cost of the book in Naira is N 24.99  

Mr. Awolowo needs to pay N 4165 at the post office.  

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The area of a 7 by 10 grid would be 70 square units.

This is calculated by multiplying the length (7 units) by the width (10 units), resulting in 7 x 10 = 70.

7/3 in four different ways is 7/12

Division is the opposite of multiplication. If 3 groups of 4 make 12 in multiplication, 12 divided into 3 equal groups give 4 in each group in division. The main goal of dividing is to see how many equal groups are formed or how many are in each group when sharing fairly.

If 100 apples are to be shared by 20 girls equally. The number of apple each girl will get is 100/20 = 5 apples each.

Similarly to put 7/3 in four different ways we have to divide 7/3 by 4

7/3 ÷ 4 = 7/3 × 1/4

= 7/12

therefore 7/12 of the four places will give 7/3

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The domain and range are x >= 3 and y >= 0

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

The graph

The domain is the set of the input values

On the graph, we have

Input values start from x = 3 and increases

So, the domain is x >= 3

The range is the set of the output values

On the graph, we have

output values start from y = 0 and increases

So, the range is y >= 0

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The maximum value of the function z = 5x + 3y subjected to the constraints is given as follows:

48.1665.

The function for this problem is defined as follows:

z = 5x + 3y.

The constraints are given as follows:

x has a higher multiplier than y, hence the value of y should be minimized to obtain the maximum value, hence:

y = 3.

Then the value of x is obtained as follows:

6x + 7(3) = 68

6x = 47

x = 7.8333.

Then the maximum value of the function is given as follows:

z = 5(7.8333) + 3(3)

z = 48.1665.

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The three statements about his solution that are true include the following:

1. He should have found the average of the number of rock songs by averaging 4 and 6 to get 5.

2. He did not multiply the numerator and denominator by the correct number to equal 1,500.

5. He should have multiplied the numerator and denominator by 75, not 30,  because 20 × 75 = 1,500.

Based on the information provided, a mathematical expression which models the number of songs of each genre on Josiah's MP3 player to be 300 songs:

here, we have,

10/20 = x/1500

Multiplying the mathematical expression by 75, we have the following:

75 × (10/20) = x/1,500

750/1500 = x/1500

1,500x = (750 × 1,500)

x = (750 × 1,500)/1,500

x = 750.

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The fraction equivalent of 7/8 + 5/12 is 31/24

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

Given here: Two fractions 7/8 and 5/12

Now sum of the two fractions are 7/8+5/12

We know When two or more fractions with different denominators are added together, then we cannot the numerators directly. Thus Make the denominators of the fractions same, by finding the LCM of denominators and rationalising them with LCM(8,12)=24

Thus, 7/8+5/12= 21+10  /24

                        = 31/24

Hence, The fraction equivalent of 7/8 + 5/12 is 31/24

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