Adding rational expressions with different Subtract. (5)/(2)-(1)/(2d) Simplify your answer as much as possible.

a) The monthly interest rate for the $40,000 loan repaid monthly over 20 years with a monthly payment of $544.53 is 0.00153. b) The monthly interest rate for the $40,000 loan repaid monthly over 20 years with a monthly payment of $544.53 comes out as 0.00153 percent

To find the monthly payment needed to repay a $40,000 loan over 20 years with a 0.5% interest rate per month, we can use the following formula: Monthly payment = (Loan amount * Monthly interest rate) / (1 - (1 + Monthly interest rate)^-Number of payments)

Plugging in the given values: Monthly payment = ($40,000 * 0.005) / (1 - (1 + 0.005)^-240) Monthly payment = $200 / (1 - 0.334) Monthly payment = $200 / 0.666, Monthly payment = $300.30

Therefore, the monthly payment needed to repay the $40,000 loan over 20 years with a 0.5% interest rate per month is $300.30.To find the monthly interest rate for a $40,000 loan repaid monthly over 20 years with a monthly payment of $544.53, we can use the same formula and rearrange it to solve for the monthly interest rate:

Monthly interest rate = (Monthly payment * (1 - (1 + Monthly interest rate)^-Number of payments)) / Loan amount. Plugging in the given values:

0.005 = ($544.53 * (1 - (1 + 0.005)^-240)) / $40,000

0.005 * $40,000 = $544.53 * (1 - (1 + 0.005)^-240)

$200 = $544.53 * (1 - (1 + 0.005)^-240)

$200 / $544.53 = 1 - (1 + 0.005)^-240

0.367 = 1 - (1 + 0.005)^-240

(1 + 0.005)^-240 = 0.633

1 + 0.005 = 0.633^-240

0.005 = 0.633^-240 - 1

0.005 = -0.367

Monthly interest rate = -0.367 / -240

Monthly interest rate = 0.00153

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Answer:

Step-by-step explanation:

18

Step-by-step explanation:

The area A of a rectangle is given by multiplying its length and width. In this case, the length is 7x - 1 units and the width is 2x + 3 units. Therefore, the area of the rectangle is:

A = (7x - 1)(2x + 3)

= 14x^2 + 19x - 3

Hence, the area of the rectangle is 14x^2 + 19x - 3 square units.

Answer:

14x^2+19x-3

Step-by-step explanation:

you have to times them together so

(7x-1)(2x+3)

14x^2+21x-2x-3

=14x^2+19x-3

The ratio of the surface areas to cube A to cube B is 12 : 7 .

What is known as a cube?

Six faces, eight vertices, and twelve edges make up the three-dimensional shape of a cube. An example of a prism in particular is a cube. These are the calculations for the volume of the cube formula: Amount = (side) 3.

                      The cube's face's diagonal length is equal to 2. (edge) Cube's cube's diagonal length is three (edge) 12 is the perimeter (edge). Each number multiplied by itself is a square number. The squared sign is (insert square symbol). Up to the number 100, the square numbers are 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100. A number multiplied by itself three times is a cube number.

The ratio of the volumes of cube A to cube B is  =  1728 : 343

                                                                       = 12 : 7

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Answer:

$0.50

Step-by-step explanation:

We know

A package of 8 hot dogs is on sale for $4

What is the price per hot dog?

4 / 8 = $0.50

So, the price per hot dog is $0.50

The value of x for the similar triangles is 8 units.

The value of x is determined by applying the principle of similar triangles as shown below.

In the given diagram, we can assume the following for the similar triangles;

length 10 is congruent to length 10 + (3x + 1 )

length 22 is congruent to length 7x -1  + 22

So we will have the following equation;

(3x + 1  + 10 )/ 10 = (7x - 1 + 22 ) / 22

(3x + 11 ) / 10 = ( 7x + 21 ) / 22

22(3x + 11 ) = 10 (7x + 21 )

66x + 242 = 70x + 210

32 = 4x

x = 32 / 4

x = 8

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Answer:

The inequality that would represent the possible values for the number of hours lifeguarding, l, and the number of hours walking dogs, d, that Katherine can work in a given week is:

l + d ≤ 14

This is because the sum of the hours worked in both jobs should not exceed 14 hours.

Subtracting -2y² from -4y² + 5d will give us -2y² + 5d.

A polynomial is a mathematical expression consisting of variables and coefficients, which are combined using arithmetic operations such as addition, subtraction, and multiplication.

To subtract the two polynomials, we first need to distribute the negative sign to the second polynomial.

So, (-4y² + 5d) - (-2y²) becomes -4y² + 5d + 2y².

Now, combine the like terms, which are the terms that contain y²:

-4y² + 5d + 2y² = (-4 + 2)y² + 5d

So, our final answer is:

-2y² + 5d.

Since our answer is in simplest terms, the final answer is -2y² + 5d.

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The measure of the central angle in the "Punk" section is 72 degrees.

The measure of the central angle in the "Punk" section can be determined by calculating the percentage of punk songs sold in relation to the total number of songs sold, and then converting that percentage to degrees.

To calculate the percentage of punk songs sold, divide the number of punk songs sold by the total number of songs sold, and multiply by 100.

For example, if 200 punk songs were sold and the total number of songs sold was 1000, the percentage of punk songs sold would be:

200/1000 * 100 = 20%

To convert this percentage to degrees, multiply the percentage by 360 (the total number of degrees in a circle).

20% * 360 = 72 degrees

Therefore, the measure of the central angle in the "Punk" section is 72 degrees.

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8×4=32

11-8=3

4×3=12

12÷2=6

32+6=38

=38inch^2

it might b wrong tho?

Answer:

15%

Step-by-step explanation:

Answer:

To find the total surface area of a square pyramid, we need to find the sum of the areas of its base and its four triangular faces.

In this case, the base is a square with side length 11.5 inches. Therefore, its area is:

Area of base = 11.5^2 = 132.25 square inches

Each triangular face has a base length equal to the side length of the square base, which is 11.5 inches. To find the height of each triangular face, we can use the Pythagorean theorem. Since the pyramid is a square pyramid, the height of each triangular face is also the slant height of the pyramid.

The slant height of the pyramid can be found using the Pythagorean theorem:

a^2 + b^2 = c^2

where a = b = 11.5/2 = 5.75 (half the length of a diagonal of the square base) and c is the slant height. Solving for c, we get:

c = sqrt(a^2 + b^2) = sqrt(2*(5.75)^2) = 8.121 inches (rounded to 3 decimal places)

The area of each triangular face can be found using the formula:

Area of triangle = (1/2) * base * height

where the base is 11.5 inches and the height is 8.121 inches.

Area of each triangular face = (1/2) * 11.5 * 8.121 = 46.876 square inches (rounded to 3 decimal places)

So, the total surface area of the square pyramid is:

Total surface area = Area of base + 4 * Area of each triangular face

Total surface area = 132.25 + 4 * 46.876 = 330.124 square inches (rounded to 3 decimal places)

Therefore, the total surface area of the square pyramid is approximately 330.124 square inches.

Answer:

The area of the whole rectangle is 28 cm^2

Step-by-step explanation:

since both triangles are congruent, they have the same area. 14 x 2 = 28

The greatest common factor of these three expressions, 28w, 8w⁵, and 20w⁴, is 4w.

The greatest common factor (GCF) of three univariate monomials is the largest factor that divides all three expressions. To find the GCF of 28w, 8w⁵, and 20w⁴, we need to find the largest factor that is common to all three expressions.

First, we need to find the GCF of the coefficients of the three expressions. The GCF of 28, 8, and 20 is 4.

Next, we need to find the GCF of the variables of the three expressions. The GCF of w, w⁵, and w⁴ is w, since it is the lowest power of w that is common to all three expressions.

Therefore, the GCF of 28w, 8w⁵, and 20w⁴ is 4w.

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Answer:

Twenty Seven (27) cubic yards

Answer:

volume =27 cubic yards

Step-by-step explanation:

Volume = Base Area x Height

Volume= 3·3·3

Volume= 27

Answer:$7.49

Step-by-step explanation:

just subtract 42.50 from 49.99
49.99-42.50=7.49

Answer:

2500

Step-by-step explanation:

Total spectator 9500

Men 6375

Women and children = 9500-6375= 3125

Women X

Children 4X

If women and children = 3125

4x + X = 3125

5x = 3125

Divide both sides by 5

X = 625

Women 625

Children 625x4 = 2500

The answer in simplest form is 9/2

The division involving a whole number and a fraction can be simplified by multiplying the whole number by the reciprocal of the fraction.

The reciprocal of a fraction is obtained by flipping the numerator and denominator.

In this case, the division is 3 ÷ (2/3). The reciprocal of (2/3) is (3/2).

So, we can multiply 3 by (3/2) to simplify the division:

3 × (3/2) = (3/1) × (3/2) = (3 × 3) / (1 × 2) = 9/2

Therefore, the answer in simplest form is 9/2.

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A double number line means the values of two different quantities are expressed in two separate lines such as corresponding values align. Here 1ml of blue water will need 3 ml of yellow water.

Here double line represents the relation between yellow water and blue water required to produce green water. 5ml of blue water needs 15ml of yellow water.

So the ratio is 5 : 15

3. One division in the line for blue water represents 1ml and 1 division in yellow water line is 3 ml.

We can also solve it using proportions

5 : 15 :: 1: x

5/15 = 1/x

x = (1×15)/5 = 3 ml

4. For 11 ml of blue water, it will require 33 ml of yellow water.

5. For 8 ml of blue water, 24 ml of yellow water is needed.

6. If we know the volume needed with 1ml of blue water, we can multiply that volume with any quantities of blue water to calculate the volume needed. For example 4 ml of blue water needs 4×3 = 12 ml of yellow water.

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The complete question is as below.

The other day, we made green water by mixing 5 ml of blue water with 15 ml of yellow water. We want to make a very small batch of the same shade of green water. We need to know how much yellow water to mix with only 1 ml of blue water.

1. On the number line for blue water, label the four tick marks shown.

2. On the number line for yellow water, draw and label tick marks to show the amount of yellow water needed for each amount of blue water.

3. How much yellow water should be used for 1 ml of blue water? Circle where you can see this on the double number line.

4. How much yellow water should be used for 11 ml of blue water?

5. How much yellow water should be used for 8 ml of blue water?

6. Why is it useful to know how much yellow water should be used with 1 ml of blue water?

The solution for u is 36.

To solve for u using the multiplicative property of equality, we need to isolate u on one side of the equation. We can do this by multiplying both sides of the equation by the reciprocal of the fraction that is attached to u. The reciprocal of (5/6) is (6/5), so we can multiply both sides of the equation by (6/5) to get:

(6/5) * 30 = (6/5) * (5/6) * u

Simplifying the right side of the equation gives us:

(6/5) * 30 = u

Multiplying the fraction and the whole number gives us:

(180/5) = u

Simplifying the fraction gives us:

36 = u

Therefore, the solution for u is 36.

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The volume of the solid is 284π/3 cubic inches.

To find the volume of the solid, we need to break it down into simpler shapes and then calculate their volumes separately.

The solid is made up of a cylinder and a hemispherical hole cut from the top of it. Let's first calculate the volume of the cylinder. The height of the cylinder is given as 12 inches and the radius can be calculated as half of the hypotenuse of the triangle (which is 10 inches). Therefore, the radius of the cylinder is 5 inches.

The formula for the volume of a cylinder is Vcylinder = πr^2h, where r is the radius and h is the height. Substituting the values, we get:

Vcylinder = π(5^2)(12) = 300π cubic inches

Now, let's calculate the volume of the hemispherical hole. The rim of the hole is 3 inches thick, which means the radius of the hole is (5 - 3) = 2 inches. The volume of a hemisphere is given by the formula Vhemisphere = (2/3)πr^3.

Substituting the values, we get:

Vhemisphere = (2/3)π(2^3) = 16π/3 cubic inches

Now, the volume of the solid can be found by subtracting the volume of the hemispherical hole from the volume of the cylinder:

Vsolid = Vcylinder - Vhemisphere

Vsolid = 300π - 16π/3

Vsolid = 284π/3 cubic inches

Therefore, the volume of the solid is 284π/3 cubic inches.

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The angle between \( \mathbf{u}=\langle-4,-1\rangle \) and \( \mathbf{v}=\langle-5,-2\rangle \) is approximately 12.5 degrees. To the nearest tenth of a degree, we can round this to 12.5 degrees.

To find the angle between two vectors \( \mathbf{u} \) and \( \mathbf{v} \), we can use the formula:
\[ \cos \theta = \frac{\mathbf{u} \cdot \mathbf{v}}{\| \mathbf{u} \| \| \mathbf{v} \|} \]
where \( \theta \) is the angle between the vectors, \( \mathbf{u} \cdot \mathbf{v} \) is the dot product of the vectors, and \( \| \mathbf{u} \| \) and \( \| \mathbf{v} \| \) are the magnitudes of the vectors.

First, we need to find the dot product of \( \mathbf{u} \) and \( \mathbf{v} \):
\[ \mathbf{u} \cdot \mathbf{v} = (-4)(-5) + (-1)(-2) = 20 + 2 = 22 \]

Next, we need to find the magnitudes of \( \mathbf{u} \) and \( \mathbf{v} \):
\[ \| \mathbf{u} \| = \sqrt{(-4)^2 + (-1)^2} = \sqrt{16 + 1} = \sqrt{17} \]
\[ \| \mathbf{v} \| = \sqrt{(-5)^2 + (-2)^2} = \sqrt{25 + 4} = \sqrt{29} \]

Now we can plug these values into the formula and solve for \( \theta \):
\[ \cos \theta = \frac{22}{\sqrt{17} \sqrt{29}} \]
\[ \theta = \cos^{-1} \left( \frac{22}{\sqrt{17} \sqrt{29}} \right) \]

Using a calculator, we find that \( \theta \approx 12.5 \) degrees.

Therefore, the angle between \( \mathbf{u}=\langle-4,-1\rangle \) and \( \mathbf{v}=\langle-5,-2\rangle \) is approximately 12.5 degrees. To the nearest tenth of a degree, we can round this to 12.5 degrees.

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Answer:

A. X = -4

Step-by-step explanation:

[tex]-6x-24=3x+12\\-9x=36\\x=-4[/tex]

Answer:

Step-by-step explanation:

I just knew now I forgot sorry lol

Answer:

Elizabeth gave away 216 marbles out of a total of 360 marbles.

To find the percentage of marbles that Elizabeth gave away, we can use the formula:

percentage = (part/whole) x 100%

where "part" is the number of marbles Elizabeth gave away, and "whole" is the total number of marbles.

So, plugging in the values we have:

percentage = (216/360) x 100%

percentage = 0.6 x 100%

percentage = 60%

Therefore, Elizabeth gave away 60% of the marbles.

The expression when evaluated is -5

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

6(− 2/3 ) − 1.5 + ( 1/2 )

To solve the given expression, we need to apply the order of operations, which is a set of rules that dictate the order in which mathematical operations should be performed.

Using the order of operations, we can simplify the given expression as follows:

6(− 2/3 ) − 1.5 + ( 1/2 ) = -4 − 1.5 + 0.5

Evaluate

6(− 2/3 ) − 1.5 + ( 1/2 ) = -5

Hence, the solution is (b) - 5

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so since 45000 split on a 7:10:13 ratio, so let's simply divide 45000 by (7+10+13) and distribute accordingly to each daughter.

[tex]\stackrel{Ana}{7}~~ : ~~\stackrel{Betty}{10}~~ : ~~\stackrel{Chandra}{13} \\\\\\ \stackrel{Ana}{7\cdot \frac{45000}{7+10+13}}~~ : ~~\stackrel{Betty}{10\cdot \frac{45000}{7+10+13}}~~ : ~~\stackrel{Chandra}{13\cdot \frac{45000}{7+10+13}} \\\\\\ \stackrel{Ana}{7\cdot 1500}~~ : ~~\stackrel{Betty}{10\cdot 1500}~~ : ~~\stackrel{Chandra}{13\cdot 1500} ~~ \implies~\hfill \stackrel{Ana}{10500}~~ : ~~\stackrel{Betty}{15000}~~ : ~~\stackrel{Chandra}{19500}[/tex]

The total surface area of the given figures is:

1) 376 sq. feet

2)92sq. feet

What is meant by surface area?

The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface. A solid object's surface area is a measurement of the overall space that the object's surface takes up. Every geometric shape has a different surface area formula, but the goal of all of them is to determine the total area occupied by all of the objects' faces.

1) This figure is a cuboid.

  It has six faces and the opposite faces are of equal dimensions.

The surface area of a cuboid is the sum of the areas of each face.

Length l = 10 ft

Width w = 6 ft

Height h = 8 ft

Surface area = 2lw+2lh+2hw = 2 ( lw+ lh+ hw)

                                     = 2 ( 10*6 + 10*8 + 8*6) = 376 sq. feet

2) This figure has 2 similar right triangle faces.

Sum of area of both triangles = 2 * 1/2 * base * height = 3 * 4 = 12 sq. feet

There are two rectangular faces.

Area of front rectangular face = 10 * 5 = 50 sq. feet

Area of base rectangular face = 10*3 = 30 sq. feet

 Total surface area = 12 + 50 + 30 = 92sq. feet

Therefore the total surface area of the given figures is:

1) 376 sq. feet

2)92sq. feet

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Answer:

78

Step-by-step explanation:

To simplify the complex fraction ((1)/(f^(3))-(1)/(a^(3)))/((1)/(f^(2))-(1)/(a^(2))), we can use the common denominator method.

Step 1: Find the common denominator for the numerator and denominator of the complex fraction. The common denominator for the numerator is (f^(3))(a^(3)) and the common denominator for the denominator is (f^(2))(a^(2)).

Step 2: Multiply each term in the numerator and denominator by the common denominator to get rid of the fractions.

Numerator: ((1)(a^(3))-(1)(f^(3)))/(f^(3))(a^(3))

Denominator: ((1)(a^(2))-(1)(f^(2)))/(f^(2))(a^(2))

Step 3: Simplify the numerator and denominator by combining like terms.

Numerator: (a^(3)-f^(3))/(f^(3))(a^(3))

Denominator: (a^(2)-f^(2))/(f^(2))(a^(2))

Step 4: Divide the numerator and denominator by the common factor (f^(2))(a^(2)).

Simplified fraction: (a-f)/(f^(1))(a^(1))

Step 5: Simplify the final fraction by canceling out the common factors.

Final answer: (a-f)/(fa)

Therefore, the simplified complex fraction is (a-f)/(fa).

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