Is the following shape a rectangle

The value of a home increases by 7%each year, by compounding the value of the home doubles approximately once each decade.

Compounding is a process where the interest is credited to the initial amount and interest, on the whole, is charged again. and this continues for t period of time.

It is given by the formula,

A=P(1+r)^t

where A is the value after t period of time,

P is the value of the asset at the beginning, and,

r is the rate of interest.

The value of the home doubles once each decade.

Given to us

The value of a home increases by 7% each year.

As it is given that the value of a home increases by 7% each year, therefore, the value of the home is compounding every year.

We know the formula of compounding,

A=P(1+r)^t

Why does the value doubles?

Now, let's assume a house whose value is 'P' today, therefore, substitute the value of the house in the formula of compounding,

A=P(1+r)^t

Substitute the rate at which the value is increasing,

A=P(1+0.07)^t

We know that in a decade there are 10 years,

A=P(1+0.07)^10=P(1.07)^10

=1.967P

Approximately

=2P

As we can see that the value of the home is almost 2 times the 'P' therefore, twice the value of the home at the beginning.

Hence, the value of the home doubles once each decade.

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Answer:

No, No, Yes, No, Yes, Yes

Step-by-step explanation:

A graph is a function if it passes the vertical line test (in other words, every vertical line that can be drawn intersects the graph at no more than one point).

This is because for a function, each input must map onto no more than one output.

1. I beleive it would be 187,5$, 75.00 + 150% = 187,5.

2. if rounding it would be 9.1$ she had to pay for one times 3 would be 27.3 for three boxes.

3. Not sure what this question is asking but I'll try my best so here: 27.3 +9% × 3 = 89.271 rounded would be 90$

4. 90$ if I did that correctly

5. 1.38 - 1.25 = 0.13 which I beleive would be 13%

0.13 as a percent woudl be 13%

This vector equation represents all the points that lie on the line passing through (-1, -1, -1) and (8, -1, 7) for any value of t. As t varies over the real numbers, the points P(t) trace the line in three-dimensional space.

The line passing through the points (-1, -1, -1) and (8, -1, 7) can be described using vector notation. Let's denote the position vector of a point on the line as P(t), where t is a real number that represents a parameter along the line. The vector equation for the line can be written as: P(t) = (-1, -1, -1) + t[(8, -1, 7) - (-1, -1, -1)].

Simplifying the equation: P(t) = (-1, -1, -1) + t(9, 0, 8) = (-1 + 9t, -1, -1 + 8t). This vector equation represents all the points that lie on the line passing through (-1, -1, -1) and (8, -1, 7) for any value of t. As t varies over the real numbers, the points P(t) trace the line in three-dimensional space.

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∫ cos (3x) cos (5x) dx = -sin (3x) cos (5x) + sin (5x) cos (3x)

To evaluate the integral of cos (3x) cos (5x) dx using repeated integration by parts, we need to begin by choosing the terms to integrate and differentiate. Let's first choose to integrate cos (3x) dx and differentiate cos (5x). This gives us the equation:

∫ cos (3x) cos (5x) dx = sin (3x) cos (5x) - ∫ sin (5x) cos (3x) dx


To continue, we now choose to integrate sin (5x) and differentiate cos (3x). This gives us the equation:

∫ sin (5x) cos (3x) dx = -cos (5x) sin (3x) + ∫ cos (3x) sin (5x) dx


Finally, we choose to integrate cos (3x) and differentiate sin (5x). This gives us the equation:

∫ cos (3x) sin (5x) dx = -sin (5x) cos (3x) + ∫ sin (5x) cos (3x) dx


Substituting the first equation back into the last equation yields:

∫ cos (3x) sin (5x) dx = -sin (5x) cos (3x) + sin (3x) cos (5x) - ∫ cos (3x) cos (5x) dx


And since this is the same integral as our initial equation, we can write:

∫ cos (3x) cos (5x) dx = -sin (5x) cos (3x) + sin (3x) cos (5x) - ∫ cos (3x) cos (5x) dx

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Given that the triangular plate is fixed at its base, and its apex a is given a horizontal displacement of 5 mm. suppose that a = 600 mm.In order to find the deflection, consider the right triangle OAB where O is the origin,

A (0,600) and B (x,y).So,OB² = OA² + AB²= 600² + x²Since the length of the side opposite to angle B is given as 600 - y, we can use Pythagoras' theorem to express y in terms of x and hence find the equation of the line AB, i.e. y = f(x).Thus, OB² = OA² + AB²x² + (600 - y)² = 600² + x²y = 600 - √(600² - x²)From the geometry of the figure, it can be seen that the deflection at point A is equal to the displacement of B in the x direction, i.e.5 mm. Therefore, the deflection at point A is 5 mm.Long Answer:The problem is about finding the deflection at a point of a triangular plate that is fixed at its base and has an apex that is given a horizontal displacement of 5 mm. It is also given that a = 600 mm. In order to solve the problem,

we need to consider the geometry of the situation and use some elementary trigonometry.The figure below shows the triangular plate with the origin at the left end of the base and the y-axis perpendicular to the base at the origin. The apex of the triangle is at point A with coordinates (0,600).Let B (x,y) be a point on the plate such that OB is perpendicular to the base. Then, OB = x and AB = y. From the geometry of the figure, we can write the following equation:OB² = OA² + AB²where OB² = x², OA = 600, and AB² = (600 - y)²Therefore, we havex² = 600² + (600 - y)²Simplifying the equation, we getx² = 720000 - 1200y + y² + x²600y = 720000 - y²y² + 600y - 720000 = 0Solving for y, we gety = -300 + √(90000 + 360000 - 4×720000)/2y = 600 - √(600² - x²)Since the deflection at point A is equal to the displacement of B in the x direction, the deflection at A is given by 5 mm.Answer: The deflection at point A is 5 mm.

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B. The system has infinitely many solutions. The solutions are of the form x₁, x₂ = (2((-25 + √985) / 12) + 10, (-25 + √985) / 12) and (2((-25 - √985) / 12) + 10, (-25 - √985) / 12)

To solve the system of equations by the method of reduction, let's rewrite the given equations:

1) 3x₁x₂ - 5x₂ = 15

2) x₁ - 2x₂ = 10

We'll solve this system step-by-step:

From equation (2), we can express x₁ in terms of x₂:

x₁ = 2x₂ + 10

Substituting this expression for x₁ in equation (1), we have:

3(2x₂ + 10)x₂ - 5x₂ = 15

Simplifying:

6x₂² + 30x₂ - 5x₂ = 15

6x₂² + 25x₂ = 15

Now, let's rearrange this equation into standard quadratic form:

6x₂² + 25x₂ - 15 = 0

To solve this quadratic equation, we can use the quadratic formula:

x₂ = (-b ± √(b² - 4ac)) / (2a)

In our case, a = 6, b = 25, and c = -15. Substituting these values:

x₂ = (-25 ± √(25² - 4(6)(-15))) / (2(6))

Simplifying further:

x₂ = (-25 ± √(625 + 360)) / 12

x₂ = (-25 ± √985) / 12

Therefore, we have two potential solutions for x₂.

Now, substituting these values of x₂ back into equation (2) to find x₁:

For x₂ = (-25 + √985) / 12, we get:

x₁ = 2((-25 + √985) / 12) + 10

For x₂ = (-25 - √985) / 12, we get:

x₁ = 2((-25 - √985) / 12) + 10

Hence, the correct choice is:

B. The system has infinitely many solutions. The solutions are of the form x₁, x₂ = (2((-25 + √985) / 12) + 10, (-25 + √985) / 12) and (2((-25 - √985) / 12) + 10, (-25 - √985) / 12)

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The solution to the given differential equation 2xy(dy/dx) = y², with the initial condition y(2) = 3, is y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\).

To solve the given differential equation

2xy(dy/dx) = y²

We will use separation of variables and integrate to find the solution.

Start with the given equation

2xy(dy/dx) = y²

Divide both sides by y²:

(2x/y) dy = dx

Integrate both sides:

∫(2x/y) dy = ∫dx

Integrating the left side requires a substitution. Let u = y², then du = 2y dy:

∫(2x/u) du = ∫dx

2∫(x/u) du = ∫dx

2 ln|u| = x + C

Replacing u with y²:

2 ln|y²| = x + C

Using the properties of logarithms:

ln|y⁴| = x + C

Exponentiating both sides:

|y⁴| = \(e^{x + C}\)

Since the absolute value is taken, we can remove it and incorporate the constant of integration

y⁴ = \(e^{x + C}\)

Simplifying, let A = \(e^C:\)

y^4 = A * eˣ

Taking the fourth root of both sides:

y = (A * eˣ\()^{1/4}\)

Now we can incorporate the initial condition y(2) = 3

3 = (A * e²\()^{1/4}\)

Cubing both sides:

27 = A * e²

Solving for A:

A = 27 / e²

Finally, substituting A back into the solution

y = ((27 / e²) * eˣ\()^{1/4}\)

Simplifying further

y = (27 *  e⁽ˣ⁻²⁾\()^{1/4}\)

Therefore, the solution to the given differential equation with the initial condition y(2) = 3 is

y = (27 * e⁽ˣ⁻²⁾\()^{1/4}\)

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Answer:

20x+35y

Step-by-step explanation:

5(2x + 5y) - 4y + 10x

distribute

10x + 25y - 4y + 10x

add like terms

20x+21y

Answer:

D. The mathematical work is correct.

Step-by-step explanation:

The student precisely squares both sides of the equation correct 2x + 11 = 12.5 by multiplying both sides by 2x + 11, resulting in (2x + 11)^2 = (12.5)^2. The student then isolates the variable x by subtracting 11^2 from both flanks of the equation and dividing both sides by 2. This results in x = -9.5. So, the student's solution and the mathematical result are correct.

Answer:

3 boxes.

Step-by-step explanation:

Solution,

Given,

The number of cookies : 7 × 5 = 35

Now,

The total number of cookies to cookies per box 35 ÷ 12 = 2.9 box

= 3 boxes.

Answer: 2289.06

Step-by-step explanation:

math expert

Answer:

r = 169.56 in. / 2π ≈ 27 in.

Now we can use the radius to find the area:

Area = πr^2 ≈ π(27 in.)^2 ≈ 2289.06 in^2

So the area of the circular table is approximately 2289.06 square inches, rounded to the nearest hundredth. The answer is option C.

The correct statistic which could be misleading is,

C. The population of each town is not known. If the population of Town A is significantly smaller than that of Town B, the conclusion does not hold.

We have to given that;

During April, an average of 318 people in Town A were unemployed and 7,901 people in Town B were unemployed.

Here, A newspaper article used this statistic to conclude that the rate of employment was much better in Town A than in Town B.

Now, We know that;

Here, without knowing the population of each town, it is difficult to accurately compare the rate of employment between the two towns based solely on the number of unemployed individuals.

Hence, The correct statistic which could be misleading is,

C. The population of each town is not known. If the population of Town A is significantly smaller than that of Town B, the conclusion does not hold.

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Step 1. When two variables are related, for example, x and y, there will be a constant of proportionality between the x-values and the y-values, this constant of proportionality ''k'' is represented in the general formula for proportionality:

Step 2. In this case, we are relating two variables: f and s, through the following equation:

If we compare this with the equation from step 1, we can see that 1/7 represents the constant of proportionality:

Answer: The constant of proportionality is 1/7

Answer:

A company can use the first can for their soup as that will cost less to the company.

Step-by-step explanation:

Given: The first can has a radius of 1.5 inches and a height of 6 inches. The second can has a radius of 3 inches and a height of 3 inches.

To find: The can that a company can use to use for their soup.

Solution:

Let r, h denote radius and height of the first can and R, H denote radius and height of the second can.

\(r=1.5\,inches\,,\,h=6\,inches\,,\,R=3\,inches\,,\,H=3\,inches\)

Volume of the first can = \(\pi r^2h=\pi (1.5)^2(6)=13.5\,\,square\,\,inches\)

Volume of the second can = \(\pi R^2H=\pi (3)^2(3)=27\,\pi\,\,square\,\,inches\)

So,

Volume of the first can \(<\) Volume of the second can

A company can use the first can for their soup as that will cost less to the company.

Answer:

15.95 or 15 and 19/20

Step-by-step explanation:

8.25+5.80= 14.05

30-14.05= 15.95

Answer:

Below

Step-by-step explanation:

All of the side lengths of a CUBE are the same

VOLUME = L x W x H  = 1/6  *  1/6 * 1/6 =  1/ (6^3) =  1 / 216  in^3

the optimal solution to maximize Z is x1 = 25 and x2 = 0, with Z = 3000.

To solve the given linear programming model graphically, we need to plot the feasible region and identify the corner points to find the optimal solution. Here's the step-by-step process:

1. Plot the constraints:

  - Plot the line x1 = 40 (vertical line at x1 = 40).

  - Plot the line x2 = 10 (horizontal line at x2 = 10).

  - Plot the line 20x1 + 10x2 = 500 (which can be rewritten as 2x1 + x2 = 50).

  - Shade the feasible region that satisfies all the constraints.

2. Identify the corner points:

  - Determine the coordinates of the corner points where the boundary lines intersect.

3. Evaluate the objective function:

  - Calculate the value of the objective function Z = 120x1 + 80x2 for each corner point.

4. Determine the optimal solution:

  - Select the corner point that maximizes the objective function Z.

Here's the graphical representation of the feasible region:

      |

 40   |           C

      |          /

      |         /

      |        /

      |       /

      |      /

      |     /    Feasible Region

 10   |_____/_________________

      0   10  20  30  40  50

            0`

The corner points of the feasible region are:

A: (0, 0)

B: (0, 10)

C: (25, 0)

D: (20, 5)

Now, we evaluate the objective function Z = 120x1 + 80x2 for each corner point:

Z(A) = 120(0) + 80(0) = 0

Z(B) = 120(0) + 80(10) = 800

Z(C) = 120(25) + 80(0) = 3000

Z(D) = 120(20) + 80(5) = 2400

From the above calculations, we can see that the maximum value of Z occurs at point C: (25, 0).

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Answer:

Below

Step-by-step explanation:

4 [x-3] + 2    = y    is not discontinuous anywhere

However    4 / [x-3]  + 2   DOES have a discontinuity at x = 3 because this would cause the denominator to be zero <===NOT allowed !!

The number of books that her sister has before giving any to Sarah is 30 books

Sarah received three fifths of her sister's book collection

Number of books that Sarah received = 18 books

The fraction of the books that Sarah received = 3/5

Consider the total number of books as x

Then we have to find the total number of books

So the equation will be

x × (3/5) = 18

Divide the terms in the equation

x × 0.6 = 18

Move 0.6 to the right hand side of the equation

x = 18 / 0.6

Divide the terms

x = 30 books

Hence, number of books that her sister has before giving any to Sarah is 30 books

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This simple proportion equation will result to 592

In mathematics, a proportion is a statement that two ratios or fractions are equal. It expresses the relationship between two quantities or sets of quantities that are proportional or have a constant ratio to each other.

For example, the statement "2/3 = 4/6" is a proportion, which means that the ratio of 2 to 3 is the same as the ratio of 4 to 6. This proportion can be simplified by dividing both sides by 2, giving "1/3 = 2/3", which means that one-third is equal to two-thirds.

Proportions are commonly used in various fields such as finance, science, and engineering to solve problems related to scaling, measurement, and comparison.

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Answer:

(0, 1)

Step-by-step explanation:

All other choices do not match the two possible vertices of the square.

Answer:

11/12

Step-by-step explanation:

Answer:

11/12

Step-by-step explanation:

Answer:

(a)z=-1

(b)48.5 pounds

(c)61.5 pounds

Step-by-step explanation:

\(z-score=\dfrac{x-\mu}{\sigma}\)

Given:

Mean, μ = 55 pounds

Standard deviation,σ = 6 pounds.

(a)For a dog that weighs 49 pounds.

x=49 pounds

The z-score

\(=\dfrac{49-55}{6}\\=\dfrac{-6}{6}\\\\=-1\)

(b)When a dog has a z-score of -1.09

\(-1.09=\dfrac{x-55}{6}\\x-55=-6.54\\x=55-6.54\\x=48.46 \approx 48.5$ pounds (to the nearest tenth)\)

The weight of a dog with a z-score of -1.09 is 48.5 pounds.

(c)When a dog has a z-score of 1.09

\(1.09=\dfrac{x-55}{6}\\x-55=6.54\\x=55+6.54\\x=61.54 \approx 61.5$ pounds (to the nearest tenth)\)

The weight of a dog with a z-score of 1.09 is 61.5 pounds.

If the dog has a z-score of -1.09, his weight is 48.46kg but if the dog has a z-score of 1.09, his weight is 61.54kg

The z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

\(z=\frac{x-\mu}{\sigma} \\\\where\ x=raw\ score,\mu=mean,\sigma=standard\ deviation\)

Given that μ = 55, σ = 6;

For x = 49:

\(z=\frac{49-55}{6} =-1\)

If the dog has a z-score of -1.09, his weight is:

\(-1.09=\frac{x-55}{6} \\\\x-55=-6.54\\\\x=48.46\)

If the dog has a z-score of 1.09, his weight is:

\(1.09=\frac{x-55}{6} \\\\x-55=6.54\\\\x=61.54\)

If the dog has a z-score of -1.09, his weight is 48.46kg but if the dog has a z-score of 1.09, his weight is 61.54kg

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The required expression would be 12p - 33q + 104 which is equivalent form of 12(p + 5) − 11(3q + 4).

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

We have been given the expression:

12(p + 5) − 11(3q + 4)

Apply the distributive property of multiplication,

12p + 12 × 5 − 11 × 3q + 11 × 4

12p + 60 - 33q + 44

Rearrange the terms likewise and apply the arithmetic operation,

12p - 33q + 60  + 44

12p - 33q + 104

Therefore, required expression would be 12p - 33q + 104 which is equivalent form of 12(p + 5) − 11(3q + 4).

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Answer:

C

Step-by-step explanation:

Answer:

Infinite solutions

Step-by-step explanation:

Substitute -2x - 5 for y in 6x + 3y = -15

Therefore, the answer is infinite solutions.