Find the dimensions of a rectangular Persian rug whose perimeter is 30 ft and whose area is 54 ft(to the second power) The Persian rug has a length (longer side) of__ft and a width (shorter side) of__ft ?

The common difference between successive terms in this sequence is -0.1.

The common difference between successive terms in a sequence is the constant value that is added or subtracted to each term to obtain the next term in the sequence. To find the common difference in the given sequence, we need to subtract each term from the term that follows it.
Subtract the first term (0.36) from the second term (0.26): 0.26 - 0.36 = -0.1
Subtract the second term (0.26) from the third term (0.16): 0.16 - 0.26 = -0.1
Subtract the third term (0.16) from the fourth term (0.06): 0.06 - 0.16 = -0.1
Based on the calculations, the common difference between successive terms in this sequence is -0.1. Therefore, the correct answer is a) -0.1.

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From the graphs in the given coordinate plane, the functions that have complex roots are function b, function d and function f.

From the question, we are to determine the functions that have complex roots in the given coordinate plane.

In a quadratic graph, if the vertex of the quadratic function lies above the x-axis, and the parabola opens upward, there will be NO x-intercepts. The graph will have complex roots.

Also, if the vertex of the quadratic function lies below the x-axis, and the parabola opens downward , there will be NO x-intercepts.

The graph will have complex roots.

In the given coordinate plane, the functions that have complex roots are function b, function d and function f.

Hence, the functions b, d, and f have complex roots.

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The -value of the test is 1.90. This indicates that the mean processing time is significantly greater than 5.5 hours, supporting the manufacturer's desire to set a standard time required by employees to complete a certain process

The t-value will be equal to 1.39 for the given statistics.

To test if the mean processing time exceeds 5.5 hours, we can use a one-sample t-test.

The null hypothesis is that the mean processing time is less than or equal to 5.5 hours:

H0: µ ≤ 5.5

The alternative hypothesis is that the mean processing time is greater than 5.5 hours:

Ha: µ > 5.5

We will use a significance level of 0.05.

The formula for the t-test statistic is:

t = (X - µ) / (s / √n)

Where:

X = sample mean

µ = hypothesized population mean

s = sample standard deviation

n = sample size

Substituting the given values, we get:

t = (6 - 5.5) / (2 / √21) = 1.386

The degree of freedom for the t-test is n-1 = 20.

Using a t-table or calculator, the p-value associated with a t-value of 1.386 and 20 degrees of freedom is 0.093.

Since the p-value (0.093) is greater than the significance level (0.05), we fail to reject the null hypothesis. Therefore, there is not enough evidence to suggest that the mean processing time exceeds 5.5 hours.

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The solution of the matrix is \(\begin{bmatrix}2 & 4 &|2 \\0 & -1 & |-3\end{bmatrix}\)

We are given the following matrix:

\(\begin{bmatrix}1 & 2 &|1 \\2 & 3 & |-1\end{bmatrix}\)

To fill in the missing entries, we will perform row operations. The given operation is "subtracting the first row from the second row." Let's proceed with this operation:

Step 1: Multiply the first row by 2:

\(\begin{bmatrix}2 & 4 &|2 \\2 & 3 & |-1\end{bmatrix}\)

Step 2: Subtract the first row from the second row:

\(\begin{bmatrix}2 & 4 &|2 \\0 & -1 & |-3\end{bmatrix}\)

By subtracting the first row from the second row, we obtain the row-reduced matrix with the missing entries filled in. The row-reduced matrix is a simplified form of the original matrix, making it easier to analyze and solve systems of linear equations.

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Complete Question:

Fill in the missing entries by performing the indicated row operations to obtain the row-reduced matrices.

\(\begin{bmatrix}1 & 2 &|1 \\ 2&3 & |-1\end{bmatrix}\underrightarrow{R_2-R_1}\begin{bmatrix}1 & 2 &|1 \\ & & |\end{bmatrix}\)

The linear inequality for the graph in this problem is given as follows:

y ≥ 2x/3 + 1.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The graph crosses the y-axis at y = 1, hence the intercept b is given as follows:

b = 1.

When x increases by 3, y increases by 2, hence the slope m is given as follows:

m = 2/3.

Then the linear function is given as follows:

y = 2x/3 + 1.

Numbers above the solid line are graphed, hence the inequality is given as follows:

y ≥ 2x/3 + 1.

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The estimated median price of a single-family home in Charleston/No. Charleston in the 1st Quarter of 2008 is $201,048. If the median price continues to decrease at the same rate for the next two years, the estimated median price of a single-family home in the 1st Quarter of 2011 would be $144,458.

(a) To estimate the median price of a single-family home in the 1st Quarter of 2008, we need to calculate the original price before the 8.15% decrease. Let's assume the original price was P. The price after the decrease can be calculated as P - 8.15% of P, which translates to P - (0.0815 * P) = P(1 - 0.0815). Given that the end of 1st Quarter of 2009 median price was $184,990, we can set up the equation as $184,990 = P(1 - 0.0815) and solve for P. This gives us P ≈ $201,048 as the estimated median price of a single-family home in the 1st Quarter of 2008.

(b) If the median price of a single-family home falls at the same rate for the next two years, we can calculate the price for the 1st Quarter of 2011 using the estimated median price from the 1st Quarter of 2009. Starting with the median price of $184,990, we need to apply an 8.15% decrease for two consecutive years. After the first year, the price would be $184,990 - (0.0815 * $184,990) = $169,805.95. Applying the same percentage decrease for the second year, the price would be $169,805.95 - (0.0815 * $169,805.95) = $156,012.32. Therefore, the estimated median price of a single-family home in the 1st Quarter of 2011 would be approximately $144,458.

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The direct route distance from the route down North Avenue and up Wolf Road distance to find the difference in distance between the two routes

What is a distance?

Distance is the measure of how far apart two objects or points are, usually measured in units such as meters, kilometers, miles, feet, or yards. It is a scalar quantity, meaning it only has magnitude and no direction. The distance can be calculated using various methods, such as using the Pythagorean theorem in a two-dimensional coordinate plane or using the distance formula in a three-dimensional space. Distance is an important concept in mathematics, physics, engineering, and other sciences, as well as in everyday life

Since we do not have the specific values for the distance between Point A and Point B, we cannot determine the exact answer to this question. However, we can use the Pythagorean theorem to estimate the difference in distance between the direct route from Point A to Point B and the route down North Avenue and up Wolf Road.

Assuming that we have the coordinates of Point A and Point B, we can use the distance formula to find the distance between them. Let's call the coordinates of Point A (x1, y1) and the coordinates of Point B (x2, y2).

Direct route:

Distance = √[(x2 - x1)^2 + (y2 - y1)^2]

Route down North Avenue and up Wolf Road:

Distance = Distance along North Avenue + Distance along Wolf Road

To find the distance along North Avenue and Wolf Road, we can use the distance formula with the coordinates of the two endpoints of each segment.

Once we have both distances, we can subtract the direct route distance from the route down North Avenue and up Wolf Road distance to find the difference in distance between the two routes

hence, The direct route distance from the route down North Avenue and up Wolf Road distance to find the difference in distance between the two routes

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The number of cans required to paint an area of 2000 square units is equal to 5 cans.

As given in the question,

Total area to be painted is equal to 2000 square units.

Area covered by one can of paint is equal to 400 square units

400 square units = 1 can of paint

⇒ 1 square units = ( 1 / 400 ) cans of paint

⇒ 2000 square units =  ( 2000 / 400 ) cans of paint

⇒ 2000 square units = 5 cans of paint

Therefore, the number of cans required to paint an area of 2000 square units using given can is equal to 5 cans.

The above question is incomplete, the complete question is:

How many cans of paint are needed to cover an area of 2000 square units if one can of paint covers in area 400 square units?

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Answer:

43°

Step-by-step explanation:

Complementary angles add up to 90° in measurement.

One angle is 47 degrees.

\(90-47=\boxed{43}\)

The measurement of the other angle would be 43°.

Hope this helps.

The measure of other angle is 43 degree.

Complementary angles are those whose combined angle is 90 degrees or less. To put it another way, two angles are said to be complimentary if they combine to make a right angle. In this case, we say that the two angles work well together.

Given that.

Two angles are complementary.

Now consider one angle = x degree

And other angle  = y degree

Then according to question,

Measure of angle x = 47 degree

We know that,

The sum of complementary angles are equal to 90 degree.

Therefore,

x + y = 90

x + 47 = 90

       x = 90 - 47

       x  = 43

Hence, the other angle is = 43 degree.

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Answer:

In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. For example, the sequence 2, 6, 18, 54, ... is a geometric progression with common ratio 3. Similarly 10, 5, 2.5, 1.25, ... is a geometric sequence with common ratio 1/2.

Answer:

see below

Step-by-step explanation:

Slope intercept form is

y = mx+b where m is the slope and b is the y intercept

Solve the equation for y

3x+3y = 6

Subtract 3x from each side

3x+3y -3x= -3x+6

3y = -3x+6

Divide each side by 3

3y/3 = -3x/3 +6/3

y = -x +2

The sope is -1 and the y intercept is 2

Answer:

y = -x + 2

hope you have a good day!

The partial derivative diffusivity equation for spherical flow is ∂²p/∂r² + (1/r) ∂p/∂r = ϕμC/k ∂p/∂t, and for hemispherical flow, it is the same equation.

1. The partial derivative diffusivity equation for spherical flow is derived from the spherical coordinate system and applies to radial flow in a spherical geometry. It can be expressed as ∂²p/∂r² + (1/r) ∂p/∂r = ϕμC/k ∂p/∂t.

2. The partial derivative diffusivity equation for hemispherical flow is derived from the hemispherical coordinate system and applies to radial flow in a hemispherical geometry. It can be expressed as ∂²p/∂r² + (1/r) ∂p/∂r = ϕμC/k ∂p/∂t.

1. For the derivation of the partial derivative diffusivity equation for spherical flow, we consider a spherical coordinate system with the radial direction (r), the azimuthal angle (θ), and the polar angle (φ). By assuming steady-state flow and neglecting the other coordinate directions, we focus on radial flow. Applying the Laplace operator (∇²) in spherical coordinates, we obtain ∇²p = (1/r²) (∂/∂r) (r² ∂p/∂r). Simplifying this expression, we arrive at ∂²p/∂r² + (1/r) ∂p/∂r.

2. Similarly, for the derivation of the partial derivative diffusivity equation for hemispherical flow, we consider a hemispherical coordinate system with the radial direction (r), the azimuthal angle (θ), and the elevation angle (ε). Again, assuming steady-state flow and neglecting the other coordinate directions, we focus on radial flow. Applying the Laplace operator (∇²) in hemispherical coordinates, we obtain ∇²p = (1/r²) (∂/∂r) (r² ∂p/∂r). Simplifying this expression, we arrive at ∂²p/∂r² + (1/r) ∂p/∂r.

In both cases, the term ϕμC/k ∂p/∂t represents the source or sink term, where ϕ is the porosity, μ is the fluid viscosity, C is the compressibility, k is the permeability, and ∂p/∂t is the change in pressure over time.

These equations are commonly used in fluid mechanics and petroleum engineering to describe radial flow behavior in spherical and hemispherical geometries, respectively.

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Answer:

(1,8)

Step-by-step explanation:

please mark me as brainliest thank you

The length of the patio in the drawing is 2 centimeters.

A scale drawing is a smaller image in terms of dimensions of an original image / building / object. The scale drawing is usually reduced at a constant dimension

The length of the drawing = 20 / 10 = 2cm

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Answer:

-12y^4+6x^4+x^2y^2\

Step-by-step explanation:

The measure of angle B is given as follows:

<B = 295º.

Angles A and B in the context of this problem are reflex angles, meaning that the sum of their measures is of 360º.

The measures are given as follows:

Hence the measure of angle B is obtained as follows:

65 + <B = 360

<B = 360 - 65

<B = 295º.

The diagram modeling the situation is given by the image presented at the end of the answer.

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Answer:

H

Step-by-step explanation:

As you can see the more shirt's that were bought the lower the price becomes per shirt.

The divergence of the vector field F is positive for y > -1/3 and negative for y <  -1/3.

To plot the vector field F(x, y) = (xy, x + y^2), we can first visualize the vectors at various points in the xy-plane. Let's choose a range of values for x and y and calculate the corresponding vectors. We'll use a step size of 1 for simplicity.

Here is a sample grid of points and their corresponding vectors:

(x, y) = (-2, -2) -> F(-2, -2) = (4, 2)

(x, y) = (-1, -2) -> F(-1, -2) = (2, 2)

(x, y) = (0, -2) -> F(0, -2) = (0, 2)

(x, y) = (1, -2) -> F(1, -2) = (0, 2)

(x, y) = (2, -2) -> F(2, -2) = (4, 2)

(x, y) = (-2, -1) -> F(-2, -1) = (2, 1)

(x, y) = (-1, -1) -> F(-1, -1) = (1, 1)

(x, y) = (0, -1) -> F(0, -1) = (0, 1)

(x, y) = (1, -1) -> F(1, -1) = (0, 1)

(x, y) = (2, -1) -> F(2, -1) = (2, 1)

... and so on for other values of y and for positive values of y.

To calculate the divergence (divF) of the vector field, we need to find the partial derivatives of the components of F with respect to x and y. Then we sum these partial derivatives.

F(x, y) = (xy, x + y^2)

∂F/∂x = y

∂F/∂y = 1 + 2y

divF = ∂F/∂x + ∂F/∂y = y + (1 + 2y) = 3y + 1

Now, we can analyze where the divergence is positive (divF > 0) and where it is negative (divF < 0).

For divF > 0:

If y > -1/3, then divF > 0.

For divF < 0:

If y < -1/3, then divF < 0.

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The probability that x is less than 5 = 0.45

Discrete probability distribution:

It is a type of probability distribution that displays all the possible values of a discrete random variable accompanying the affiliated probabilities. We can also say that a discrete probability distribution provides the chance of occurrence of every possible value of a discrete random variable.

Discrete probability distribution:

x          = -10      0       10        20

P(X=x) = 0.35  0.10   0.15     0.40

The probability that x is less than 5:

P(X<5) = 1 - P (X = 10) - P(X= 20)

1 - 0.15 - 0.40 = 0.45

The probability that x is less than 5 is = 0.45

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Answer oor the question

12x+20y

sup

The two expressions are not equal, so the function f(x) = 2x² is also not linear.

To determine if a function is linear, we need to verify if it satisfies the linearity property, which states that for any x and y in the domain of the function and any scalars α and β, the function should satisfy f(αx + βy) = αf(x) + βf(y).

Let's examine each function and determine if it is linear:

f(x) = 3x - 2

To check linearity, we need to verify if f(αx + βy) = αf(x) + βf(y). Let's substitute the values:

f(αx + βy) = 3(αx + βy) - 2

= 3αx + 3βy - 2

On the other hand:

αf(x) + βf(y) = α(3x - 2) + β(3y - 2)

= 3αx - 2α + 3βy - 2β

Comparing the two expressions, we can see that they are not equal, so the function f(x) = 3x - 2 is not linear.

f(x) = 2x²

Using the same logic, let's check linearity:

f(αx + βy) = 2(αx + βy)²

= 2(α²x² + 2αβxy + β²y²)

= 2α²x² + 4αβxy + 2β²y²

On the other hand:

αf(x) + βf(y) = α(2x²) + β(2y²)

= 2αx² + 2βy²

The two expressions are not equal, so the function f(x) = 2x² is also not linear.

In conclusion, neither of the given functions is linear since they do not satisfy the linearity property.

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The distance between the points A ( -2 , -5 ) and B ( -7 , -7 ) is 5.4 units

What is the distance between two points?

Let the two points be A ( x₁ , y₁ ) and B ( x₂ , y₂ )

The distance from A to B is the same as the distance from B to A

Distance between two points is the length of the line segment that connects the two points in a plane.

The formula to find the distance between the two points is usually given by D = √( ( x₂ – x₁ )² + ( y₂ – y₁ )²)

This formula is used to find the distance between any two points on a coordinate plane or x-y plane

Given data ,

Let the first point be A ( x₁ , y₁ )

The value of A ( x₁ , y₁ ) = A ( -2 , -5 )

Let the second point be B ( x₂ , y₂ )

The value of B ( x₂ , y₂ ) = B ( -7 , -7 )

Now , the distance between the two points is given by the formula

D = √( ( x₂ – x₁ )² + ( y₂ – y₁ )²)

where D is the distance

Substituting the values in the equation , we get

Distance D = √ [ ( -7 - (-2) )² + ( ( -7 - (-5) )² ]

On simplifying the equation , we get

Distance D = √ (-7 + 2 )² + ( -7 + 5 )²

Distance D = √ ( -5 )² + ( -2 )²

So , the value of D is

Distance D = √ ( 25 + 4 )

Distance D = √29 units

So , the approximate value of distance D = 5.39 units

Therefore , the value of Distance D = 5.4 units

Hence ,

The distance between the points A ( -2 , -5 ) and B ( -7 , -7 ) is 5.4 units

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Simplifying the expression and evaluating the limit will give us the value of f′(−1).

The function f(x) = 3 - x² is given, and we need to find f′(−1) using the limit definition of a derivative at a point. The derivative of a function at a specific point represents the rate of change of the function at that point. In this case, we are interested in finding the derivative at x = -1.

To find f′(−1) using the limit definition of a derivative, we can start by determining the slope of the tangent line at x = -1. The slope of a tangent line is equivalent to the derivative of the function at that point. Using the limit definition, we have:

f′(−1) = lim(h→0) [(f(-1 + h) - f(-1))/h]

Substituting the function f(x) = 3 - x² into the formula, we have:

f′(−1) = lim(h→0) [(3 - (-1 + h)² - (3 - (-1)))/h]

Simplifying the expression and evaluating the limit will give us the value of f′(−1).

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Answer:

32%

Step-by-step explanation:

at least twenty caters long

Answer:

There are 7 five dollar bills in the jar.

Step-by-step explanation:

There are 7 because 16 + y + 4 = 27 → 20 + y = 27 → y = 7

The company's claim can be evaluated using a hypothesis test. The null hypothesis, denoted as H0, assumes that the true proportion of chips that do not fail in the first 1000 hours is 55% or lower.

Ha stands for the alternative hypothesis, which assumes that the real proportion is higher than 55%. This test has a significance level of 0.01.

A sample of 800 chips was taken based on the information provided, and it was discovered that 60% of them do not fail in the first 1000 hours. A one-sample percentage test can be used to verify the assertion.  The test statistic for this test is the z-score, which is calculated as:

\(\[ z = \frac{{p - p_0}}{{\sqrt{\frac{{p_0(1-p_0)}}{n}}}} \]\)

If n is the sample size, p0 is the null hypothesis' assumed proportion, and p is the sample proportion.

If we substitute the values, we get:

\(\[ z = \frac{{0.6 - 0.55}}{{\sqrt{\frac{{0.55(1-0.55)}}{800}}}} \]\)

The z-score for this assertion is calculated, and we find that it is approximately 2.86.

In order to determine whether there is sufficient data to support the company's claim, we compare the computed z-score with the essential value. At a significance level of 0.01 the critical value for a one-tailed test is approximately 2.33.

Because the estimated z-score (2.86) is larger than the determining value (2.33), we reject the null hypothesis. Therefore, the company's assertion that more than 55% of the chips do not fail in the first 1000 hours of use is supported by sufficient data at the 0.01 level.

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Answer:

m=-5

Step-by-step explanation:

Slope means inclination of the line

Intercept means the point where the line cuts the y axis

general form of the quation is

y= mx + b. Here m is the slope(inclination) , and b is intercept

then replace m=1/5. b=-4

y=(1/5)x + (-4) = (1/5)x -4