Given the set = {, }, = {, }. Find the Cartesian product
and cardinality | |

Answer:

5000

Step-by-step explanation:

312.5 = .25 x .25 x p so .25 times .25 is .0625, divide 312.5 by .0625 and its 5000

Consider using 3D printing technology to create the spherical fountain. This would allow for precise and customizable designs, and could potentially be more cost-effective than traditional manufacturing methods for complex shapes.

Use a mathematical formula to design the fountain. Here are the steps to design a spherical fountain:

Determine the desired size of the fountain. This will be the diameter of the sphere. Let's say your client wants a fountain with a diameter of 6 feet.

Calculate the radius of the sphere by dividing the diameter by 2. In this case, the radius is 3 feet.

Use the formula for the surface area of a sphere to determine the surface area of the fountain. The formula is: SA = 4π\(r^2\), where r is the radius of the sphere and π is a mathematical constant (approximately 3.14). In this case, the surface area is:

SA = 4π\((3)^2\)

SA = 4π(9)

SA = 36π

SA ≈ 113.1 square feet

Use the desired water flow rate to determine the volume of water that will flow through the fountain per minute. Let's say your client wants a flow rate of 50 gallons per minute.

Use the formula for the volume of a sphere to determine the volume of the fountain. The formula is: V = (4/3)π\(r^3\). In this case, the volume is:

Calculate the amount of time it will take for the fountain to cycle through all of its water. This is known as the turnover time, and it is important to maintain water quality. The turnover time is calculated by dividing the volume of water in the fountain by the flow rate. In this case, the turnover time is:

Use these calculations to design the fountain, taking into account any necessary adjustments for the manufacturer's limitations.

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Full Question: Your client wants you to design a spherical fountain for a new garden bed. It is hard to find a manufacturer that can create perfect curved surfaces. You will need to modify the sphere to a series of cylindrical slabs with gradually decreasing radii.

In case of linear function the graph will be a straight line as the change is constant in every interval. But in case of non-linear function, instead of straight line the graph will generate curve line as the change is not constant in every interval.

The points X(5,-3), Y(4,-1) and Z(6,-2) can be plotted as given below. From the obtained graph ∠XYZ is the obtuse angle.

The given coordinates are X(5,-3), Y(4,-1) and Z(6,-2).

We need to classify ∠XYZ whether it is right, acute, or obtuse.

A cartesian plane or coordinate plane can be defined as a plane formed by the intersection of two coordinate axes that are perpendicular to each other. The horizontal axis is called the x-axis and the vertical one is the y-axis. These axes intersect with each other at the origin whose location is given as (0, 0). Any point on the cartesian plane is represented in the form of (x, y). Here, x is the distance of the point from the y-axis and y is the distance from the x-axis.

Now, X(5,-3), Y(4,-1) and Z(6,-2) can be plotted as given below:

The given points X(5,-3), Y(4,-1) and Z(6,-2) have positive x-coordinate and negative y-coordinate.

In the cartesian plane, the fourth quadrant positive x-coordinate and negative y-coordinate.

So, all points X(5,-3), Y(4,-1) and Z(6,-2) lie in the fourth quadrant.

From the graph, we can see that the two lines make an obtuse angle, which is more than 180° and less than 360°.

From the obtained graph ∠XYZ is the obtuse angle.

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ANSWER and EXPLANATION

a) To simplify the radical, we have to:

1) First, express the number inside the radical as a product of a perfect square and a number that is not a perfect square.

2) Next, we separate the numbers into two radicals and find the square root of the perfect square.

3) Finally, we find the product of the number and the remaining radical.

B) Following the steps above:

STEP 1

STEP 2

STEP 3

Answer:

x = 9

Step-by-step explanation:

since the terms are in AP then there is a common difference between consecutive terms, that is

a₂ - a₁ = a₃ - a₂ ( substitute values )

x - 7 = 11 - x ( add x to both sides )

2x - 7 = 11 ( add 7 to both sides )

2x = 18 ( divide both sides by 2 )

x = 9

Answer:

9

Step-by-step explanation:

The nth term of an AP has the formular

a+ ( n - 1 ) d

a = first term

n = number of terms

d = common difference

common difference d = T2 - T1 0r T3 - T2

d = x - 7 or 11 - x

Therefore,

3rd term

a + (3 - 1)d

a + 2d

Hence,

7 +2d = 11

substitute the value of d above

7 + 2 (x -7) = 11

7 + 2x - 14 = 11

2x = 11 +14 -7

2x = 18

dividing bothsides by 2

x = 18/2

x = 9

The maximum value of the function is 10368 and the minimum value is 0.

The given function is f(x, y) = x² +2y², and the constraint is 12-216y = 15648.

Therefore, the maximum and minimum values of the function are to be found.

Now, to find the maximum and minimum values of the given function, we use the method of Lagrange Multipliers.

We need to maximize and minimize the function f(x, y) subject to the constraint 12-216y = 15648.

So, we need to find the critical points of the function F(x, y, λ) = f(x, y) + λ(12-216y - 15648).

F(x, y, λ) = x² +2y² + λ(12-216y - 15648)

Differentiating F(x, y, λ) w.r.t x, y, and λ and equating to 0, we get the following equations:

2x + 0y + λ(0) = 0 ...(1)

0x + 4y + λ(-216) = 0 ...(2)

12-216y - 15648 = 0 ...(3)

From equations (1) and (2), we get:

λ = 0

And, 4y - 216λ = 0 or λ = 4y/216

Now, equating the two values of λ, we get:

0 = 4y/216or y = 0

Also, from equation (3), we get:12 - 216y = 15648or y = -72

The critical points of the function are (0, 0) and (0, -72).

Now, let's find the values of the function at these points.

f(0, 0) = 0²+ 2(0)² = 0

f(0, -72) = 0² + 2(-72)² = 10368

Thus, the correct answer is:

Maximum = 10368

Minimum = 0.

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Test statistic using the given data:Observed frequency (O)Expected frequency (E)(O - E)2/E27 33.33 2.063232.33 0.901445.33 1.45838 33.33 0.36227 33.33 1.4631 33.33 0.16Σ(O - E)2/E = 7.36Critical value:We will use a chi-square table to find the critical value for a 0.025 significance level with 5 degrees of freedom (6 - 1). The critical value is 12.833.

Hypothesis testing is a statistical method to determine the probability of an event based on the data analysis of a sample collected from the population. It involves setting up two competing hypotheses, a null hypothesis and an alternative hypothesis. In this question, we will conduct a hypothesis test to determine whether a die is loaded or not.Here is the given data:Outcomes of die = 1, 2, 3, 4, 5, and 6Number of times rolled = 200Observed frequencies = 27, 32, 45, 38, 27, 31We can calculate the expected frequency of each outcome for a fair die using the formula:Expected frequency = (Total number of rolls) x (Probability of the outcome)The probability of getting each outcome in a fair die is 1/6. Therefore,Expected frequency = (200/6) = 33.33We will now set up our null and alternative hypotheses:Null hypothesis (H0): The die is fair and the outcomes are equally likely.Alternative hypothesis (H1): The die is loaded and the outcomes are not equally likely.We will use a 0.025 significance level to test our hypothesis.

Test statistic:The test statistic used for this test is chi-square (χ2). It can be calculated using the formula:χ2 = Σ(O - E)2/Ewhere,Σ = SummationO = Observed frequencyE = Expected frequencyWe can calculate the test statistic using the given data:Observed frequency (O)Expected frequency (E)(O - E)2/E27 33.33 2.063232.33 0.901445.33 1.45838 33.33 0.36227 33.33 1.4631 33.33 0.16Σ(O - E)2/E = 7.36Critical value:We will use a chi-square table to find the critical value for a 0.025 significance level with 5 degrees of freedom (6 - 1). The critical value is 12.833.Conclusion:Our test statistic (χ2) is 7.36 and the critical value is 12.833. Since the test statistic is less than the critical value, we fail to reject the null hypothesis. This means that there is not enough evidence to suggest that the die is loaded. Therefore, we conclude that the outcomes are equally likely and the loaded die does not behave differently than a fair die.

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Approximately it will take 2 minutes to pass before they are 3 miles apart.

The time can be defined as the ratio of distance covered by an object to a unit speed. Time refers to the progression of events.

The Formula of Time of a given body can be expressed as,

Time = Distance÷Speed

one group takes a taxi uptown, traveling north at 35 miles per hour

The rest of the friends share another taxi, traveling south at 44 miles per hour

Suppose X as a time before they are 3 miles apart

so forming the equations:

35x+44x=3

79x=3

x=3/79hours.

To convert into minutes multiply x by 60 because 1 hour=60 min

x=3/79*60

x=0.0379*60

x=2.278

x=2 minutes.

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At the point of diminishing returns, spending $1000 on advertising would result in sales of $2900.

A. To find the point of diminishing returns, we need to find the first derivative of the given function and set it equal to zero.

S(x) = -0.02x³ + 3x² + 100

S'(x) = -0.06x² + 6x0

      = -0.06x² + 6x0

      = x(0.06x - 6)0

      = x(0.06x - 6)x

      = 0 or 100 from the interval [0,80]

So, the value of x when the rate of sales is decreasing is x = 1000 i.e., $1000 should be spent on advertising.

B. To find the amount of sales resulting from $1000 advertising, substitute x = 1000 in the given function:

S(x) = -0.02x³ + 3x² + 100S(1000)

      = -0.02(1000)³ + 3(1000)² + 100

      = -200 + 3000 + 100

      = 2900

Thousands of dollars in sales would result from $1000 advertising is $2900.

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Sale Price = $157.5 (answer). This means the cost of the item to you is $157.5. You will pay $157.5 for a item with original price of $175 when discounted 10%. In this example, if you buy an item at $175 with 10% discount, you will pay 175 - 17.5 = 157.50 dollars.

Hope this helps!

The inner product of two vectors A = (2, -3,0) and B = (-1,0,5) is -2 / √(13×26).

Solving the given system of equations using Gaussian elimination:

2x + 3y + z = 2 y + 5z = 20 -x+2y+3z = 13

Matrix form of the system is

[A] = [B] 2 3 1 | 2 0 5 | 20 -1 2 3 | 13

Divide row 1 by 2 and replace row 1 by the new row 1: 1 3/2 1/2 | 1

Divide row 2 by 5 and replace row 2 by the new row 2: 0 1 1 | 4

Divide row 3 by -1 and replace row 3 by the new row 3: 0 0 1 | 5

Back substitution, replace z = 5 into second equation to solve for y, y + 5(5) = 20 y = -5

Back substitution, replace z = 5 and y = -5 into the first equation to solve for x, 2x + 3(-5) + 5 = 2 2x - 15 + 5 = 2 2x = 12 x = 6

The solution is (x,y,z) = (6,-5,5)

Therefore, the solution to the given system of equations using Gaussian elimination is (x,y,z) = (6,-5,5).

The given two vectors are A = (2, -3,0) and B = = (-1,0,5). The inner product of two vectors A and B is given by

A·B = |A||B|cosθ

Given,A = (2, -3,0) and B = (-1,0,5)

Magnitude of A is |A| = √(2²+(-3)²+0²) = √13

Magnitude of B is |B| = √((-1)²+0²+5²) = √26

Dot product of A and B is A·B = 2(-1) + (-3)(0) + 0(5) = -2

Cosine of the angle between A and B is

cosθ = A·B / (|A||B|)

cosθ = -2 / (√13×√26)

cosθ = -2 / √(13×26)

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Answer:

Standard form:

x^5+9x³-4x²+16

Leading coefficient:

1

(coefficient of x^5=1)

Answer:

15

Step-by-step explanation:

x + 2y

Putting x = 7, y = 4, we have

7 + 2(4)

= 7 + 8

= 15

Hope it helps.

If you have any query, feel free to ask.

Step-by-step explanation:

It's saying x = 7 and y = 4, which means everywhere there is an x, you'll place a 7 and everywhere there is a y, you'll place a 4

x + 2y turns into (7) + 2(4)

Now we can answer the bottom question

2(4) = 8

7 + 8 = 15

so...

If x =7 and y=4, then x+2y= 15

Answer:

The dimensions of the rectangle are 22 and 55 feet

Step-by-step explanation:

We can set the Width to be X and the Length to be 3x-11 since it is 11 less than 3 times the width.

the perimeter is 2 widths plus 2 lengths so x + x + 3x-11 + 3x-11 or 8x -22
since the perimeter is also 154, we get that 8x-22 = 154, we can add 22 to both sides and get that 8x = 176 if we divide both sides by 8 we get that X or the width is 22 and since the length is 3 times the width minus 11 it is

66-11 or 55.

Answer:

14x+13y-15

Step-by-step explanation:

This is pretty simple. When it asks to combine terms, simply add up all of the same terms. So, all the numbers with x, all with y, and all with no value. For example, for x, we simply add up 5x+8x+x, with x equaling 1.

Hope this helps!

Answer:

14x+13y−15

Step-by-step explanation:

\(5x+3y+8x+x+10y-15 \\ 5x + 8x + x + 10y + 3y - 15 \\ 13x + x + 13y - 15 \\ 14x+13y−15 \)

By using the given exchange rate, we can see that your friend will get $65.75 dollars.

We know that the current exchange rate is:

$1 = 124 Nepalese rupees

Then we can rewrite the equation as:

1 Nepalese rupees = ($1/124)

Now if we multiply both sides by 8,153 we will get:

8,153*1 Nepalese rupees = 8,153*($1/124)

8,153 Nepalese rupees = $65.75

So if your friend exchanges their 8,153 Nepalese rupees, they will get 65.75 U.S. dollars.

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Answer:

x=12

Step-by-step explanation:

x^9=12^9

power of 9 cancel eachother at both sides of equation.

so

x=12

Hi there.

Glad to see you using Brainly!

Equation:

a^2-b^2c^2

Then, multiply the terms with equal exponents.

(We can do this by multiplying their bases)

After:

a^2 - (b c)^2

Now, using a^2 - b^2 = (a-b)(a+b) we factor.

Therefore, after using that we get:

(a-bc) x (a+bc)

Therefore, our solution is

(a - bc) x (a+bc)

Thanks for using Brainly!

- Tutor John

Answer:

\( {a}^{2} - {b}^{2} {c}^{2} = (a - bc)(a + bc) \)

The exact area of each hexagonal shape is 181.5sqrt(3) cm^2. Option B

To determine the exact area of each hexagonal shape formed by the equilateral triangles, we need to calculate the area of one equilateral triangle and then multiply it by the number of triangles that make up the hexagon.

The formula to calculate the area of an equilateral triangle is:

Area = (sqrt(3) / 4) * side^2

Given that the side of each tile measures 11 cm, we can substitute this value into the formula to find the area of one equilateral triangle:

Area = (sqrt(3) / 4) * (11 cm)^2

= (sqrt(3) / 4) * 121 cm^2

= 121sqrt(3) / 4 cm^2

Now, since the hexagon is formed by six equilateral triangles, we can multiply the area of one triangle by 6 to find the total area of the hexagon:

Hexagon Area = 6 * (121sqrt(3) / 4 cm^2)

= 726sqrt(3) / 4 cm^2

= 181.5sqrt(3) cm^2

Therefore, the exact area of each hexagonal shape is 181.5sqrt(3) cm^2.

The correct answer is B: 181.5√3 cm^2.

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The binary relation P={(x,y)∈A×A∣y=x2}, where A={x∈Z∣−25≤x≤25}, consists of pairs (x,y) where y is the square of x. In this case, P contains all the pairs (x, y) such that y is the square of x within the range of -25 to 25.

To find the members of P, we need to identify the pairs (x, y) that satisfy the given condition. In this case, for each x in the range -25 to 25, we need to check if y is equal to \(x^2\). Let's go through each value of x in A and calculate the corresponding value of y:

For x = -25, y = (-25)^2 = 625.

For x = -24, y = (-24)^2 = 576.

For x = -23, y = (-23)^2 = 529.

...

For x = 0, y = 0^2 = 0.

...

For x = 24, y = 24^2 = 576.

For x = 25, y = 25^2 = 625.

Therefore, the members of P are:

(-25, 625), (-24, 576), (-23, 529), ..., (0, 0), ..., (24, 576), (25, 625).

To find P∘P, we need to compose the relation P with itself. This means we need to find all pairs (x, z) such that there exists a y for which (x, y)∈P and (y, z)∈P. In other words, we need to find all pairs (x, z) such that there exists a y satisfying y = x^2 and z = y^2. By substituting the value of y in terms of x, we can find z in terms of x. The resulting pairs will be the members of P∘P.

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Christo and Jeanne-Claude worked for over 26 years on "The Gates," a large-scale public art installation in Central Park consisting of thousands of saffron-colored fabric panels along 23 miles of walkways, which was on display for 16 days in February 2005.

Christo and Jeanne-Claude were artists known for their large-scale public art installations. "The Gates" was a project they worked on for over 26 years, from its conception in 1979 to its installation in Central Park in February 2005. The installation involved placing thousands of saffron-colored fabric panels along 23 miles of walkways in the park, creating a visually stunning and immersive experience for visitors.

The project was met with both praise and criticism, but it ultimately succeeded in bringing people together to appreciate art in a public space. The installation remained in place for 16 days before it was dismantled.

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Answer:

18

Step-by-step explanation:

Answer:

Your answer is 18

Step-by-step explanation:

The way to get the answer is...

is over of=percent over 100

so for this situation it would look like this...

\(\frac{x}{40}\) = \(\frac{45}{100}\)

Cross multiply and you will get...

1800 = 100x

get x by itself, so divide 100 by both sides

So you get

x=18

I hope this helps you. Have a great day and good luck! :)

Answer:

x=3/2 (or 1.5)

Step-by-step explanation:

Subtract 3/8 from both sides

Simplify

Subtract 1/2x from both sides

Simplify

Multiply both sides by 4

Simplify

Divide both sides by -3

y = (1/4)x^2 - x + 2

which is the same equation we obtained earlier.

Since the given conic is a parabola, we know that it has the general form:

y = a(x - h)^2 + k

where (h, k) is the vertex and the sign of "a" determines the direction of the parabola.

We also know that the focus of the parabola is (4, 2). Since the vertex is given as (4, 1), we can see that the axis of symmetry is parallel to the y-axis and the focus lies 1 unit above the vertex.

To find the value of "a", we can use the fact that the distance between the focus and vertex is equal to 1/(4a). Thus, we have:

1/(4a) = 2 - 1

=> 1/(4a) = 1

=> a = 1/4

Substituting this value of "a" and the vertex (h, k) = (4, 1) into the general form of the parabola, we get:

y = (1/4)(x - 4)^2 + 1

Therefore, the equation of the parabola is:

y = (1/4)x^2 - x + 2

Alternatively, we can also use the focus-directrix property of the parabola to find its equation. Since the focus is (4, 2) and the vertex is (4, 1), we know that the directrix is the line y = 0.5 (which is 1 unit below the vertex). The distance from any point on the parabola to the focus is equal to its distance to the directrix. Using the distance formula and simplifying, we get:

sqrt((x - 4)^2 + (y - 2)^2) = abs(y - 0.5)

Squaring both sides and simplifying, we get:

(x - 4)^2 + (y - 2)^2 = 4(y - 0.5)^2

Expanding and rearranging, we get:

x^2 - 8x + 16 + y^2 - 4y + 4 = (1/4)x^2 - x + 1

Simplifying further, we get:

y = (1/4)x^2 - x + 2

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Answer: its c

Step-by-step explanation:

took the quiz

Answer:

Step-by-step explanation:

its C I got yall

Answer:

-2 or -2/1

Step-by-step explanation:

Since the equation is in y = mx + b form with m equaling the slope, we can see that -2 is in m's place, so -2 is the slope.

a) Part A: The perceived image of Jet Airways

Jet Airways is one of the well-known airlines in India. It is headquartered in Mumbai and operates both domestic and international flights. The perceived image of Jet Airways in the minds of its customers is important to the success of the airline. Perceived image refers to what the customers think about the airline, and this is important for customer loyalty and retention.

Constructing a seven-item and semantic differential scale to measure the perceived image of Jet Airways would be as follows:

1. Reliability: how reliable is Jet Airways on a scale of 1 to 7 (with 1 being extremely unreliable and 7 being extremely reliable)

2. Responsiveness: how responsive is Jet Airways to the needs of its customers on a scale of 1 to 7 (with 1 being extremely unresponsive and 7 being extremely responsive)

3. Empathy: how empathetic is Jet Airways to the concerns of its customers on a scale of 1 to 7 (with 1 being extremely unempathetic and 7 being extremely empathetic)

4. Assurance: how assured do you feel when you travel with Jet Airways on a scale of 1 to 7 (with 1 being extremely unassured and 7 being extremely assured)

5. Tangibles: how do you rate the physical appearance of Jet Airways on a scale of 1 to 7 (with 1 being extremely poor and 7 being extremely good)

6. Price: how do you rate the price of Jet Airways on a scale of 1 to 7 (with 1 being extremely expensive and 7 being extremely affordable)

7. Convenience: how convenient is it to travel with Jet Airways on a scale of 1 to 7 (with 1 being extremely inconvenient and 7 being extremely convenient)

The above semantic differential scale helps in measuring the perceived image of Jet Airways. The seven-item and semantic differential scale ensure that the seven under each format correspond to the same seven dimensions.

By answering each question, the customers can rate Jet Airways on various factors, and the airline can use this feedback to improve its service and overall image.

b) Part B:

Examination of a technical and business report

The structure of a technical and business report includes a title page, abstract, table of contents, introduction, main body, conclusion, and references. An examination of a technical and business report from the internet reveals some deviations from the stated structure. One of the significant deviations is the absence of the abstract section. The abstract provides a brief summary of the report, including the purpose, methodology, and findings. The report from the internet did not have an abstract section, and this deviation could be due to the report being a short summary of a more extensive study.

The report from the internet did not have a separate conclusion section. The conclusion is important as it summarizes the findings of the study and provides recommendations for further research. The report from the internet integrated the findings and recommendations into the main body of the report, and this deviation could be due to the length of the report.

Another deviation is the lack of a reference section. The reference section is essential as it provides the sources used in the study. The report from the internet did not have a reference section, and this deviation could be due to the type of report and the fact that it was not a formal research report.

In conclusion, technical and business reports should follow a specific structure to ensure that they are clear, concise, and easily understood. Deviations from the stated structure can affect the quality and accuracy of the report. The deviations in the report from the internet could be due to the length, type, and purpose of the report.

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