Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C.
F = (x2 + y2)i + (x - y)j; C is the rectangle with vertices at (0, 0), (2, 0), (2, 9), and (0, 9)
A) 144 B) 180 C) 0 D) -144, Answer is D

Answer:

$15.27

Step-by-step explanation:

80.00 - 64.73

Take -1 from each digit until all digits are subtractable

7-6 = 1

9-4 = 5

9-7 = 2

10-3 = 7

15.27

Natasha get $15.27 in change.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Natasha bought a pair of boots for $64.73.

Natasha  gave the cashier $80.00.

So, she get

= 80- 64.73

= $15.27

Hence, Natasha get $15.27 in change.

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Answer:

5---6

Step-by-step explanation:

Given, the package of invitations contain \(12\) invitations and package of envelopes contain \(10\) envelopes.

Let \(x\) and \(y\) denote the number of invitation packages bought by Ronnie respectively.

It is given that, Ronnie bought the fewest number of invitations and envelopes so that there is exactly one envelope per invitation with none left over.

That is,\(12x-10y=0\).

When, \(x=1\) the value of \(y\) becomes \(1.2\).

It is not possible, since the number package cannot be in decimals.

When, \(x=2\) the value of \(y\) becomes \(2.4\).

This is not possible, since the number package cannot be in decimals.

When, \(x=3\) the value of \(y\) becomes \(3.6\).

This is not possible, since the number package cannot be in decimals.

When, \(x=4\) the value of \(y\) becomes \(4.8\).

This is not possible, since the number package cannot be in decimals.

When, \(x=5\) the value of \(y\) becomes \(6\).

This is not possible, since the number package cannot be in decimals.

Thus, Ronnie bought \(5\) packages invitations and \(6\) packages envelopes so that there is exactly one envelope per invitation with none left over.

Answer:

7) 16 sq units

8) L = 22 cm

Step-by-step explanation:

7) A = 1/2h·(sum of bases)

= 1/2(4)(5+3)

= 2(8) or 16 sq units

8) A (trapezoid) = 1/2(7)(10+12)

= 1/2(22)(7)

= 11(7) or 77 sq cm

To find 'l' in triangle:

A = 1/2·L·7

77 = 7L /2

7L = 154

L = 22 cm

Answer:

wHaT?

Step-by-step explanation:

Answer:

Step-by-step explanation:

Solving by completing square

Structure number one is the most basic compound.

In determining the basicity of a compound, several factors come into play, including the strength of the conjugate acid, stability, and delocalization. Among the given structures, structure number one is considered the most basic compound. This conclusion is based on the understanding that the weaker the acid, the stronger its conjugate base, and therefore, the more basic the compound.

When a compound acts as an acid, it donates a proton (H+) to another compound. The strength of the acid is determined by the ease with which it loses a proton. Conversely, when a compound acts as a base, it accepts a proton. The basicity of a compound is dependent on the stability and availability of the lone pair of electrons on the atom that can accept the proton.

Structure number one, being the weakest acid among the given options, indicates that its conjugate base is more stable. This stability arises from the delocalization of the negative charge over a larger area, typically achieved through resonance or electron delocalization. The presence of resonance structures allows the negative charge to be spread out, increasing stability. Consequently, the lone pair of electrons on the atom is more accessible for accepting a proton, leading to a higher basicity.

It is important to note that basicity is not solely determined by the strength of the acid. Other factors, such as the electronegativity of the atom bearing the negative charge and the presence of any electron-withdrawing or electron-donating groups, can also influence basicity. However, in the context of the given structures, structure number one exhibits the characteristics of a strong conjugate base and is therefore the most basic compound.

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The value of k from the equation is k = -20

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

y = kx   be equation (1)

Let the first point be P ( 4 , -80 )

Substituting the values in the equation , we get

-80 = 4k

Divide by 4 on both sides of the equation , we get

k = - ( 80/4 )

On simplifying the equation , we get

k = -20

Hence , the equation is k = -20

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Answer:

A, B, and D

Step-by-step explanation:

Substitute all the coordinates into the equation. (x, y)

3(-2) - (-7) = 1

-6 - (-7) = 1

1 = 1

3(-1) - (-4) =1

-3 - (-4) = 1

1 = 1

3(0) - (1) = 1

0 - (1) = 1

-1 does not equal 1

3(3) - (8) = 1

9 - (8) = 1

1 = 1

Answer:

50% off

Step-by-step explanation:

Answer:

50% off

Step-by-step explanation:

50 is half of 100

Answer:

8 sides (octagon)

Step-by-step explanation:

sum of exterior angles is always 360º

360 / 45 = 8 sides

Answer:

8 sides

Step-by-step explanation:

If all the angles of the polygon are the same, divide the angle by 360 and u get the answer.

Given DataMass, m = 74.0 kg, Acceleration, a = 1.36 m/s²

Initial velocity, u = 0

Distance covered before constant velocity, s = 34 m

Distance remaining, s' = 100 - 34 = 66 m

Formula Used The equation for calculating distance is given by: s = ut + (1/2)at²

Where,s = Distance

u = Initial velocity

a = Acceleration

t = Time , The equation for calculating time is given by:t = √((2s)/

a)Calculation Acceleration remains constant, so the equation for calculating time will be:

t = √((2s)/a)t = √((2(34))/1.36)t = 5.11 s

Now, for calculating the remaining time taken by the sprinter to complete the race, we need to find the final velocity of the sprinter. The equation used is given by:v² - u² = 2as'

Where,v = Final velocity, u = Initial velocity, a = Accelerations' = Distance remaining

v² = u² + 2as'v² = 0 + 2(1.36)(66)v² = 179.52v = 13.4 m/sNow, we can calculate the time taken by the sprinter for the remainder of the race.t' = s'/vt' = 66/13.4t' = 4.93 s

The total time taken by the sprinter for the race is given by:Total time taken, t_total = t + t' = 5.11 + 4.93 ≈ 10.04 s

Therefore, the time taken by the sprinter to complete the race is approximately 10.04 seconds.

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The mathematical expression with unequal sides is known as an inequality in mathematics. Inequality is referred to in mathematics when a relationship results in a non-equal comparison between two expressions or two numbers. In this instance, any of the inequality symbols, such as greater than symbol (>), less than symbol (), greater than or equal to symbol (), less than or equal to symbol (), or not equal to symbol (), is used in place of the equal sign "=" in the expression. Polynomial inequality, rational inequality, and absolute value inequality are the various types of inequalities that can exist in mathematics. A linear inequality looks precisely like a linear equation, but the symbol connecting two expressions is different.

Let x represent the number of roast beef dinners and y represent the number of teriyaki chicken dinners.

The total cost of the roast beef dinners is 5x dollars and the total cost of the teriyaki chicken dinners is 3y dollars.

Therefore, the total cost of all the dinners is 5x + 3y dollars.

We know that the total cost of all the dinners must be less than or equal to $1200, so we can write the inequality:

5x + 3y <= 1200

We also know that we must serve at least 240 customers, which means that we must serve at least 240 dinners. Since we are serving two different meals, this means that we must serve at least 120 of each meal. Therefore, we can write the following system of inequalities:

x >= 120

y >= 120

5x + 3y <= 1200

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The mathematical expression with unequal sides is known as an inequality in mathematics. Inequality is referred to in mathematics when a relationship results in a non-equal comparison between two expressions or two numbers. In this instance, any of the inequality symbols, such as greater than symbol (>), less than symbol (), greater than or equal to symbol (), less than or equal to symbol (), or not equal to symbol (), is used in place of the equal sign "=" in the expression. Polynomial inequality, rational inequality, and absolute value inequality are the various types of inequalities that can exist in mathematics. A linear inequality looks precisely like a linear equation, but the symbol connecting two expressions is different.

Let x represent the number of roast beef dinners and y represent the number of teriyaki chicken dinners.

The total cost of the roast beef dinners is 5x dollars and the total cost of the teriyaki chicken dinners is 3y dollars.

Therefore, the total cost of all the dinners is 5x + 3y dollars.

We know that the total cost of all the dinners must be less than or equal to $1200, so we can write the inequality:

5x + 3y <= 1200

We also know that we must serve at least 240 customers, which means that we must serve at least 240 dinners. Since we are serving two different meals, this means that we must serve at least 120 of each meal. Therefore, we can write the following system of inequalities:

x >= 120

y >= 120

5x + 3y <= 1200

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Answer:

\(2 \frac{2}{3}\)

Answer:

1=yes

2=no

3=no

4=no

5=yes

6=yes(im not sure on this last one)

Step-by-step explanation:

If no vertical line can intersect the curve more than once, the graph does represent a function.

Answer:

Graph 1= It's a function

Graph 2= No

Graph 3= No

Graph 4= No

Graph 5= Yes

Graph 6= Yes

Step-by-step explanation:

Step-by-step explanation

Here ...I'm not too sure about the question as you have written

P = 2 ( 1 + 6 ) and ask to solve for L ...

.So I guess the question you have written is wrong .. ...and I guess there should be L in the place of 1.

...So let me correct the question....

P = 2 ( l + 6 )

P = 2l + 12

P - 2l = 12

- 2l = 12 - P

- 2l = - P + 12

Change the sign of both side of the equation...

2l = P + 12

divide both side by the same number...

L = ( P + 12 ) ÷ 2

\(l = \frac{1}{2} p - 12 \times \frac{1}{2} \\ \)

Calculate the product of rational numbers...

\(l = \frac{1}{2} p - 6 \\ \)

The probability of selecting exactly 3 one hundred dollar bills is `0.0643`. The value of variance is `0.78`.

Firstly, we need to find the total number of bills in the bowl.

So, the Total number of bills in the bowl=6 + 3 + 16=25

So, the total number of ways of selecting 5 bills from the bowl containing 25 bills is:

`25C5 = (25 × 24 × 23 × 22 × 21)/(5 × 4 × 3 × 2 × 1) = 53,130`

a. To find the probability that exactly 3 one hundred dollar bills will be chosen,

we need to find the number of ways of selecting 3 one hundred dollar bills out of 6 and 2 more bills from the remaining 19 bills such that they are not the one hundred dollar bills.

Thus, The number of ways to select 3 one hundred dollar bills from 6 one hundred dollar bills is:

`6C3 = 20`

The number of ways of selecting 2 bills from the remaining 19 bills is:

`19C2 = 171`

So, the total number of ways of selecting exactly 3 one hundred dollar bills is:

`20 × 171 = 3,420`

Thus, the probability of selecting exactly 3 one hundred dollar bills is:

`(3,420)/(53,130) ≈ 0.0643

`b. The variance of a discrete probability distribution is given by the formula: `σ^2 = ∑(x - μ)^2P(x)` where x is the number of one hundred dollar bills that are chosen, μ is the mean of the distribution, and P(x) is the probability of x occurring.In this case, the mean of the distribution is:

`μ = E(X) = np = 5 × (6/25) = 6/5`

Now, we need to calculate `σ^2 = ∑(x - μ)^2P(x)` for each possible value of x.

Number of one hundred dollar bills, x             0             1             2             3             4             5

Probability, P(x)                   0.0653      0.2469      0.3846      0.2602      0.0399      0.0031

The mean of the distribution is `μ = E(X) = np = 5 × (6/25) = 6/5`.

Now, we need to calculate `σ^2 = ∑(x - μ)^2P(x)` for each possible value of x.

After calculating, the value of variance will be `σ^2 ≈ 0.78`.

Therefore, the probability of selecting exactly 3 one hundred dollar bills is `0.0643`.

The value of variance is `0.78`.

The probability of selecting exactly 3 one hundred dollar bills is `0.0643`. The value of variance is `0.78`.

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The area of the shaded region is approximately 8.215π square millimeters, for the given radius of small circle of 0.5 mm.

To find the area of the shaded region, we need to subtract the area of the small circle from the area of the large circle.

Given the radius of the small circle as 0.5 mm, we can find the area of the small circle using the formula for the area of a circle:

Area of small circle = πr²

where r is the radius of the small circle.

Area of small circle = π(0.5)²

= π(0.25)

= 0.785 mm²

Given the area of the large circle as 28.26 mm², we can find the radius of the large circle using the formula for the area of a circle:

Area of large circle = πR²

where R is the radius of the large circle.

28.26 = πR²

R² = 28.26/π

R² = 9

R = √(9)

R = 3 mm

Now that we know the radius of the large circle, we can find its area using the same formula:

Area of large circle = πR²

= π(3)²

= 9π mm²

Finally, we can find the area of the shaded region by subtracting the area of the small circle from the area of the large circle:

Area of shaded region = Area of large circle - Area of small circle

= 9π - 0.785

= 8.215π mm² (rounded to three decimal places)

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Yes, the true mean of 33 is within the margin of error of the sample mean, we can conclude that the confidence interval does contain the true mean.

To determine whether the confidence interval contains the true mean of 33, we need to calculate the margin of error for the confidence interval. The margin of error is a measure of the precision of the estimate, and it is calculated using the sample size, the standard deviation of the population, and the desired level of confidence.

For a 95% confidence interval, the margin of error can be calculated using the following formula:

The margin of error = 1.96 * (standard deviation / √sample size)

Plugging in the values, we get:

Margin of error = 1.96 * (14 / √42)

Performing the calculation, we find that the margin of error is 3.39. This means that the sample mean of 31 is likely to be within 3.39 units of the true mean, with a confidence level of 95%.

Since the true mean of 33 is within the margin of error of the sample mean, we can conclude that the confidence interval does contain the true mean. This means that our estimate of the population mean, based on the sample size 42, is likely to be accurate.

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The diagonals of the parallelogram intersect at the center. Then the value of the variable 'x' is 38.

It is a polygon with four sides. The total interior angle is 360 degrees. A parallelogram's opposite sides are parallel and equal. Its diagonals intersect in the center.

Given parallelogram A B C D below, DE = 31 If EB = x - 7.

By the definition, then the equation is given as,

EB = DE

x - 7 = 31

Simplify the equation, then we have

x - 7 = 31

x = 31 + 7

x = 38

The value of the variable 'x' is 38.

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Answer:

-2, -12

-1,-3

0,0

1,-3

2,-12

Step-by-step explanation:

Used algebraic calculator

The value of x in the given inequality 6x ≤ 18, is S:3 out of all the given options.

The correct answer is S:3.

To solve for x, we divide both sides of the inequality by 6. When dividing by a negative number, we flip the direction of the inequality sign. This gives us x ≤ 3.

Therefore, the possible values of x are 3, 2, 1, 0, and so on. The answer can not be 26, 14, or 7, because those values would make x greater than 3.

Here is the solution in steps:

6x ≤ 18

6x/6 ≤ 18/6 (divide both sides by 6)

x ≤ 3

Therefore, the value of x is 3.

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Answer:

m+12=26       m=14

Step-by-step explanation:

Richard spent m. Jordan spent 12. TOGETHER they spent 26. Together means total and finding the total means adding.

The largest possible difference between two different 3-digit numbers with the same digits in reverse order is 792.

Let's assume the two numbers are ABC and CBA. The largest possible difference is achieved when the digits A and C have the largest possible difference.

If A > C, then the difference would be (ABC - CBA) = (100A + 10B + C) - (100C + 10B + A) = 99A - 99C = 99(A - C).

If A < C, then the difference would be (CBA - ABC) = (100C + 10B + A) - (100A + 10B + C) = 99C - 99A = 99(C - A).

Since we want the largest possible difference, we want to maximize the difference between A and C. The maximum possible difference between two single-digit non-zero numbers is 9. So, we want A = 9 and C = 1.

Therefore, the two numbers are 901 and 109, and the largest possible difference is (901 - 109) = 792.

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The statement is false. A counterexample can be found by considering the real number x = 1.5. In this case, ⌊x^2⌋ = ⌊1.5^2⌋ = ⌊2.25⌋ = 2, while ⌊x⌋^2 = ⌊1.5⌋^2 = 1^2 = 1. Therefore, the equation ⌊x^2⌋ = ⌊x⌋^2 does not hold for all real numbers x.

In the counterexample x = 1.5, we can see that ⌊x^2⌋ is equal to the greatest integer less than or equal to x^2, which is 2. On the other hand, ⌊x⌋^2 is equal to the greatest integer less than or equal to x, squared. In this case, ⌊1.5⌋^2 is equal to 1^2, which is 1.

Since 1 is not equal to 2, we can conclude that the statement ⌊x^2⌋ = ⌊x⌋^2 is false for the counterexample x = 1.5. Therefore, the original statement is false.

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Answer:

15+8+6+2=31

Step-by-step explanation:

highest no. is 15

15-7=8

31-15-8=8

middle number 8

8-6=2

CHECK: 15+8+6+2=31

i don't know if my answer is right haha

i checked online it says the answer is 5,6,8,12

To show that the matrix A = [XX - X'Z(ZZ)^(-1)Z'X] is positive definite, we need to demonstrate two properties: (1) A is symmetric, and (2) all eigenvalues of A are positive.

Symmetry: To show that A is symmetric, we need to prove that A' = A, where A' represents the transpose of A. Taking the transpose of A: A' = [XX - X'Z(ZZ)^(-1)Z'X]'. Using the properties of matrix transpose, we have:

A' = (XX)' - [X'Z(ZZ)^(-1)Z'X]'. The transpose of a sum of matrices is equal to the sum of their transposes, and the transpose of a product of matrices is equal to the product of their transposes in reverse order. Applying these properties, we get: A' = X'X - (X'Z(ZZ)^(-1)Z'X)'.  The transpose of a transpose is equal to the original matrix, so: A' = X'X - X'Z(ZZ)^(-1)Z'X. Comparing this with the original matrix A, we can see that A' = A, which confirms that A is symmetric.  Positive eigenvalues: To show that all eigenvalues of A are positive, we need to demonstrate that for any non-zero vector v, v'Av > 0, where v' represents the transpose of v. Considering the expression v'Av: v'Av = v'[XX - X'Z(ZZ)^(-1)Z'X]v

Expanding the expression using matrix multiplication : v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv. Since X and Z have full column rank, X'X and ZZ' are positive definite matrices. Additionally, (ZZ)^(-1) is also positive definite. Thus, we can conclude that the second term in the expression, v'X'Z(ZZ)^(-1)Z'Xv, is positive definite.Therefore, v'Av = v'X'Xv - v'X'Z(ZZ)^(-1)Z'Xv > 0 for any non-zero vector v. Implications in econometrics: In econometrics, positive definiteness of a matrix has important implications. In particular, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] guarantees that it is invertible and plays a crucial role in statistical inference.

When conducting econometric analysis, this positive definiteness implies that the estimator associated with X and Z is consistent, efficient, and unbiased. It ensures that the estimated coefficients and their standard errors are well-defined and meaningful in econometric models. Furthermore, positive definiteness of the matrix helps in verifying the assumptions of econometric models, such as the assumption of non-multicollinearity among the regressors. It also ensures that the estimators are stable and robust to perturbations in the data. Overall, the positive definiteness of the matrix [XX - X'Z(ZZ)^(-1)Z'X] provides theoretical and practical foundations for reliable and valid statistical inference in econometrics.

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Coordinates of parallelogram ABCD are A at (−2, 4), B at (0, 3), D at (−3, 2) and C at (-1, 1) .

Given, that ABCD is a parallelogram.

Properties of a parallelogram: A parallelogram is a quadrilateral with opposite sides that are parallel and congruent. The opposite angles are also congruent.

1. Plot the given points: Plot point A at (-2, 4), point B at (0, 3), and point D at (-3, 2) on a coordinate plane.

2. Find the vector AB: To find the vector AB, subtract the coordinates of point A from the coordinates of point B. In this case, AB = (0 - (-2), 3 - 4) = (2, -1).

3. Use the vector AB to find point C: Starting from point D, add the vector AB to the coordinates of point D. In this case, C = (-3 + 2, 2 - 1) = (-1, 1).

4. Check if the opposite sides are parallel and congruent: Once you have the coordinates of point C, calculate the distances between AB and CD, and BC and AD. If the distances are equal, it means the opposite sides are congruent.

He has plotted A at (−2, 4), B at (0, 3), and D at (−3, 2). C (-1, 1) coordinate could be the location of point C

Based on the given coordinates of points A, B, and D, the location of point C could be C (-1, 1) as it satisfies the properties of a parallelogram.

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The location of point C in the parallelogram is (-1,1). This is because to construct a parallelogram, the opposite sides should have the same slope, which is -0.5 for both AB and DC when C is at (-1,1).

In constructing a parallelogram, the opposite sides should be parallel. Let’s understand how to choose the correct point for C.

We already have coordinates for A, B, and D. To ensure AB is parallel to DC, we need to verify that the slope of AB equals the slope of DC.

The slope formula is (y2 - y1) / (x2 - x1). Let's calculate the slope of AB: (3 - 4) / (0 - (-2)) = -1 / 2 = -0.5.

Let's use each potential C point with D (-3, 2) to find out which one gives us the same slope:

So, the coordinate of the location of point C is (-1,1).

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Answer:

Step-by-step explanation:

If you distribute 6 to the  numbers inside the parenthesis, it means that you multiply both number by 6
2 x 6 = 12
3 x 6 = 18
the expression can be rewritten like the following:

12 + 18 = 30