Find 0.038 as a fraction in its lowest terms

A point which is a solution of the system of linear equations include the following: A. (1, 1).

In order to to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;

x − 3y = −2      ......equation 1.

y = −3x + 4  ......equation 2.

Next, we would use an online graphing calculator to plot the given system of equations as shown in the graph attached below.

Based on the graph (see attachment), we can logically deduce that the solution to the given system of equations is the point of intersection of the lines on the graph representing each of them, which lies in Quadrant I and it is given by the ordered pair (1, 1).

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Answer:

   yes because it is a terminating decimal

Step-by-step explanation:

2.1 To show that all partial derivatives of u and v exist at (x, y) = (0, 0) and satisfy the Cauchy-Riemann equations, we need to calculate the partial derivatives of u and v and check their existence and the Cauchy-Riemann conditions.

The function is given as u(x, y) = xy and v(x, y) = x² + y².

Partial derivatives of u:

∂u/∂x = y

∂u/∂y = x

Partial derivatives of v:

∂v/∂x = 2x

∂v/∂y = 2y

All partial derivatives exist at (x, y) = (0, 0) since they are simple functions and do not have any singularities.

Now, let's check if the Cauchy-Riemann equations are satisfied:

∂u/∂x = ∂v/∂y

y = 2y

This equation holds true for all values of y, including y = 0.

∂u/∂y = -∂v/∂x

x = -2x

This equation also holds true for all values of x, including x = 0.

Therefore, all partial derivatives of u and v exist at (x, y) = (0, 0), and they satisfy the Cauchy-Riemann equations.

2.2 To show that f is not continuous at (0, 0) and hence not differentiable at (0, 0), we can examine the behavior of f as (x, y) approaches (0, 0).

The function f(x, y) = u(x, y) + iv(x, y) = xy + i(x² + y²)

As (x, y) approaches (0, 0), both u(x, y) = xy and v(x, y) = x² + y² approach 0. However, f(x, y) = xy + i(x² + y²) approaches 0 + i(0) = i(0) = 0i = 0, which is a different value.

Therefore, f is not continuous at (0, 0), and hence it is not differentiable at (0, 0).

2.3 To investigate whether f is analytic or not, we need to check if it is differentiable in a neighborhood around every point.

Since we have already shown that f is not differentiable at (0, 0), it implies that f is not analytic because differentiability is a necessary condition for analyticity.

2.4 To investigate whether f has a harmonic complex conjugate or not, we need to check if u and v satisfy the Laplace's equation (∇²u = 0 and ∇²v = 0) and if they satisfy the Cauchy-Riemann equations.

The Laplace's equation is not satisfied by u(x, y) = xy because ∇²u = ∂²u/∂x² + ∂²u/∂y² = 0 + 0 ≠ 0.

Therefore, f does not have a harmonic complex conjugate.

2.5 To show that the function f(x, y) = x² - y² - iy is harmonic, we need to demonstrate that it satisfies the Laplace's equation (∇²u = 0 and ∇²v = 0).

For u(x, y) = x² - y², we have ∇²u = ∂²u/∂x² + ∂²u/∂y² = 2 - 2 = 0.

For v(x, y) = -y, we have ∇²v = ∂²v/∂x² + ∂²v/∂y² = 0 + 0 = 0.

Both u and v satisfy the Laplace's equation, indicating that f(x, y) = x² - y² - iy is a harmonic function.

To determine the harmonic conjugate of f, we can integrate the partial derivative of v with respect to x and y, and obtain the imaginary part of the function:

h(x, y) = ∫ (∂v/∂y) dy = ∫ 0 dy = C(y)

Where C(y) is an arbitrary function of y.

The harmonic conjugate of f is given by:

g(x, y) = u(x, y) + ih(x, y) = x² - y² + iC(y)

Therefore, the harmonic conjugate of f(x, y) = x² - y² - iy is g(x, y) = x² - y² + iC(y), where C(y) is an arbitrary function of y.

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To show that all partial derivatives of u and v exist at (x, y) = (0, 0) and satisfy the Cauchy-Riemann equations, we need to calculate the partial derivatives of u and v and check their existence and the Cauchy-Riemann conditions.

The function is given as u(x, y) = xy and v(x, y) = x² + y².

Partial derivatives of u:

∂u/∂x = y

∂u/∂y = x

Partial derivatives of v:

∂v/∂x = 2x

∂v/∂y = 2y

All partial derivatives exist at (x, y) = (0, 0) since they are simple functions and do not have any singularities.

Now, let's check if the Cauchy-Riemann equations are satisfied:

∂u/∂x = ∂v/∂y

y = 2y

This equation holds true for all values of y, including y = 0.

∂u/∂y = -∂v/∂x

x = -2x

This equation also holds true for all values of x, including x = 0.

Therefore, all partial derivatives of u and v exist at (x, y) = (0, 0), and they satisfy the Cauchy-Riemann equations.

2.2 To show that f is not continuous at (0, 0) and hence not differentiable at (0, 0), we can examine the behavior of f as (x, y) approaches (0, 0).

The function f(x, y) = u(x, y) + iv(x, y) = xy + i(x² + y²)

As (x, y) approaches (0, 0), both u(x, y) = xy and v(x, y) = x² + y² approach 0. However, f(x, y) = xy + i(x² + y²) approaches 0 + i(0) = i(0) = 0i = 0, which is a different value.

Therefore, f is not continuous at (0, 0), and hence it is not differentiable at (0, 0).

2.3 To investigate whether f is analytic or not, we need to check if it is differentiable in a neighborhood around every point.

Since we have already shown that f is not differentiable at (0, 0), it implies that f is not analytic because differentiability is a necessary condition for analyticity.

2.4 To investigate whether f has a harmonic complex conjugate or not, we need to check if u and v satisfy the Laplace's equation (∇²u = 0 and ∇²v = 0) and if they satisfy the Cauchy-Riemann equations.

The Laplace's equation is not satisfied by u(x, y) = xy because ∇²u = ∂²u/∂x² + ∂²u/∂y² = 0 + 0 ≠ 0.

Therefore, f does not have a harmonic complex conjugate.

2.5 To show that the function f(x, y) = x² - y² - iy is harmonic, we need to demonstrate that it satisfies the Laplace's equation (∇²u = 0 and ∇²v = 0).

For u(x, y) = x² - y², we have ∇²u = ∂²u/∂x² + ∂²u/∂y² = 2 - 2 = 0.

For v(x, y) = -y, we have ∇²v = ∂²v/∂x² + ∂²v/∂y² = 0 + 0 = 0.

Both u and v satisfy the Laplace's equation, indicating that f(x, y) = x² - y² - iy is a harmonic function.

To determine the harmonic conjugate of f, we can integrate the partial derivative of v with respect to x and y, and obtain the imaginary part of the function:

h(x, y) = ∫ (∂v/∂y) dy = ∫ 0 dy = C(y)

Where C(y) is an arbitrary function of y.

The harmonic conjugate of f is given by:

g(x, y) = u(x, y) + ih(x, y) = x² - y² + iC(y)

Therefore, the harmonic conjugate of f(x, y) = x² - y² - iy is g(x, y) = x² - y² + iC(y), where C(y) is an arbitrary function of y.

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Answer:

10a - 11y

Step-by-step explanation:

3(2a - y) - 4(2y - a)

open the parenthesis

6a - 3y - 8y + 4a

combine like terms

6a + 4a - 3y - 8y

10a - 11y

Answer: 16%

Step-by-step explanation:

1. 60% not working = 40% working

2. 40% ^ 2, or 40% x 40% = 16%

Answer:

Step-by-step explanation:

X axis intercept (y=0)

3x+2(0)=5

3x=5

x=5/3

Y axis intercept (x=0)

3(0)+2y=5

2y=5

y=5/2

so, the interception points are: (5/3,0) and (5/2,0)

Answer:

y=(1/2)x+4

Step-by-step explanation:

Since slope-intercept form is y=mx+b, all we need to do is divide both sides by 2:

2y=x+8

y=1/2x+4

Thus, the equation would be y=1/2x+4

Answer:

6.3

Step-by-step explanation:

square root of (14.9k^2 - 13.5k^2)

$1.48 is the sales tax

Step-by-step explanation:

$15.50 times 6% = 1.48

6%=.06. 1. amount of cost multiplied by amount sales tax,but you have to turn sales tax into decimal

Answer:

B.

Step-by-step explanation:

You convert this to y=mx+b and b=y-value. So, the answer is B.

A linear regression function, f(t), that estimates the day's coffee sales with a high temperature is f(t) = -58t + 6,182.

The correlation coefficient (r) is -0.94.

Yes, r indicates a strong linear relationship between the variables because r is close to -1.

In order to determine a linear regression function and correlation coefficient for the line of best fit that models the data points contained in the table, we would have to use an online graphing tool (scatter plot).

In this scenario, the high temperature would be plotted on the x-axis of the scatter plot while the y-values would be plotted on the y-axis of the scatter plot.

From the scatter plot (see attachment) which models the relationship between the x-values and y-values, the linear regression function and correlation coefficient are as follows:

f(t) = -58t + 6,182

Correlation coefficient, r = -0.944130422 ≈ -0.94.

In this context, we can logically deduce that there is a strong linear relationship between the data because the correlation coefficient (r) is closer to -1;

-0.7＜|r| ≤ -1.0   (strong correlation)

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Missing information:

State the linear regression function, f(t), that estimates the day's coffee sales with a high temperature of t.  Round all values to the nearest integer. State the correlation coefficient, r, of the data to the nearest hundredth.  Does r indicate a strong linear relationship between the variables?  Explain your reasoning.

Answer:

1 2 3 ways for it to function

Step-by-step explanation:

Marty's taxable income of $510,000 falls within the last tax bracket, his marginal tax rate would be 37%.

To determine Marty's marginal tax rate, we need to refer to the tax brackets for the given year. However, as my knowledge is based on information up until September 2021, I can provide you with the tax brackets for that year. Please note that tax laws may change, so it is always best to consult the current tax regulations or a tax professional for accurate information.

For the 2021 tax year, the marginal tax rates for individuals are as follows:

10% on taxable income up to $9,950

12% on taxable income between $9,951 and $40,525

22% on taxable income between $40,526 and $86,375

24% on taxable income between $86,376 and $164,925

32% on taxable income between $164,926 and $209,425

35% on taxable income between $209,426 and $523,600

37% on taxable income over $523,600

Since Marty's taxable income of $510,000 falls within the last tax bracket, his marginal tax rate would be 37%. However, please note that tax rates can vary based on changes in tax laws and regulations, so it's essential to consult the current tax laws or a tax professional for the most accurate information.

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The evaluation approach described in the given scenario is B.) forced distribution.

Forced distribution is an evaluation approach where performance ratings are distributed among employees according to predetermined percentages. In this case, the professor has predetermined that 10% of the class will receive an "A", 20% will receive a "B", 40% will receive a "C", 20% will receive a "D", and 10% will receive an "F".

This approach imposes a forced ranking system that restricts the distribution of grades based on predetermined proportions. Forced distribution can be useful in certain contexts as it helps differentiate performance levels and prevent grade inflation or deflation.

However, it also has limitations, as it may not accurately reflect individual performance and can create a competitive environment among students. It is important for educators to carefully consider the implications and potential drawbacks of using forced distribution in educational settings.

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The expression for h is h = 2 × √(99)

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

An expression is a combination of numbers, variables, and operations that can be evaluated to produce a value. Expressions can be as simple as a single variable, such as x, or complex, involving multiple variables, constants, and functions.

According to the given information:

We can use the Pythagorean theorem to relate the slant height, the radius, and the height of a cone:

s² = r² + h²

Since s = 5r and r = 4, we have:

s = 5r = 5(4) = 20

Plugging this into the equation above, we get:

20² = 4² + h²

Simplifying and solving for h, we have:

h² = 20² - 4² = 396

h = √(396) = √(4 × 99) = 2 ×√(99)

Therefore, the expression for h is h = 2 × √(99) when r = 4 and s = 5r.

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Based on the given linear equation of y = - 3/4x + 5, the graph is shown attached.

When given a linear equation, you graph it by coming up with x values and then using the equation to find the corresponding y values.

The linear equation is y = - 3/4x + 5.

If the value x = -1, then y would be:

y = - 3/4x + 5

= -3/4(-1) + 5

= 5.75

If the value x = 0, then y would be:

y = -3/4(0) + 5

= 5

If the value x = 1, then y would be:

= -3/4(1) + 5

= 4.25

If the value x = 2, then y would be:

= -3/4(2) + 5

= 3.5

If the value x = 3, then y would be:

= -3/4(3) + 5

= 2.75

The points would be:
(-1, -5.75) (0, 5) (1, 4.25) (2, 3.5) (3, 2.75)

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Answer:

No

Step-by-step explanation:

It would work for the bottom equation, but plugging in to the top equation would equal -4>3, which is false.

Answer:

no

when the point is plugged into the first inequality, it does not work therefore it is not a solution

Answer:

Step-by-step explanation:

Here we have:

If we assume width = x, then:

If we assume length = x, then:

Answer options:

Answer:

2, 3, 4, 5

Step-by-step explanation:

2. 2 x + x = 18

3. 2 (x) + 2 (2 x) = 18

4. x + 1/2 x + x + 1/2 x = 18

5. 2 (x + 1/2 x) = 18

I got it right on edge!!

As per the combination method, the number of ways can the ribbons be awarded is 24,024

The general formula to calculate the combination is written as,

nCr = n!/r! (n - r)!

where n refers the set or population and r refers subset of n or sample set

Here we have given that there are 14 dogs in a particular class at a dog show. blue, red, yellow, and white ribbons will be awarded to the first through fourth place finishers,

Here we need to find the number of different ways can the ribbons be awarded.

While we looking into the given question, the following details are given in it,

Total number of dogs = 14

Number of ribbons = 5

Which means that the value on n = 14 and the value of r = 5.

As per the given question we know that,

There are 14 possibilities for blue one

And then there are 14 - 1 = 13 possibilities for red ribbon.

And for the next yellow one has 12 possibilities

Then the white one has 11 possibilities.

Therefore, the total number of ways is

=> 14 x 13 x 12 x 11

=> 24024

Therefore, option (c) is correct.

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Answer:

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

Step-by-step explanation:

Given Equation of line: y=mx+c,

where m = slope of line.

So, we will have to make y the subject to find the slope.

\(2x-3y=19\\2x-3y-2x=19-2x\\-3y=-2x+19\\y=\frac{-2x+19}{-3} \\y=\frac{2}{3} x-\frac{19}{3}\)

From here, we can see the slope of the line is \(\frac{2}{3}\).

Answer: 2/3

Step-by-step explanation:

2x-3y=19

minus 2x from both sides

-3y=-2x+19

divide both sides by -3

y=2/3x-19/3

slope is 2/3

We can solve this equation by setting B2 = [c d], so that AB2 = [c+d 1] = [0 1]. This gives us the system of equations c + d = 0 and c = 1. Solving this system, we have c = 1, where I is the 2x2 identity matrix

Let A be the given 2x2 matrix A = [1 2 ; 1 1]. To find a 3x2 matrix B such that AB = I, where I is the 2x2 identity matrix, we can use the hint provided: If B1 and B2 are the columns of B, then ABj = Ij. This means that for each column j of B, we need to solve the equation ABj = Ij. For j = 1, we have AB1 = I1 = [1 0]. We can solve this equation by setting B1 = [a b], so that AB1 = [a+b 1] = [1 0]. This gives us the system of equations a + b = 1 and a = 0. Solving this system, we have a = 0 and b = 1, so B1 = [0 1].For j = 2, we have AB2 = I2 = [0 1]. We can solve this equation by setting B2 = [c d], so that AB2 = [c+d 1] = [0 1]. This gives us the system of equations c + d = 0 and c = 1. Solving this system, we have c = 1.

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Answer:

The answer is ≈3 to the nearest whole number

Step-by-step explanation:

using SOH CAH TOA

BCA

sin0=opp/hyp

sin0=7.9/11

0=sin‐¹(7.9/11)

0=46 to the nearest degree

<A=<D

so,<EDF=46°

tan0=adj/hyp

tan46=x/3.3

x=tan46×3.3

x=3 to the nearest whole number

The angular velocity of link CD when angle BAD = 60° is 21.16 rad/s.

The given values are:

AD = 150 mm

AB = 40 mm

CD = 80 mm

The crank AB rotates at 120 r.p.m. clockwise.

BC and AD are of equal length.

To find:

The angular velocity of link CD when angle BAD = 60°.

From the given data, we have to first find the value of angle BCD.

Angle BCD can be calculated as follows:

AB = 40 mm

BC = AD

= 150 mm

In ΔABC,

By using Cosine rule;

AC² = AB² + BC² - 2 × AB × BC × Cos ∠ABC∴ AC² = (40)² + (150)² - 2 × 40 × 150 × Cos 180°

∴ AC = 160.6 mm

In ΔBCD,

By using Cosine rule;

BD² = BC² + CD² - 2 × BC × CD × Cos ∠BCD

∴ BD² = (150)² + (80)² - 2 × 150 × 80 × Cos ∠BCD

In ΔABD,By using Cosine rule;

BD² = AB² + AD² - 2 × AB × AD × Cos ∠BAD

∴ BD² = (40)² + (150)² - 2 × 40 × 150 × Cos 60°

∴ BD = 184.06 mm

In ΔABD,By using Sine rule;

AB / Sin ∠BAD = BD / Sin ∠ABD

∴ Sin ∠ABD = BD × Sin ∠BAD / AB

∴ ∠ABD = Sin⁻¹ [BD × Sin ∠BAD / AB]

∴ ∠ABD = Sin⁻¹ [184.06 × Sin 60° / 40]

∴ ∠ABD = 87.2°∠ACD = ∠ABD - ∠ACB

∴ ∠ACD = 87.2° - 180°

∴ ∠ACD = - 92.8°∠BCD

= 180° - ∠ACD

∴ ∠BCD = 180° - (- 92.8°)

∴ ∠BCD = 272.8°

As we know that for four-bar mechanism, we have a formula for finding the angular velocity of link CD.

ωCD / Sin ∠BCD = ωAB / Sin ∠BADωCD / Sin 272.8°

= ωAB / Sin 60°

Substituting the values, ωCD / Sin 272.8° = ωAB / Sin 60°ωCD

= ωAB × Sin 272.8° / Sin 60°

But, ωAB = 2 × π × N / 60

= 2 × π × 120 / 60

= 4 × π rad/s

∴ ωCD = 4 × π × Sin 272.8° / Sin 60°ωCD

= 21.16 rad/s

Therefore, the angular velocity of link CD when angle BAD = 60° is 21.16 rad/s.

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The standard deviation of the value of the variable at the end of 3 years is 3√3.

a) To find the expected value of the variable x after 3 years, we can use the properties of the Wiener process. The expected value of the variable at any given time t is given by:

E[x(t)] = x(0) + a * t

Given that x(0) = 10 and a = 2, we can substitute these values into the equation:

E[x(3)] = 10 + 2 * 3 = 10 + 6 = 16

Therefore, the expected value of the variable x after 3 years is 16.

b) The standard deviation of the value of the variable at the end of 3 years can be calculated using the formula:

σ = √(b^2 * t)

Given that b = 3 and t = 3, we can substitute these values into the formula:

σ = √(3^2 * 3) = √(9 * 3) = √27 = 3√3

Therefore, the standard deviation of the value of the variable at the end of 3 years is 3√3.

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Step-by-step explanation:

first u need to pick a random coordinate to substitute the X . example 0

y = 2(0) + 1

y =1 , X= 0

X= 1

y= 2(1) + 1

y= 3, X= 1

then you continue this same process and again until u have at least two points to draw a straight line. it kinda depended if u want to fill the entire graph.

The volume of this right prism that has a triangular base is equal to 108 cubic meters.

Mathematically, the volume of a right prism is given by this formula:

V = L x W x H

Where:

Given the following data:

Length of base = 6 meters.

Width of base = 4 meters. cm.

Height of prism = 4.5 meters.

Substituting the given parameters into the formula, we have;

V = 6 x 4 x 5

V = 108 cubic meters.

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Answer: 54 m³

Step-by-step explanation: proof with more answers

According to given diagram:

The correct answer is option c) infinitely many solutions..

To solve the system of equations using the substitution method, we'll substitute the value of y from the second equation into the first equation and solve for x.

Given:

-6x + 2y = 8 ---(1)

y = 3x + 4 ---(2)

Substitute equation (2) into equation (1):

-6x + 2(3x + 4) = 8

Simplify:

-6x + 6x + 8 = 8

8 = 8

We obtained a true statement (8 = 8), which means the two equations are equivalent. This solution shows that the system has infinitely many solutions.

Therefore, the correct answer is option c) infinitely many solutions..

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Answer: 115

Step-by-step explanation: trust me bro free lee

Two angles are supplementary if their sum is 180° thus the angle supplementary to angles m∠AED are m∠DEB and m∠AEC and their measure is 115° both.

The angle is the measurement of the angular distance for example for linear motion we have a meter inch but for angular rotation, we don't have the measurement so the angle is useful to measure the angular rotation.

As per the given lines, AB intersect CD at E has been drawn below,

m∠AED = 65° (given)

m∠AED + m∠DEB = 180° (supplementary)

m∠DEB = 180° - 65° = 115°.

m∠AED + m∠AEC = 180° (supplementary)

m∠AEC = 180° - 65° = 115°.

Hence "Two angles are supplementary if their sum is 180° thus the angle supplementary to angles m∠AED are m∠DEB and m∠AEC and their measure is 115° both".

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