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Rachel went to the grocery store and spent $68. She now has only $23 to get gasoline with before she returns home. How much money did Rachel have before she went grocery shopping? Create an equation to represent the situation. Make sure to identify and label your variable. Solve for the variable and describe your answer. Show your work and prove your solution to be correct

If Kylie is working in after-school job each week then the function that models the situation is discrete function hence  \(f(x)\) is a discrete function where the function defining the situation is"\(f(x)\)"

As per the question statement, Kylie records the number of hours she works in her after-school job each week and then graphs the function that models the situation. We are supposed to use the graph to determine if the function that models this situation is discrete, continuous, or neither.

Now, as the working hours after the school is variable i.e., not fixed hence this function can not be a continuous function, hence it has to be a discrete function.

Let the number of hours she works in her after school job each week be "\(x\) " then the function defining the situation will be "\(f(x)\)"

Hence \(f(x)\) is a discrete function.

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To calculate the frequencies and eigenvectors for the given system, you can use MATLAB's eig function. Here's a MATLAB code snippet that demonstrates how to perform these calculations:

% Define the system matrices

M = [0 1; 2 0];

C = [3 2; -2 2];

K = [3 -2; -2 2];

% Solve the eigenvalue problem

[V, W] = eig(K, M);

% Extract eigenvalues and frequencies

eigenvalues = diag(W);

frequencies = sqrt(abs(eigenvalues)) / (2*pi);

% Display the results

disp("Eigenvalues:");

disp(eigenvalues);

disp("Frequencies:");

disp(frequencies);

% Extract eigenvectors

eigenvectors = V;

disp("Eigenvectors:");

disp(eigenvectors);

In this code, the system matrices `M`, `C`, and `K` represent the mass, damping, and stiffness matrices, respectively. The `eig` function is used to solve the eigenvalue problem, where `K` and `M` are the input matrices. The resulting eigenvectors are stored in the matrix `V`, and the eigenvalues are stored in the matrix `W`. The frequencies are then calculated from the eigenvalues by taking the square root of the absolute values and dividing by `2*pi`.

Finally, the code displays the eigenvalues, frequencies, and eigenvectors using the `disp` function. Note that the code assumes a 2x2 system, as indicated by the provided system equations. You can modify the code accordingly if your system has a different dimension.

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(a) Since M is the midpoint of DE, we have ME = (1/2)b.

Also, CXE is a straight line, so C, X, and E are collinear.

Therefore, we have CX + XE = CE, or a - b + FE = b + (2a - b), which simplifies to FE = a.

(b) n = a/b - 1.

X is the point on FM such that

FX:XM =n:1,

we have FX = nX and XM = X.

Since M is the midpoint of DE, we have ME = (1/2)b,

so that  DX = DE - EX = b - (n + 1)X.

Using the fact that CXE is a straight line,

we have CX + XE = CE, or a - b + FE = b + (2a - b),

which simplifies to FE = a.

Therefore, we have FX + FE = AX, or nX + a = a + b + (n + 1)X.

Simplifying, we get b = (n + 1)X - nX = X.

We know that  DX = b - (n + 1)X = 0, so X = b/(n + 1).

Therefore, we have n/(n + 1) = FX/X = (a-b)/b.

Calculating  for n, we have  n = a/b - 1.

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The equation of motion for a medium can be given as gvi = p fit (x+p) √3, i5 + ß vi, Ĵ5. In this equation, the known constants are p, g, ß, and Ĵ5. The components of the stress tensor & or a continuum are given as ti^= x Sij dkk +2ß dij depending on the strain tensor.

We have to show that the equations of motion for this medium can be written in the above form.Let us consider the stress tensor's divergence to derive the equations of motion for this medium.

According to the principle of conservation of mass, the divergence of the stress tensor is equal to the force density, which is given by the following equation:ti^,j = fjHere, the comma indicates partial differentiation. Therefore, the force density is given as:f = tii,j = x Sij,k dkk,j + 2ß dij,j = x (∂Sij/∂xi + ∂Sij/∂xj) dkk + 2ß ∂dij/∂xjThe equilibrium of forces in this medium can be given as follows:gvi = - fi - p δi3 (x+p) √3.

The divergence of the stress tensor and the force density is used to derive the above equation. Now, let us consider the force density to derive the equations of motion of the medium. According to Newton's second law of motion, the force acting on a body is equal to the product of its mass and acceleration.

Therefore, the force density can be given as:f = p(dv/dt)Here, p is the density of the medium. The acceleration of the medium can be given as follows:a = dv/dtTherefore, the force density can be rewritten as:f = paHere, a is the acceleration of the medium.

Equating the two expressions for force density, we get:pa = x (∂Sij/∂xi + ∂Sij/∂xj) dkk + 2ß ∂dij/∂xjWe know that the stress tensor is symmetric. Therefore, the above equation can be simplified as:pa = x (∂Sij/∂xi + ∂Sji/∂xi) dkk + 2ß ∂dij/∂xjNow, we can simplify the above equation further by introducing a tensor notation.

Therefore, the above equation can be given as:pa = x (∂Si j/∂xi) dkk + 2ß (∂di j/∂xj)The above equation is the equation of motion for the medium in tensor notation. We can simplify this equation further by introducing the stress tensor and the Kronecker delta.

Therefore, the equation of motion can be given as follows:pa = x (∂Si j/∂xi) δkk + 2ß (∂di j/∂xj)Here, the Kronecker delta is used to simplify the above equation. Therefore, we can rewrite the equation as:

pa = x (∂Si j/∂xi) δij + 2ß (∂di j/∂xj)Here, we have used the Einstein summation convention to simplify the above equation.

Therefore, the equations of motion for this medium can be written as:gvi = p fit (x+p) √3, i5 + ß vi, Ĵ5.

The equations of motion for a medium can be derived using the stress tensor's divergence and the force density. The stress tensor components & or a continuum can be given as ti^= x Sij dkk +2ß dij depending on the strain tensor.

The equations of motion for this medium can be written as gvi = p fit (x+p) √3, i5 +ß vi, Ĵ5.

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Answer:

You can use 2+8

Step-by-step explanation:

Answer:

cost = 112

profit= 168

Step-by-step explanation:

280÷100=2.8

2.8×40=112

profit = price - cost

= 280-112

= 168

There are 1000 milliseconds in one second.

One one thousandth of a second is known as a millisecond (ms). To put this into perspective, a human eye blinks every 100 to 400 milliseconds, or every tenth to every half-second.

A second is a unit of time and a millisecond is a unit of time as well, with one second being equal to 1000 milliseconds. This means that if you were to measure a duration of one second, it would be equivalent to 1000 milliseconds.

So, to convert seconds to milliseconds, you simply multiply the number of seconds by 1000. This conversion factor can be useful in a variety of applications such as measuring the duration of events or calculating time intervals.

It's worth noting that the second is one of the seven base units of the International System of Units (SI) and is widely used as a standard of time all over the world, while the millisecond is a commonly used sub-unit of the second for measuring short durations of time.

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Answer:

b =  c − 2a

     ------------

          2

Step-by-step explanation:

2a + 2b = c

2b = c − 2a

b =  c − 2a

     ------------

          2

The number of elements in the sample space for this experiment is 969.

If a person eating at a cafeteria must choose 3 of 19 vegetables on offer, we can calculate the number of elements in the sample space, or the total number of possible outcomes, using the formula for combinations:

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

where n is the total number of items in the set and r is the number of items being chosen.

In this case, we have 19 vegetables and we want to choose 3 of them, so we can plug in n = 19 and r = 3:

19C3 = 19! / [3!(19 - 3)!]

= 19! / (3!)(16!)

= 969

Therefore, there are 969 possible combinations of 3 vegetables that a person can choose from a selection of 19 vegetables.

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Answer:

x = 0.45882352

Step-by-step explanation:

-1.95 = -1.7 x/0.4

-1.95 = -4.25x

x = 0.45882352

the probability density function is  , \(P(x ≤ 1/2) = 2/3.\)

To find the probability P(x ≤ 1/2) for the given probability density function (PDF) f(x), we need to integrate the PDF over the interval [0, 1/2].

The PDF is given by:

\(f(x) = 2/(1+x)^2, for x in [0, 1]\)

To find P\((x ≤ 1/2),\)we integrate the PDF from 0 to 1/2:

\(P(x ≤ 1/2) = ∫[0,1/2] f(x) dx\)

Substituting the PDF into the integral:

\(P(x ≤ 1/2) = ∫[0,1/2] 2/(1+x)^2 dx\)

Let's evaluate this integral:

\(P(x ≤ 1/2) = ∫[0,1/2] 2/(1+x)^2 dx\)

=\([-2/(1+x)]|[0,1/2]\)

=\([-2/(1+1/2)] - [-2/(1+0)]\)

=\([-2/(3/2)] - [-2/1]\)

= -\(4/3 + 2\)

= \(-4/3 + 6/3\)

= 2/3

Therefore, \(P(x ≤ 1/2) = 2/3.\)

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Answer:b is the answer

Step-by-step explanation:

Answer:

\(no \: solution\)

Step-by-step explanation:

1) Expand.

\(7a + 5a + 15 = 8a + 4a+ 8\)

2) Simplify 7a + 5a + 15 to 12a + 15.

\(12a + 15 = 8a + 4a+ 8\)

3) Simplify 8a + 4a + 8 to 12a + 8.

\(12a + 15 = 12a + 8\)

4) Cancle 12a from both sides.

\(15 = 8\)

5) Since 15 = 8 is false, there's no solution.

\(no \: solution\)

Therefor, this equation has no solution.

The z-score corresponding to the value of 144 is -0.6.

To find the z-score corresponding to a given value, we can use the formula:

z = (x - μ) / σ

where z is the z-score, x is the given value, μ is the mean, and σ is the standard deviation.

In this case, the mean μ is 150 and the standard deviation σ is 10. The given value x is 144.

Substituting these values into the formula, we have:

z = (144 - 150) / 10

Calculating the numerator:

144 - 150 = -6

Dividing by the standard deviation:

-6 / 10 = -0.6

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We have that, using Euclid's algorithm, we find the inverse of 200 modules 1001 is -5 (or 1001+5).

To find the inverse of a module m using Euclid's algorithm, the steps are as follows:

1. Calculate the greatest common divisor (GCD) of a and m using the Euclidean algorithm.

2. Let a = GCD * s + m*t, where s is the inverse of a module m.

3. The GCD in terms of a and my is written as 1 = m-s*a.

4. Find s = -a, so the inverse of a module m is -a (or m+s).

For example, a = 2, m=17, so GCD = 1 = 17-8*2 and the inverse of 2 modulo 17 is -8 (or 17+8). Similarly, for a = 34, m= 89, the GCD = 1 = 89-34*2 and the inverse of 34 modulo 89 is -34 (or 89+34). Finally, for a = 200, m= 1001, the GCD = 1 = 1001-5*200 and the inverse of 200 modulo 1001 is -5 (or 1001+5).

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Answer:

8x-4 they have altogether

Step-by-step explanation:

6x-7+2x+3=8x-4

Answer:

the graph has a positive slope with a y-intercept of 5

y = 1/4x + 5

Step-by-step explanation:

i found the slope by using points (0,5) and (4,6)

slope formula says to subtract the y-values and divide by difference of x-values:

(6-5) / (4-0) = 1/4

Answer:

\(x=\frac{1}{7}y+\frac{3}{7}\)

Step-by-step explanation:

\(y=7x-3\)

\(7x-3=y\)

\(7x-3+3=y+3\)

\(\frac{7x}{7}= \frac{y+3}{7}\)

\(x=\frac{1}{4}y+\frac{3}{7}\)

1.738 kg of coffee are required to produce 200 cups of coffee.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal.

Now it is given that,

1 pound of coffee yield 50 cups.

Since 1 pound = 0.4535 kg

Therefore, 0.4535 kg of coffee yield 50 cups.

Let x be the kgs of coffee that yields 200 cups of coffee.

Thus by proportion we can write,

0.4345 / 50 = x / 200

By cross multiplication we get,

50 x = 0.4345 * 200

⇒ 50x = 86.9

⇒ x = 86.9 / 50

⇒ x = 1.738 kgs

which is the required amount of coffee need to yield 200 cups.

Thus, 1.738 kg of coffee are required to produce 200 cups of coffee.

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The translation T‹1, -3› (x, y) can be expressed as a composition of a horizontal translation and a vertical translation as (x + 1, y - 3).

To express the translation T‹1, -3› (x, y) as a composition of a horizontal translation and a vertical translation, we can break it down into two separate translations:

Horizontal translation: T‹1, 0› (x, y)

This translation shifts the coordinates of a point horizontally by 1 unit without affecting the vertical position. It can be expressed as (x + 1, y).

Vertical translation: T‹0, -3› (x + 1, y)

This translation shifts the coordinates of a point vertically by -3 units without affecting the horizontal position. It can be expressed as (x + 1, y - 3).

Combining these two translations, we get the composition:

T‹1, -3› (x, y) = T‹0, -3› (x + 1, y) = (x + 1, y - 3)

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Step-by-step explanation:

F(x) = 4x^3 - 3x^2 + 5 neither

F(x) = -7x^2+1 even

y = cos (-x) even

y = csc x odd

y = sin x/cos x odd

To prove the transitive closure of a relation, you would need to show that the relationship satisfies the transitive property. The transitive property states that if A is related to B and B is related to C, then A is also related to C.

For example, if you have a relation R defined as a set of ordered pairs (A, B) where A is related to B, you can prove the transitive closure of R by showing that for any three elements A, B, and C in the set, if (A, B) and (B, C) are both in the set, then (A, C) must also be in the set.

To prove the transitive closure of a relation, you would need to demonstrate that this property holds true for all elements in the set. This can be done by showing that the relation is reflexive, symmetric, and transitive. Reflexivity means that every element is related to itself, symmetry means that if A is related to B, then B is related to A, and transitivity means that if A is related to B and B is related to C, then A is also related to C. If a relation satisfies these properties, it is considered to be a transitive closure.

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Answer:

\(\angle BAC=180^{\circ}-\frac{13\sin 23^{\circ}}{6}\)

Step-by-step explanation:

\(\frac{\sin(\angle BAC)}{13}=\frac{\sin 23^{\circ}}{6} \\ \\ \sin \angle BAC=\frac{13\sin 23^{\circ}}{6} \\ \\ \angle BAC=180^{\circ}-\frac{13\sin 23^{\circ}}{6}\)

Answer: No.

Step-by-step explanation: This is not a right triangle because if you add up all the sides, it does not equal 90 degrees.