Russell and Valerie start to walk away from the Cafeteria to their classes.
Russell walks 10 yards due West, then turns 40° toward South and walks 5 yards.
Valerie walks 10 yards due East, then turns 60° toward North and walks 5 yards.
Which student is farther from the cafeteria? Explain how you know using a diagram and words.

Answer:

\( \sf \: {( - 6)}^{3} = - 216\)

Step-by-step explanation:

Given problem,

→ (-6)⁸/(-6)⁵

Let's evaluate the problem,

→ (-6)⁸/(-6)⁵

→ 1679616/-7776

→ (1679616) ÷ (-7776)

→ -216

→ (-6)³

Hence, the answer is (-6)³.

Carla's behavior of putting in extra practices to become faster can be seen as an example of (Option A.) compensation. This is because she is trying to make up for her perceived lack of speed by working harder to become as fast as her teammates.

Carla's behavior of putting in extra practices to become faster can be seen as an example of compensation. This is because she is trying to make up for her perceived lack of speed by working harder to become as fast as her teammates.

By engaging in extra practices, Carla is attempting to compensate for her lack of speed and improve her performance. This is different from rationalization, which is the act of making excuses for one's behavior, or from regression, which is the act of reverting to a younger age in response to a stressful situation.

Finally, displacement is the act of redirecting one's emotions or anger onto another person or object.

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Answer:

60 units^2

Step-by-step explanation:

In order to find the area of a triangle, you do baseXheight/2. However, we don't have the height. So, we use the pythagorean theorem to solve for the missing side.

8^2+x^2=17^2

64+x^2=289

x^2=225

x=15

So, now we can solve for the area.

15*8=120

And divide by 2 we get 60

Based on our analysis, the set that is a basis in R^4 is S₃ = {(0,1,0,0), (0,0,1,0), (0,0,0,1), (0,-2,0,0)}. Therefore, the correct choice is E) (S₃).

To determine which set is a basis in R^4, we need to check if the vectors in each set are linearly independent and if they span R^4.

Let's analyze each set:

S₁ = {(1,2,1,0), (0,0,0,0)}

The second vector in S₁ is the zero vector, so S₁ cannot be a basis because a basis must consist of linearly independent vectors.

S₂ = {(1,0,-1,0), (1,-1,1,1), (1,3,2,-1)}

To check if the vectors in S₂ are linearly independent, we can construct a matrix using these vectors as columns and perform row operations to determine if the matrix is row-equivalent to the identity matrix.

Taking the augmented matrix [S₂ | 0], we can row reduce it to obtain:

[1 0 -1 0 | 0]

[0 1 1 1 | 0]

[0 0 0 0 | 0]

The row reduction shows that there is a nontrivial solution to the homogeneous system of equations, indicating that the vectors in S₂ are linearly dependent. Therefore, S₂ is not a basis in R^4.

S₃ = {(0,1,0,0), (0,0,1,0), (0,0,0,1), (0,-2,0,0)}

The vectors in S₃ form the standard basis for R^4, which means they are linearly independent and span R^4. Therefore, S₃ is a basis in R^4.

S₄ = {(1,1,-1,-1), (1,0,0,0), (0,2,0,0), (0,0,3,0)}

To check if the vectors in S₄ are linearly independent, we can again construct the augmented matrix [S₄ | 0] and row reduce it:

[1 1 -1 -1 | 0]

[1 0 0 0 | 0]

[0 2 0 0 | 0]

[0 0 3 0 | 0]

The row reduction shows that the matrix is row-equivalent to the identity matrix, indicating that the vectors in S₄ are linearly independent. Therefore, S₄ is a basis in R^4.

Based on our analysis, the set that is a basis in R^4 is S₃ = {(0,1,0,0), (0,0,1,0), (0,0,0,1), (0,-2,0,0)}. Therefore, the correct choice is E) (S₃).

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y(e2) = 4e^2 + (53 - 4e^2)e^(-16e^2), found by integrating the ODE y′ = 16x and using the initial condition y(e) = 53.

What is differential equation ?

A differential equation is an equation which contains one or more terms and the derivatives of one variable (i.e., dependent variable) with respect to the other variable.

mu(x) = e^(int 16 dx) = e^(16x^2/2)

multiply both sides of the differential equation by the integrating factor to obtain:

mu(x) * y′ = 16x * mu(x)

Integrating both sides with respect to x, we get:

mu(x) * y = 8x^2 + C

Dividing both sides by the integrating factor, we get:

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

Using the initial condition y(e) = 53, we can find the value of the constant C:

53 = 4e^2 + Ce^(-16e^2/2)

Solving for C, we get:

C = 53 - 4e^2

So the general solution for the differential equation is:

y = 4x^2 + (53 - 4e^2)e^(-16x^2/2)

Finally, to find y(e2), we plug in x = e2 into the general solution:

y(e2) = 4e^2 + (53 - 4e^2)e^(-16e^2)

And that gives us the value of y at x = e2.

y(e2) = 4e^2 + (53 - 4e^2)e^(-16e^2), found by integrating the ODE y′ = 16x and using the initial condition y(e) = 53.

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Answer:

1/3

Step-by-step explanation:

\(\frac{6}{9}*\frac{1}{2}\)

\(\frac{6*1}{9*2}\)

\(=\frac{6}{18}\)

Reduce by dividing both the numerator and denominator by the Greatest Common Factor GCF(6,18) = 6

\(\frac{6/6}{18/6}=\frac{1}{3}\)

Therefore:

\(\frac{6}{9}*\frac{1}{2}=\frac{1}{3}\)

[RevyBreeze]

We can use the Divergence Theorem to find the flux of the vector field F through the portion of the plane in the first octant. The Divergence Theorem states that the flux of a vector field through a closed surface is equal to the volume integral of the divergence of the vector field over the enclosed volume.

First, we need to find the unit normal vector to the plane passing through the three points. We can do this by taking the cross-product of two vectors that lie on the plane. Let's take the vectors (4,0,0) and (0,8,0) and find their cross-product:

(4,0,0) x (0,8,0) = (-8,0,32)

This vector is normal to the plane passing through the points (4,0,0), (0,8,0), and (0,0,10). To make it a unit normal vector, we divide it by its magnitude:

||(-8,0,32)|| = sqrt(8^2 + 0^2 + 32^2) = sqrt(1088) = 8sqrt(17)

So the unit normal vector to the plane is:

n = (-1/sqrt(17), 0, 4/sqrt(17))

Next, we need to find the divergence of the vector field F:

div(F) = ∂/∂x(1) + ∂/∂y(Y) + ∂/∂z(-z) = 0 + 1 - 1 = 0

Since the divergence is zero, the flux of the vector field through any closed surface is also zero. Therefore, the flux of F through the portion of the plane in the first octant is also zero.

If we had been asked to find the flux through the portion of the plane in the first octant bounded by the coordinate planes, we would have needed to find the limits of integration for the volume integral using the equations of the planes x=0, y=0, and z=0. However, since we are not given such limits, we assume that the portion of the plane in the first octant is unbounded and extends infinitely in all directions. In this case, the Divergence Theorem tells us that the flux is zero.

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Answer:

D- 38

Step-by-step explanation:

So out of 200 75.5% gave answers

And 38 would be 75.5% of 50

The Jacobi iteration, used to solve the system Ax = b, can be written in the form \(x(k+1) = x(k) + D^(-1)r(k)\), where x(k) is the approximate solution at iteration k, r(k) is the residual vector at iteration k, and \(D^(-1)\) is the inverse of the diagonal matrix D.

In the Jacobi iteration method, we update the current solution x(k) by adding the correction term \(D^(-1)r(k)\), where D is the diagonal matrix of the coefficients of the system Ax = b.

First, let's rewrite the equation Ax = b in terms of the residual vector:

Ax = b

=> Ax - b = 0

=> Ax - Ax(k) - b + Ax(k) = 0

=> A(x - x(k)) = b - Ax(k)

=> r(k) = b - Ax(k)

Now, multiplying both sides of the equation \(r(k) = b - Ax(k) by D^(-1)\), we get:\(D^(-1)r(k) = D^(-1)(b - Ax(k))\)

Substituting this into the update equation for Jacobi iteration, we have:

\(x(k+1) = x(k) + D^(-1)r(k)\) => \(x(k+1) = x(k) + D^(-1)(b - Ax(k))\)

Therefore, the Jacobi iteration can be written as \(x(k+1) = x(k) + D^(-1)r(k)\), where x(k) is the current approximation, r(k) is the residual vector, and D^(-1) is the inverse of the diagonal matrix D.

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The solution to the system of equations y = 1/3x - 10 and 2x + y = 4 is (6, -8).

A system of equations is a collection of two or more equations with a same set of unknowns.

The substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation.

The given system of linear equations are :

y = 1/3x - 10 and 2x + y = 4

On solving two equations by using substitution method, It is given that

\(y = \frac{1}{3}x-10\)    … (1)

2x + y = 4       … (2)

Substituting (1) in (2)

⇒ \(2x + (\frac{1}{3}x-10) = 4\)

By further calculation

⇒ \(2x + \frac{1}{3}x - 10 = 4\)

⇒ \(2x + \frac{1}{3} x = 4 + 10\)

⇒ \(2x + \frac{1}{3} x = 14\)

Taking LCM

⇒ \(\frac{(6+1)}{3}x = 14\)

⇒ \(\frac{7}{3}x = 14\)

By cross multiplication

⇒ 7x = 14 × 3

⇒ 7x = 42

Divide both sides by 7

⇒ x = 6

Substitute the value of x in equation (1)

\(\Rightarrow\ y = (\frac{1}{3} \times (6) - 10)\)

So we get

⇒ y = (2-10)

⇒ y = -8

Therefore, the solution to the system of equations is (6, -8).

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Answer:

\(\frac{100}{3}\)

Step-by-step explanation:

I hope this helps!

Answer:

a= 10     b=1

Step-by-step explanation:

I had the same question

Answer:

Step-by-step explanation:

The slope of line 2=\(\frac{-3-(-3)}{7-5}\)

                               =0

Answer: The probability of event B, P(B), is 2.00.

Step-by-step explanation:

1. The formula for the probability of two independent events A and B occurring together is P(A and B) = P(A) * P(B).

2. We know that P(A) = 0.02 and P(A and B) = 0.04.

3. Substituting these values into the formula, we get 0.04 = 0.02 * P(B).

4. Solving for P(B), we divide both sides of the equation by 0.02.

5. This gives us P(B) = 0.04 / 0.02 = 2.00.

Please note that probabilities typically range from 0 to 1, so a probability of 2.00 seems unusual. It might be worth double-checking the provided probabilities for events A and B.

The box measures 100.79 cm by 100.79 cm by 50.40 cm in size, which minimizes the quantity of material used.

Given,

Let the side of the square base be x

h be the height of the box

Volume V = x²h

512000 = x²h

h = 512000/x² ..... 1

Surface area =  x² + 2xh + 2xh

Surface area S =  x² + 4xh  ...... 2

Substitute 1 into 2;

From 2;

S =  x² + 4xh

S = x² + 4x(512000/x²)

S = x² + 2048000/x

To minimize the amount of material used;

dS/dx = 0

dS/dx = 2x - 2048000/x²

0 = 2x - 2048000/x²

0 = 2x³ - 2048000

2x³ = 2048000

x³ = 1024000

x = ∛1024000

x = 100.79 cm

Since Volume = x²h

512000 = 100.79²h

h = 512000/10158.62

h = 50.40 cm

Hence the dimensions of the box that minimize the amount of material used is 100.79 cm by 100.79 cm by 50.40 cm

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Answer:

k = 2/3 x

y = 2/3.

Step-by-step explanation:

y = kx where k is a constant

y = 2 when x = 3 so:

2 =k*3

k = 2/3.

The equation is y = 2/3 x.

When x = 1

y = 2/3 * 1 = 2/3.

If the value of the constant k is 2/3. Then the value of y at x = 1, is 2/3

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

If y varies directly as x.

y ∝ x

y = kx

Where k is a constant.

At x = 3, the value of y will be 2.

2 = 3k

k = 2/3

Then the value of y at x = 1, we have

y = (2/3) 1

y = 2/3

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The price per night for a Suite room for check-in on Friday and Saturday would be amount $278.50 .

The price per night for a Suite room for check-in on Friday and Saturday would be amount $278.50.

1. Calculate the price of a Deluxe room for check-in on Sunday until Thursday:

$223 / 1.70 = $131.18

2. Calculate the price of a Deluxe room for check-in on Friday and Saturday:

$131.18 x 1.25 = $163.98

3. Calculate the price of a Suite room for check-in on Friday and Saturday:

$163.98 x 1.70 = $278.50

The price per night for a Suite room for check-in on Friday and Saturday would be $278.50.

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Answer:

1. Sides of ∠4 are DC and DG

2. Vertex of ∠2 = Point D

3. Another name for ∠3 = ∠EDG

4. ∠5 is an acute angle

5. ∠CDE is a straight angle

6. m ∠CDF = m∠5 + m∠1 = 42 + 117 = 159°

7. m ∠FDE = 17°

Step-by-step explanation:

For # 7 note that since DG is perpendicular to DF, m ∠GDF = 90°

m ∠GDF = m ∠3 + m ∠FDE
Since m ∠3 = 73°, m∠FDE = 90 - 73 = 17°

Given a point with coordinates (x, y), to rotate 90º counterclockwise, the rule is:

In thisc ase, we have the point:

Applying the rule:

Among the 769 team members, 706 of them are assigned to operates in 2 shifts schedule. The proportion of team members not assigned to one of the stations is 63 / 769

Proportion means a share from total set being discussed.

Data from the given case:

- The assembly has 769 team members.

- The assembly has 353 stations

- At each station, there are 2 shifts operations.

Assuming that 1 person is assigned to 1 shift operation, then there will:

353 x 2 = 706 person assigned.

The remaining team members that not assigned is:

769 - 706 = 63 person.

Therefore, the share or the proportion of unassigned team members is:

63/769

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Answer:

c

Step-by-step explanation:

Answer: you would use the last option

Answer:

x>-2 and x<-1

Step-by-step explanation:

just do it

∝

The solution set in which all the the possible values of x which satisfy the given compound inequality is -

x ∈ A , where A = (- ∞, -1)

In mathematics, inequality refers to a relationship that makes a non-equal comparison between two numbers or other mathematical expressions.

Given is the following compound inequality -

2(x – 2) + 7 > –1

and

5 – 4x > 9

Inequality - 1

2(x – 2) + 7 > –1

2x - 4 + 7 > - 1

2x + 3 > - 1

2x + 3 - 3 > - 1 - 3

2x > -4

x > -2

x < 2

Inequality - 2

5 – 4x > 9

5 - 5 - 4x > 9 - 5

- 4x > 4

-x > 1

x < - 1

Since x < - 1 and x < 2, therefore the inequality → x < -1 represent all the solutions. We can write the solution set as -

x ∈ A , where A = (- ∞, -1)

Therefore, the solution set in which all the the possible values of x which satisfy the given compound inequality is -

x ∈ A , where A = (- ∞, -1)

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The null and alternative hypotheses for the above scenario are

H0: Their van has a miles/gallon (MPG) rating equal to 57.2 miles/gallon

Ha: Their van has a miles/gallon (MPG) rating that is different from 57.2 miles/gallon

Given that,

One automaker says that their van gets 57.2 miles per gallon (mpg). An impartial testing business has been hired to evaluate the mpg for this van. They tested 91 vans, and the results showed that the average mileage was 56.9 with a standard deviation of 1.8 mpg. Is there adequate proof that the vans don't meet their mpg rating at the 0.025 level

To find: state the null and alternative hypotheses for the above scenario.

The null and alternative hypotheses for the above scenario are

H0: Their van has a miles/gallon (MPG) rating equal to 57.2 miles/gallon

Ha: Their van has a miles/gallon (MPG) rating that is different from 57.2 miles/gallon

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The Cartesian equation of the line that contains the points A and B, where A is the intersection point of the given plane with the x-axis and B is the intersection point with the z-axis, is x = 1 and z = 3.

To find the Cartesian equation of the line, we need to determine the values of x and z while allowing y to vary freely. Since point A lies on the x-axis, its y-coordinate is 0, so we have x = 1 and y = 0 for point A. Similarly, since point B lies on the z-axis, its y-coordinate is also 0, so we have z = 3 and y = 0 for point B.

Thus, the equation x = 1 represents the line that contains point A, and the equation z = 3 represents the line that contains point B. Since y can vary freely, we do not include it in the equations. Therefore, the Cartesian equation of the line that contains points A and B is x = 1 and z = 3.

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Answer:

120 * 0.90 = 108 km

Step-by-step explanation:

Answer:

108km

Step-by-step explanation:

Answer:

7/2

Step-by-step explanation: