using separation of variables, solve the differential equation, e−ycos(x) dydxsin2(x)=0. use c to represent the arbitrary constant.

The MAD value will be = 3.

Given,

Last four months sale : 8 , 10 , 15 , 9 .

Last four forecasts were 5, 6, 11, and 12 units.

Now, we have to find the Mean Absolute Deviation (MAD) of these forecasts.

Now, the mean of the forecast values for the four months is .

Therefore, the sum of absolute deviations of the forecast values from that mean will be = |5 - 8.5| + |6 - 8.5| + |11 - 8.5| + |12 - 8.5| = 3.5 + 2.5 + 2.5 + 3.5 = 12.

Therefore, the MAD value will be = 12/4

MAD = 3

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Answer:

x=10

Step-by-step explanation:

When peers at work offer suggestions to correct a weakness, it is important for the person to respond in a thoughtful and constructive manner.

Here are some guidelines for effectively addressing such suggestions:

Listen and be open-minded: Actively listen to the suggestions without becoming defensive or dismissive. Remember that your peers are offering their perspectives to help you improve. Keep an open mind and be willing to consider their viewpoints.

Express gratitude: Appreciate the effort and willingness of your peers to provide feedback. Thank them for their suggestions and acknowledge their input. Demonstrating gratitude fosters a positive and collaborative work environment.

Seek clarification, if needed: If you need further clarification on any of the suggestions, ask your peers for more information. This shows your commitment to understanding their feedback and ensures you can address the weakness effectively.

Reflect on the feedback: Take some time to reflect on the suggestions offered. Evaluate their validity and consider whether they align with your own self-assessment. Honest self-reflection is crucial in recognizing and addressing weaknesses.

Develop an action plan: Once you have understood the suggestions and reflected on them, create an action plan to address the weakness. Break down the steps you need to take to improve and set realistic goals for yourself. This proactive approach demonstrates your commitment to personal growth and professional development.

Seek support if necessary: If you require additional resources or assistance to address the weakness, don't hesitate to ask for help. Reach out to mentors, supervisors, or relevant professionals who can provide guidance or training. Collaborating with others can accelerate your progress in overcoming the weakness.

Communicate progress: Keep your peers informed about the steps you are taking to improve. Sharing your progress demonstrates your commitment to growth and allows them to see your efforts. It also encourages ongoing support and accountability from your colleagues.

Show resilience: Addressing weaknesses takes time and effort. Be prepared for setbacks and challenges along the way. Stay resilient and maintain a positive mindset, focusing on continuous improvement rather than being discouraged by temporary obstacles.

Remember, accepting and addressing weaknesses is a part of personal and professional growth. Embrace the feedback from your peers as an opportunity to enhance your skills and become a stronger professional.

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a.

5 minutes

b.

30 litres per minute

The probability that a student is left-handed is 13%, so the probability that a student is right-handed is 87%.

Out of 200 seats, 30 are designed for left-handers. Therefore, the number of seats designed for right-handers is 200 - 30 = 170.

If a class has 188 students, and 13% of them are left-handed, then the number of left-handed students is 188 * 0.13 = 24.44, which we can round up to 25.

This means that the number of right-handed students in the class is 188 - 25 = 163.

The probability that a right-handed student is forced to use a lefty arm tablet is equal to the probability that there are no more right-handed seats available when they arrive.

The probability that the first student who arrives is right-handed and gets a right-handed seat is 170/200 = 0.85.

If a right-handed student takes a right-handed seat, then there are 169 right-handed seats left out of 199 total seats remaining.

The probability that the second student who arrives is also right-handed and gets a right-handed seat is 169/199.

Continuing in this way, the probability that all 163 right-handed students get right-handed seats is:

(170/200) * (169/199) * (168/198) * ... * (8/38) * (7/37) * (6/36)

The probability that at least one right-handed student is forced to use a lefty arm tablet is equal to 1 minus the probability that all 163 right-handed students get right-handed seats:

1 - [(170/200) * (169/199) * (168/198) * ... * (8/38) * (7/37) * (6/36)]

Using a calculator, we find that this probability is approximately 0.358 or 35.8%.

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An equation of the line that passes through the given point and is

(a) parallel to is y = -3x - 7

(b) perpendicular to is y = (1/3)x + 1/3.

a) Parallel line

The slope of the given line is -3. The slope of a parallel line is also -3. So, the equation of the parallel line will be of the form:

y = -3x + b

Plug the point (-2, -1) into this equation to solve for b, the y-intercept.

-1 = -3(-2) + b

-1 = 6 + b

-7 = b

Therefore, the equation of the parallel line is:

y = -3x - 7

b) Perpendicular line

The slope of a perpendicular line is the negative reciprocal of the slope of the given line. The slope of the given line is -3, so the slope of the perpendicular line is 1/3. So, the equation of the perpendicular line will be of the form:

y = (1/3)x + b

Plug the point (-2, -1) into this equation to solve for b, the y-intercept.

-1 = (1/3)(-2) + b

-1 = -2/3 + b

1/3 = b

Therefore, the equation of the perpendicular line is:

y = (1/3)x + 1/3

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The correct option is the third one; (14, 4); The vertex represents the maximum profit.

For a general quadratic equation

y = ax² + bx + c

The vertex is at the x-value:

x = -b/2a

Here the quadratic function is:

f(x)=  -x² + 28x - 192

The vertex is at:

x = -28/2*-1 = 14

Evaluating in x= 14 we get:

f(14) = -14² + 28*14 - 192 = 4

So the vertex is at (14, 4), and because the leading coefficient is negative, this is the maximum profit.

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Answer:

The answer is explained below

Step-by-step explanation:

Statement                                                        Reason

Triangle ACD is isosceles and                         Given

<1 = <3 (<1 is congruent to <3)                                                            

∠3 = ∠4                                                             Isosceles   triangle base angles.

∠1 = ∠4                                                              Substitution Theorem

∠1 = ∠4                                                             They are produced by two lines .                                                                         AB and CD cut by transversal  

.                                                                         line AD

Segment AB || Segment CD                           Alternate interior angle theorem  

The Alternate interior angle theorem states that if two lines cut by a transversal line form congruent alternate interior angles, then the two lines are parallel to each other.

The expected value of sales at a price of $1 is 11.015 for the given regression demand equation.

In the regression demand equation e(log(sales | price)) = 11.015 - 2.442 log(price), you want to find the expected value of sales at a price of $1. To find the expected value of sales, you need to substitute the given price of $1 into the equation and solve for the sales. Substituting the price of $1 into the equation, you get: e(log(sales | 1)) = 11.015 - 2.442 log(1). Since log(1) = 0, the equation simplifies to: e(log(sales | 1)) = 11.015 - 2.442 * 0, e(log(sales | 1)) = 11.015
Therefore, the expected value of sales at a price of $1 is 11.015.

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Answer:

4

Step-by-step explanation:

4/1 or 4

y over x, and simplify

Answer:

1 by 2 is o

Step-by-step explanation:

so slope is 1 by 2 of o .

Given:

The figure of a triangle.

To find:

The exterior angle of the triangle m∠NPI.

Solution:

According to the exterior angle theorem, value of exterior angle of a triangle is equal to the sum of the opposite interior angles.

Using the exterior angle theorem, we get

\(m\angle NPI=65^\circ+78^\circ\)

\(m\angle NPI=143^\circ\)

Therefore, the measure of angle NPI is 143 degrees.

Thomas can pack the items into a maximum of 20 bags, with each bag containing 24 items after calculated with greatest common divisor.

To find the maximum number of bags Thomas can pack, we need to find the greatest common divisor (GCD) of 120, 168, and 192. The GCD will represent the maximum number of items that can be packed into each bag.

To find the GCD, we can use the Euclidean algorithm. First, we find the GCD of 120 and 168:

168 = 1 * 120 + 48

120 = 2 * 48 + 24

48 = 2 * 24 + 0

Therefore, the GCD of 120 and 168 is 24.

Next, we find the GCD of 24 and 192:192 = 8 * 24 + 0

Therefore, the GCD of 120, 168, and 192 is 24.

So, Thomas can pack 24 items into each bag. To find the maximum number of bags he can get, we divide the total number of items by 24:

Total number of items = 120 + 168 + 192 = 480

Number of bags = 480 / 24 = 20

Therefore, Thomas can get a maximum of 20 bags.

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The number of individuals needed to produce the sample data used to find the regression equation is 21.

Given,

In the question:

A researcher who is evaluating the significance of a multiple regression equation with two predictor variables, obtains an F-ratio with df = 2, 18.

To find the regression equation.

Now, According to the question:

F test:

In the multiple regression, the relationship between the variables is statistically significant can be check by F-test. The F-test used to determine the statistical regression models which is best suited for the population.

A value of 2 represents the degrees of freedom due to regression.

and, the value 18 represents the degrees of freedom due to or residuals.

The formula of degree of freedom due to residual is:

\(df_r_e_s_i_d_u_a_l\) = n - k - 1

The number of individuals in the sample data (n) can be calculated as:

\(df_r_e_s_i_d_u_a_l\) = n - k - 1

18 =  n - 2 - 1

18 =  n - 3

18 + 3 = n

21 = n  OR

n = 21

Hence, The number of individuals needed to produce the sample data used to find the regression equation is 21.

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The correct answer for the equation of the line perpendicular to \(y = 2x+4\) and passes through the point (4,6) is   \(y = -\dfrac{1}{2}x +8\).

Given:

The equation of the line is \(y = 2x+4\)

Points: (4,6)

calculate the slope of the line, as the slope of the perpendicular lines are negative reciprocals of each other.

The given line has a slope of \(2\), The negative reciprocal of 2 is  (-1/2)

Use the point-slope form of the equation:

The point-slope form of the equation with slope (-1/2) and passes through the point (4,6) is:

\(y-y_1 = m(x-x_1)\)

\(x_1 = 4\)

\(y_1 = 6\)

Put the value of \(x_1\) and \(y_1\) in the formula:

\(y -6 = -\dfrac{1}{2} x + 2\)

\(y = -\dfrac{1}{2}x +8\)

The equation of the line is  y = (-1/2)x + 8

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To find the equation of a line perpendicular to y = 2x + 4, we need to find the negative reciprocal of the slope and use the point-slope form of a line to determine the equation.

To find the equation of a line that is perpendicular to y = 2x+4, we need to find the negative reciprocal of the slope of the given line. The slope of y = 2x+4 is 2, so the negative reciprocal of 2 is -1/2. Now we have the slope of the perpendicular line.

Next, we can use the point-slope form of a line to find the equation. The point-slope form is y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.

Substituting the values (4, 6) and -1/2 into the point-slope form, we get y - 6 = (-1/2)(x - 4). Simplifying the equation gives us y = -x + 8. Therefore, the correct answer is B. y = -x + 8.

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Answer:

y=6/5x+3

Step-by-step explanation:

Get into y=mx+b from

Subtract 6x

-5y=-6x+12

Divide by -5

y=6/5x-12/5

Use y-y1=m(x-x1)

y-(-3)=6/5(x-(-5))

Negative times a negative is a positive

y+3=6/5(x+5)

Distribut

y+3=6/5x+6

Subtract 3

y=6/5x+3

Hope this helped!

Answer:

1/3

Step-by-step explanation:

The exterior angle m∠DEF (6x - 10)° is derived to be equal to 56°

The exterior angle of a triangle is equal to the sum of the two opposite interior angles.

interior opposite angles are (2x°- 4)° and (2x + 16)°

m∠DEF = m∠CDE + m∠ECD

6x - 10 = 2x - 4 + 2x + 16

6x - 2x - 2x = 10 + 16 - 4 {collect like terms}

2x = 22

x = 22/2 {divide through by 2}

x = 11

m∠DEF = 6(11) - 10

m∠DEF = 56°

Therefore, the exterior angle m∠DEF (6x - 10)° is derived to be equal to 56°

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The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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Answer:

no

Step-by-step explanation:

using the Factor theorem.

If (x + h) is a factor of f(x) then f(- h) = 0

for factor (x + 3) then evaluate P(- 3)

P(- 3) = (- 3)³ - 5(- 3)² + 3(- 3) + 9 = - 27 - 45 - 9 + 9 = - 72

since f(- 3) ≠ 0 then (x + 3) is not a factor of P(x)

Answer:

Step-by-step explanation:

Whatever you do to the left you must do to the right, he multiplied 12 but forgot to multiply the -4 on the left and the + 1 on the right by the number 12

Answer:

9,7

Step-by-step explanation:

subtract 6 from 15 and 9 from 16

Answer:

$ 1,232

Step-by-step explanation:

Answer:

Try the links below

do CTRL+F and then look up micah also trims bushes.

Your answer should be there

Step-by-step explanation:

https://mmayo.weebly.com/uploads/8/3/8/3/8383777/istep_extended_response_review.docx

http://stalbaum.weebly.com/uploads/1/4/0/8/14088751/istep_review.pdf

Answer:

I thinks is

\( \frac{1}{200} \)

Answer:

A ≈ 14.8 units²

Step-by-step explanation:

the area (A) of the triangle is calculated as

A = \(\frac{1}{2}\) yz sin Y ( that is 2 sides and the angle between them )

where x is the side opposite ∠ X and z the side opposite ∠ Z

here y = XZ = 4.3 and z = XY = 7 , then

A = \(\frac{1}{2}\) × 4.3 × 7 × sin79°

   = 15.05 × sin79°

   ≈ 14.8 units² ( to 1 decimal place )

Answer:

1300/100 X 105 = 1365

1365/4 = 341.25 per week

341.25/40= 8.53125

$8.53

Step-by-step explanation:

if the solution has "nice" numbers, we can split the expression into 2 factors in the form

(x + a)(x + b) = x² + (a+b)x + ab

as this is equal to x² + 4x - 21.

ab = -21

so, one is positive and one is negative.

and 4 = a + b

we know the typical factors of 21 : 3×7

and then we see easily : 7-3 = 4

so,

we have

(x + 7)(x - 3) >= 0

this has 2 x-intercepts (x-values when y = 0) :

x = -7

x = 3

because the coefficient of x² is positive (1), we know that the parabola (or quadratic equation) is opening upwards.

that means the y-values for x-values between -7 and +3 are negative (< 0), but the y-values for everything else are positive.

so, the solution are the intervals

x <= -7 and x >= 3

in these areas is the expression x² + 4x - 21 >= 0.

Answer: Not applicable

Step-by-step explanation:

To determine the profit earned from Jamal's sales, we need more information such as the price of each item and the total profit earned from each item. Without this information, it is impossible to calculate the profit earned from Jamal's sales.