tan(-x)cos(-x) simplify

Answers

Answer 1

The trigonometric equation be tan(-x)cos(-x) then we get -sin (x).

What is meant by trigonometric functions?

A function of an angle is a trigonometric function. They are utilized to connect the triangle's angles and sides' lengths.

Trigonometry is the study of angles and the angular connections between figures in two and three dimensions. The trigonometric functions that make up trigonometry are cosecant, cosine, cotangent, secant, sine, and tangent. These are also known as the circle functions.

Trigonometry is used to define directions such as the north, south, east, and west. It also tells you the direction to point the compass in order to travel straight forward. It helps to locate a certain location during navigation. The shore's separation from a certain place in the sea can likewise be determined using this method.

Let the given function be tan (-x) cos (-x)

Use the negative angle identity: tan (-x) = -tan (x)

= cos (x) (-tan (x))

Remove parentheses: (-a)= -a

= -cos (x) tan (x)

Express with sin, cos

= -sin (x)

Therefore, simplifying the equation, tan(-x)cos(-x) we get -sin (x).

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Answer 2

tan(-x).cos(-x) = -sin(x)

What are trigonometric ratios?

Sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant are the six trigonometric ratios (sec). A branch of mathematics called trigonometry in geometry deals with the sides and angles of a right-angled triangle. Trig ratios are therefore assessed in relation to sides and angles.are therefore assessed in relation to sides and angles.

We know that, tan(x) = sin(x)/cos(x)

Now, calculating tan(-x).cos(-x)

⇒ [tex]\frac{sin (-x).cos (-x)}{cos (-x)}[/tex]

⇒ sin(-x)

Since, sin function is an odd function, it can be expressed as below.

sin(-x) = -sin(x)

Thus, tan(-x).cos(-x) = -sin(x)

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Related Questions

explain how to show that the table of values below represents the equation y = 2/3x + 1

Answers

Answer: plug -15 in for x and if we get get -9 out because 2/3 of -15 is -10 and -10+1 =-9
we can do the same for the rest of these and we see that they'll come out to the y value

Trevor is making payments on a car that costs 26,555 dollars. He makes 36 equal payments. If he rounds the equal payments up to the nearest whole dollar, about how much will he overpay after 36 months? Explain.

Answers

Answer:

$13 overpayment

Step-by-step explanation:

We can find the amount Trevor should pay each month by dividing the $26,555 by 36 months:

               ($26,555/(36 months)) = $737.64 per month

Since Trevor decide to round up to the nearest dollar, he will pay $738 each month.  That's an overpayment of $0.361 each month.

After 36 months of overpaying by $0.361 each month, Trevor will have overpaid:

  ($0.36/month)*(36 months) = $13 overpayment


Find AB in simplest form, if A(-3, 4) and B(4, 7).

Answers

Answer: AB≈7.62 units

Step-by-step explanation:

A(-3,4)      B(4,7)

[tex]\boxed {L=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} }\\\\x_1=-3\ \ \ \ x_2=4\ \ \ \ y_1=4\ \ \ \ y_2=7[/tex]

Hence,

[tex]AB=\sqrt{(4-(-3))^2+(7-4)^2} \\\\AB=\sqrt{(4+3)^2+3^2} \\\\AB=\sqrt{7^2+9} \\\\AB=\sqrt{49+9} \\\\AB=\sqrt{58} \\\\AB\approx7.62\ units[/tex]

When the following expression is written in simplest form, what is the coefficient of the variable term?

-2.5y + 8y - 10.5y

5.5
0
-21
-5

Answers

Answer: -5

Step-by-step explanation:

[tex]-2.5y + 8y - 10.5[/tex]

[tex]= 5.5y - 10.5y[/tex]

[tex]= -5y[/tex]

Hence, the answer is [tex]-5[/tex].

Answer:

D)  -5

---------------------------------------------

All terms have same variable of y.

Collect all terms and simplify by adding up the coefficient:

-2.5y + 8y - 10.5y = (- 2.5 + 8 - 10.5)y = (-5)y = -5y

The coefficient of the variable is -5.

What is the slope for (-5, 8); (-4, 2)

Answers

Answer: -10

Step-by-step explanation:

y2-y1

---------

x2-x1

a thin, 120 g disk with a diameter of 8.00 cm rotates about an axis through its center with 0.18 j of kinetic energy.

Answers

The speed of a point on the rim  is 2.44 m/s.

What is a quick answer for diameter?

The diameter is the distance along the circle's center that must travel in order to touch two points on its edge.

First convert diameter into radius

r = d/2 = 0.08/2 = 0.04 m

The moment of inertia of disc is given by

I = 0.5mr²

Where m is the mass and r is the radius of the disk

I = 0.5(0.1)(0.04)²

I = 0.00008 kg.m²

and since we are dealing with rotational motion then rotational kinetic energy is given by

E  =  0.5 I ω²

we have to separate ω

ω² = E/0.5 I

ω = √E/0.5 I

ω = √0.15/0.5(0.00008)

ω = 61.23 rad/sec

Finally we know that speed is given as

v = ω r

v = 61.23 (0.04)

v = 2.44 m/s

Therefore, the speed of a point on the rim  is 2.44 m/s.

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The complete question is -

A thin, 100 g disk with a diameter of 8.0 cm rotates about an axis through its center with 0.15 J of kinetic energy. What is the speed of a point on the rim

State the relationship between the congruent angles

Answers

Answer:

1. Alternate exterior angles

2. Vertically opposite angles

3. Alternate interior angles

4. Corresponding angles

How do you convert 0.51 as a fraction?

Answers

Step-by-step explanation:

Just write the number in the numerator place.

[tex] \frac{51}{} [/tex]

and then check the decimal point means how many number before is the point.

e. g. here is two numbers.

Then write 1 and 0 in the place of denominator.

Note: write 0 that times in which the decimal point is before the number.

[tex] \frac{51}{100} [/tex]

and at last simplify the fraction. if possible here is not. it is the simplest form of the fraction.

hope understand

A wire is used to anchor a 20-foot-tall pole. One end of the wire
is attached to the top of the pole. The other end is fastened to a
stake five feet away from the bottom of the pole. Find the length
of the wire.

Answers

The length of the wire attached to the pole is 20.62 feet

What is the length of the wire?

The pole is perpendicular to the ground in the direction of the point where the wire is attached to the ground to form a right angle triangle.

A leg of the triangle is 20 feet(length of the pole from the surface of the ground to the top)

The other leg is5 feet(distance from the base of the pole to the point where the wire is attached to the ground)

The third side of the right angle triangle is the hypotenuse(length of the wire)

Applying Pythagoras theorem;

Hypotenuse² = Opposite² + Adjacent²

= 20 feet ² + 5 feet²

= 400 + 25

Hypotenuse² = 425

Find the square root of both sides

Hypotenuse = √425

= 20.6155

Approximately,

Hypotenuse = 20.62 feet

In conclusion, the hypotenuse side of the right angle triangle is 20.62 feet

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15 points please help!,

There are some nickles, dimes, and quarters in a large piggy bank. For every 2 nickles there are 3 dimes. For every 2 dimes there are 5 quarters. There are 500 coins total.

1. How many nickles, dimes, and quarters are in the piggy bank? Explain.

2.How much are the coins worth?

Answers

The number of nickels is 173.

The number of dimes is 258.

The number of quarters is 69.

The coins are worth $51.7.

What is an expression?

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

For every 2 nickles, there are 3 dimes.

For every 2 dimes, there are 5 quarters.

This means,

Let,

Nickles = N

Dimes = D

Quarters = Q

2N = 3D

N = 3D/2

2D = 5Q

Q = 2D/5

Now,

N + D + Q = 500

3D/2 + D + 2D/5 = 500

15D + 10D + 4D = 500 x 10

29D = 5000

D = 5000/29

D = 173

Now,

N = 3 x 172 / 2

N = 3 x 86

N = 258

Q = 2 x 172 / 5

Q = 69

Now,

Total coins = 500

173 + 258 + 69 = 500

Now,

20 nickels = $1

10 dimes = $1

4 quarters = $1

So,

173 nickels = $1 x 173 / 20 = $8.65

258 dimes = $1 x 258 / 10 = $25.8

69 quarters = $1 x 69 / 4 = $17.25

The total worth.

= $8.65 + $25.8 + $17.25

= $51.7

Thus,

The number of nickels is 173.

The number of dimes is 258.

The number of quarters is 69.

The coins are worth $51.7.

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which triangle pairs are not necessarily congruent? select all that apply

Answers

The second triangle pairs are not necessarily congruent.

Option 2 is true.

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

There are some triangles is shown in figure.

Now,

We know that;

Two triangles are congruent by theorem of SAS , ASA theorem.

So, When the ''two sides and one angle'' or ''two angle and one side'' are equal to another triangle then the triangles are congruent.

Here, In second option we have;

Only angles are equal, which make them similar not congruent.

Thus, We get;

The second triangle pairs are not necessarily congruent.

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Is (6, 4) a solution to this system of
y = 2x - 8
y = -1/3x + 6
3
yes
no

(This is on IXL)

Answers

Answer:

Yes

Step-by-step explanation:

y = 2x - 8  Plug is 6 for x and 4 for y

4 = 2(6) - 8

4 = 12 - 8

4 = 4

(6,4) is a solution for this equation

y = -1/3 x + 6

4 = -1/3(6) + 6

4 = -2 + 6

4 = 4

(6,4) is a solution for this equation too.

Magan went to the grocery store and purchased cans of soup and frozen dinners. Each can of soup has 350 mg of sodium and each frozen dinner has 650 mg of sodium. Magan purchased a total of 11 cans of soup and frozen dinners which collectively contain 4750 mg of sodium. Determine the number of cans of soup purchased and the number of frozen dinners purchased.

and please add how many cans of soup and boxed dinners she purchased

Answers

The number of cans of soup bought is 8 and the number of frozen dinners purchased is 3.

How many cans of soup and frozen dinners was purchased?

s + f = 11 equation 1

350s + 650f = 4750 equation 2

Where:

s = number of soup cans that Magan bought f = number of frozen dinner that Magan bought

The elimination method would be used to solve for the required values:

Multiply equation 1 by 350

350s + 350f = 3850 equation 3

Subtract equation 2 from equation 3 :

300f = 900

f = 900 / 300

f = 3

Substitute for f in equation 1 :

s + 3 = 11

s = 11 - 3

s = 8

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when does a parametric equations describe a physical situation where a standard relationship between two variables does not suffice

Answers

Parametric equations describe a physical situation only when we have to draw the coordinates of the figure which actually didn't have any such coordinates.

There are many reasons. The best way to answer any “why?” question in math is to work, at least a little, with the subject to see what it can do.

With parametric equations you will find that they simplify many problems that are a complex jumble of variables if viewed in rectangular coordinates.

To illustrate a very simple case:

Define a certain circle as: x^2 + y^2 = 25 in rectangular coordinates.

Switching to polar coordinates we have: x = 5*cos(theta) and y = 5*sin(theta).

We have parameterized an equation in two variables into two simpler equations in the one variable theta. We did this by finding a single variable (the parameter theta) that will show the behavior of x and y independently.

This can be a very powerful tool if we have an equation in many variables and can reduce it to many equations but in fewer variables.

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The coordinates of the endpoints A B are given. A (7,6) and B (-9,-6). Point K is located on AB so that AK= 3/1. What is the x-coordinate of point K?

Answers

The x-coordinate of the point K that divides AB in 3:1 will be -5.

What is the section of the line?

Let A (x₁, y₁) and B (x₂, y₂) be a line segment. Then the point P (x, y) divides the line segment in the ratio of m:n. Then we have

x = (mx₂ + nx₁) / (m + n)

y = (my₂ + ny₁) / (m + n)

The directions of the endpoints A and B are given. A (7,6) and B (- 9,- 6). Point K is situated on the Stomach muscle with the goal that AK: KB = 3/1.

Then the x-coordinate of the point K is given as,

x = (mx₂ + nx₁) / (m + n)

x = [3(-9) + 1(7)] / (3 + 1)

x = (- 27 + 7) / 4

x = - 20 / 4

x = - 5

The x-coordinate of the point K that divides AB in 3:1 will be -5.

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In the following diagram HI is parallel JK

Answers

Answer:there is no diagram

Step-by-step explanation:

The length of a picture frame is 8 inches more than the width. For what values of x is the perimeter of the picture frame greater than 160 ​inches?

Answers

Hi I believe it is 21 (not the meme but 21 the number lol) 160/8=20. Add 8 which is an extra 1 to make it 21 hope it makes sense

10) if ( x, y ) is a point on the line y = mx + b and if z is the distance between ( x, y ) and ( 0, b ) then z=
a) mx + b
b) absolute value of( x) √1 + m²
explain pleasseeee

Answers

Refer to the photo taken. Let me know if you have any questions.

Q1. Which of the following are quadratic equations? 11= - 4x2-x3

Answers

The given equation 11= - 4x^2-x^3 is not quadratic. It is a cubic.

What is quadratic?

The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the general form ax^2 + bx + c = 0. where a, b, and c are numerical coefficients and x is an unknown variable.

Is a quadratic 2 or 4?

Quadratic expressions are those involving powers of x up to the second power, not the fourth power, hence the prefix quad signifies "four" rather than "two."

As highest power with the variable is 3 so it is a cubic expression not a quadratic.

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Hello guys I need help with this if you don’t mind.

Answers

Answer:

2? – (-6)x +(-27), x² + 6x – 27 = 0

Step-by-step explanation:

i used a calculator

Convert 79 pounds to kilograms. (1 pound = 0.454 kilogram)

17.4 kilograms
35.866 kilograms
174 kilograms
358.66 kilograms

Answers

Option B is correct answer, 79 pounds is equal to 35.866 kilograms.

What is unit conversion?

A unit conversion is used to express the same property in a different unit of measurement. Minutes can be used to measure time instead of hours, and feet, kilometers, or any other measurement can be used to measure distance in place of miles. Measurements are typically provided in one system of measurement, such as feet, but are necessary in a different system, such as chains. A mathematical formula known as a conversion factor enables an equivalent exchange of feet for chains.

As it is given in the question,

1 Pound =  0.454 Kilograms,

So, In order to convert 79 pounds into kilograms we have to multiply 0.454 by 79.

79 pounds = 79(0.454) kilograms

79 pounds = 35.866 kilograms

Therefore, option B is correct answer.

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Answer: 79 pounds = 35.866 kilograms. Option B is correct!

The Expert was correct. Can I get brainliest because it's right?

if all multiples of 4 and all multiples of 5 are removed from the set of integers from 1 through 100, how many integers remain?

Answers

Total 56, integers are remained if all multiples of 4 and all multiples of 5 are removed from the set of integers from 1 through 100.

We have given that,

from the set of first 100 integers numbers, all the multiples of 5 and 4 are removed.

According to the question,

The multiples of 4 upto 100,

S = { 4, 8, 12......, 96}

it is an Arithmetic progression sequence with

a = 4 , l = 96 , d = 4

using an = a + (n-1)d where

n --> number of terms in sequence

d ---> common difference between two consecutive terms

a ---> first term

=> 96 = 4 + (n-1)4

=> (n-1) = 92/4

=> n = 23 + 1 = 24

Total multiples of 4 upto 100 is 24 .

Now, multiples of 5 upto 100

Q = { 5, 10, 15, ....,100}

Similarly as for above case

a = 5 , d = 5 , l = 100

=> 100 = 5 + (n-1)5

=> (n-1)5 = 95

=> n-1 = 19

=> n = 20

Total multiples of 5 upto 100 is 20.

Remained integers upto 100 = 100 - 20 -24

= 56

Hence, the required number of integers are 56.

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Can someone help me really quick

Answers

One would expect the foreword of a book to be found:

C. At the beginning of the book

What is the foreword in a book?

The foreword in a book refers to the introductory part of the book that is written by an expert on the subject discussed by the book. The foreword of a book is located at the beginning part of the book and it provides reasons that readers should consider reading the book.

The foreword is not meant to dissuade the readers but to encourage them on the importance and content of the book. It is logical then to expect this feature of books to be located at the beginning of the book.

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If i have 964 stones and rajesh took 493 stones so gow much i have?​

Answers

Answer:

After Rajesh took 493 stones, you would have 471 stones left.

Step-by-step explanation:

If you started with 964 stones and Rajesh took 493 stones, then you would have 964 - 493 = 471 stones left.

You have 471 stones left
(964-493 )stones
= 471stones

I need help with this question please

Answers

Answer:

1512 inches

Step-by-step explanation:

42 x 36

If x^2=a. For what values of a are there: 2 solutions or 1 solution or No solutions
Use at least 2 examples in each part to explain your answer. You must include further reasoning to justify your answer but do not write more than 1 page in total.

Answers

There are two solutions if a is positive, one solution if a is 0, and no solutions if a is negative.

How to determine for what values of a are there 2 solutions or 1 solution or No solutions?

If x² = a, then x can be either positive or negative.

Thus, there are two solutions if a is positive, one solution if a is 0, and no solutions if a is negative.

Example 1: a = 9

If a = 9, then x² = 9,

so x can be either 3 or -3.

Thus, there are two solutions in this case: x = 3 or x = -3.

Example 2: a = 0

If a = 0, then x²= 0,

so x can only be 0.

Thus, there is one solution in this case: x = 0.

Example 3: a = -4

If a = -4, then x² = -4, which is not possible because the square of a real number cannot be negative.

Thus, there are no solutions in this case.

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at the city museum, child admission is and adult admission is 5.20 on thursday, tickets were sold for a total sales of . how many child tickets were sold that day?

Answers

On solving the provided question we can say that - 112 child tickets were sold that day

What is equation?

equation: a statement that two expressions having variable- and/or number-filled expressions are equivalent. Since equations are essentially questions, finding a way to respond to them has been a major driving force behind the development of mathematics.

Call the number for children and the number for adults to get:

[tex]5.20c+8.50\\ a=1097.60[/tex]

and

a=4c

indicating that there were four times as many adults as youngsters.

Using this value in place of a

into the first equation we get:

[tex]5.2c+8.5(4c)=1097.6\\ 5.2c+34c=1097.6[/tex]

rearranging:[tex]c=1097.639.2=28[/tex]

and so:

[tex]a=4c=4⋅28=112[/tex]

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Calculate the initial value for -12x - 10y = -50

Answers

The initial value for the equation, -12x - 10y = -50, is: 5.

How to Determine the Initial Value of a Linear Equation?

The initial value of a linear equation is also known as the y-intercept of the  equation. Th equation in slope-intercept form can be expressed as y = mx + b, where the initial value of the equation is represented as the value of b, while m is the slope.

Given the linear equation, -12x - 10y = -50, in standard form, to find the initial value, b, we have to rewrite the equation in slope-intercept form:

-12x - 10y = -50

Add 12x to both sides of the equations:

-10y = 12x - 50 [addition property of equality]

Divide both sides by -10

-10y/-10 = 12x/-10 - 50/-10 [division property of equality]

y = -6/5x + 5

Thus, the initial value of the y-intercept of the equation is: 5.

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if your sample gave a negative result for the disease-causing agent, does this mean that you do not have the disease? what reasons could there be for a negative result when you actually do have the disease?

Answers

A negative result does not mean that you do not have the disease. It could be a false negative.

The reasons that could be there for a negative result when there is  actually the presence of the disease

The ELISA may not be sensitive enough to detect very low concentration  of the disease agent, as might occur when one is tested soon after infection before a proper immune response occurs.

As HIV buds from the surface of the host cell, it incorporates some of the host cell Human leukocyte antigen into its envelope. False negatives usually occurs during the window between infection and an antibody response to the virus which is known as seroconversion.

Therefore, if the sample gave a negative result for the disease-causing agent, it does not mean that you do not have the disease

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what happens to the graph of the normal curve as the standard deviation decreases?

Answers

The standard deviation is decreases then the graph of the normal z - score curve is increases.

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

The standard deviation is calculated as the square root of variance by determining each data point's deviation relative to the mean. If the data points are further from the mean, there is a higher deviation within the data set; thus, the more spread out the data, the higher the standard deviation.

In mathematics, the Z score is used to quantify how many standard deviations the raw score deviates from or approaches the mean. Giving the z score are:

z = (x - μ ) / σ

Where,

x = raw score

μ = mean

σ = standard deviation

For a sample size,

z =  (x - μ ) / σ / [tex]\sqrt{n}[/tex]

The z score affects the area under the curve. The area under the curve increases as the z score increases and decreases as the z score decreases.

The standard deviation has an inverse relationship with the area under the curve (z score). The z score drops as the standard deviation rises, diminishing the area under the curve.

The area under the curve grows as the standard deviation is reduced because the z score increases.

Therefore,

The standard deviation is decreases then the graph of the normal z - score curve is increases.

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Solve the equation mx" + Bx' = mg for r(t), given that you step off the bridge-no jumping, no diving! Stepping off means (0) = -100, x' (0) = 0, You may use mg = 160, B = 1, and g = 32. Use the solution from Problem 1 to compute the length of time t, that you freefall (the time it takes to go the natural length of the cord: 100 feet). typical job titles in finance include chief financial officer, vice-president of finance, bank officer, consumer credit officer, financial analyst, financial planner, loan officer, insurance analyst, and investment account executive. which of the following is not one of the qualifications to have a career in finance? write out the form of the partial fraction decomposition of the function (see example). do not determine the numerical values of the coefficients. (if the partial fraction decomposition does not exist, enter dne.) 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Find the actual distance, in metres, which is represented by 6.4 cm on the map.Show working Rewrite using a single positive exponent. 5^7/5^4 how do the demographics of the u.s. change in the 1980s and 1990s and what does this diversity mean for american society and politics? when should you organize your report by convention? when writing reports that should begin with the most important item and proceed to the least important when writing reports that are organized by components such as location, geography, and division when writing reports that follow a prescribed plan that everyone understands 5. Marcus, Alaina, and Tory recorded the number of text messagesthey sent on a certain day. Marcus sent 24 text messages, Alainasent 8 fewer messages than Marcus, and Tory sent twice as manymessages as Alaina. What is the ratio of the number of texts that Torysent to the total number of texts sent by all three friends? Lincolns view of salary and his emerging view of the governments role in setting the salary issue Why is Gold non-reactive? How are the two equation representations equivalent? What should you mention about the interview in your thank you letter?; What form of thank you letter would you prefer to send snail mail or e mail handwritten or typed?; When should a thank you letter be sent 3 days after the interview B 1 week after the interview?; What information should be included in the closing paragraph of a thank you letter? PLS HELP ASAP QUESTION ON SCREENSHOT Match the following descriptions to the appropriate element of Lean Manufacturing A system involving every employee that is based on making little changes on a regular basis, anywhere changes can be made, to reduce process, delivery, and quality problems Managers must support LEAN Manufacturing by providing subordinates with the skills, tools, time, and other necessary resources to identify problems and implement solutions Move people and materials when and where needed, and as soon as possible A systematic process of effective workplace organization and standardization which allows identification of variations from standard operating conditions Firms reduce costs by eliminating wait times, Inventories, material and people movement processing steps, variability, and any other non value-adding activity Kanban I Kanbans Workforce Commitment Lean Layout Waste Reduction Continuous Improvement Changeover Time Reduction Setup Time Reduction Lean Supply Chain Relationships Small Batch Scheduling Setup Time Reduction Lean Supply Chain Relationships Small Batch Scheduling Acceptance Sampling The Five S's Pull Approach Respect for People Total Quality Management Uniform Plant Loading you have a galaxy that is too far away to see individual stars, but you can see a little smudge of light from the galaxy. what would be the best way to find the distance to this galaxy? the relational aspect of humanity comes from a material aspect that god gave to only mankind. Cumulative preferred stockholders of Rale Company receive $.80 per share. The company has 70,000 shares outstanding. For the last 9 years, Rale paid no dividends. This year, Rale paid $400,000 in dividends. What is the amount of dividends in arrears that is still owed to preferred stockholders? An American company that sells consumer electronics products has manufacturing facilities in Mexico, Taiwan, and Canada. The average hourly wage, output, and annual overhead cost for each site are as follows:Mexico Taiwan CanadaHourly wage rate $1.50 $3.00 $6.00Output per person 10 18 20Fixed overhead cost $150,000 $90,000 $110,0001. Given these figures, is the firm currently allocating its production resources optimally? If not, why do you think so? Consider output per person as a proxy for marginal product.2. Suppose the firm wants to consolidate all of its manufacturing into one facility. Where should it locate? Is there any difference in treating cost information between (1) and (2)?3. In deciding to consolidate its manufacturing into one facility, what are other factors the firm needs to consider? Please list and explain your reasons.4. Nike outsources its manufacturing operation whereas New Balance does not. In terms of marginal productivity (output per person) and hourly wage rate, explain why New Balance did not outsource its production whereas Nike did briefly.