The sin (theta) = -2/5, and theta lies in quadrant IV. Find the exact values of the sine and cosine of 2 theta.

The Sin (theta) = -2/5, And Theta Lies In Quadrant IV. Find The Exact Values Of The Sine And Cosine Of

Answers

Answer 1

[tex]\displaystyle\\Answer:\ sin(2\theta)=-\frac{4\sqrt{21} }{25} ,\ cos(2\theta)=\frac{17}{25}[/tex]

Step-by-step explanation:

[tex]\displaystyle\\sin(\theta)=-\frac{2}{5} \ \ \ \ \ \ \ \ 270^0 < \theta < 360^0\\\\sin^2(\theta)+cos^2(\theta)=1\\\\cos^2(\theta)=1-sin^2(\theta)\\\\Hence,\\\\cos^2(\theta)=1-(-\frac{2}{5})^2 \\cos^2(\theta)=1-\frac{4}{25} \\\\cos^2(\theta)=\frac{25(1)-4}{25} \\\\cos^2(\theta)=\frac{21}{25} \\\\[/tex]

Extract the square root of both parts of the equation:

[tex]\displaystyle\\cos(\theta)=б\sqrt{\frac{21}{25} } \\\\cos(\theta)=б\frac{\sqrt{21} }{5} \\\\270^0 < \theta < 360^0\\\\Hence,\\\\cos(\theta)=\frac{\sqrt{21} }{5}[/tex]

[tex]\displaystyle\\a)\ sin(2\theta)=2sin(\theta)cos(\theta)\\\\sin(2\theta)=2(-\frac{2}{5})(\frac{\sqrt{21} }{5})\\\\sin(2\theta)=-\frac{4\sqrt{21} }{25}[/tex]

[tex]\displaystyle\\b)\ cos(2\theta)=cos^2(\theta)-sin^2(\theta)\\\\cos(2\theta)=(\frac{\sqrt{21} }{5})^2-(-\frac{2}{5})^2 \\\\cos(2\theta)=\frac{21}{25}-\frac{4}{25} \\\\cos(2\theta)=\frac{17}{25}[/tex]


Related Questions

What is 1x1 because I do not know what is it

Answers

Answer:

The answer is 1

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

A bag holds 23 cups of sugar. A recipe for chocolate chips cookies uses 1 cups of sugar. How many batches of chocolate chip cookies can be made with one bag of sugar?

Please have a step by step explanation so I can mark you as Brainliist. ​

Answers

Answer: 1 batch

Step-by-step explanation:

1 batch = 24 - 36 cookies

So here we have 23 cups of sugar, and we know that each chocolate chip cookie uses 1 cup, so we can only make 23 cookies

Which is only 1 batch of cookies can be made.

Answer:

23 batches of cookies

Step-by-step explanation:

I think this problem is kind of straightforward:

1 bag = 23 cups

1 batch = 1 cup

We need to find how many batches = 1 bag

To find that out, we have to divide bags by batches, but we don't know the number of batches yet. (Also, they're not the same units)

Instead, we can use the respective cups of sugar to divide (because they do have the same units)

So we divide the number of cups of sugar in a bag (23) by the number of cups in a batch (1):

23 ÷ 1 = 23 batches

I hope this explanation was simple enough

For a recipe, harris uses 2 cups of sugar for each cup of flour. how many cups of flour does harris need when he uses 1 cup of sugar?

Answers

Answer:

1/2 a cup of flour

Step-by-step explanation:

Sugar to flour ratio:
2 to 1
That means for every 2 sugar Harris needs 1 cup flour
There are twice as many cups of sugar of cups of flour
Since 1/2 times 2 is 1 that means the ratio is ture

2 to 1 = 0.5 to 1

Hope this helps :) im kinda bad at explaining

How do I solve for x in #34 and #35?

Answers

Answer:

  34. x = 3 1/3

  35. x = 5.2

Step-by-step explanation:

Given figures involving triangles with angle bisectors and parallel segments, you want to solve for x.

In each case, you need to make use of two proportional relationships. An angle bisector divides the triangle proportionally. An segment parallel to one side of the triangle divides it proportionally.

34.

Using the angle bisector relation, you have ...

  QP/PT = QS/ST

  x/3 = 5/ST   ⇒   x = 15/ST

Using the parallel segment relation, you have ...

  PT/QR = ST/SR

  3/2 = ST/3   ⇒   ST = 9/2

Using the value of ST in the equation for x gives ...

  x = 15/(9/2) = 30/9 = 10/3

  x = 3 1/3

35.

Using the angle bisector relation, you have ...

  EF/ED = CF/CD

  7.2/9 = CF/6   ⇒   CF = 6(7.2/9) = 4.8

Using the parallel segment relation, you have ...

  CB/BA = CF/FE

  x/7.8 = 4.8/7.2

  x = 7.8(4.8/7.2)

  x = 5.2

__

Additional comment

In each case, we assigned a numerical value to the intermediate variable (ST, CF). We didn't actually need to do that.

What is the 5th term in this sequence? 1, -8, -17

Answers

The value of the fifth term in the given sequence as represented in the task content is; -35.

What is the value of the fifth term in the sequence as given?

It follows from the task content that the value of the fifth term in the given sequence is to be determined.

On this note, it follows from the observation that the given sequence is arithmetic and the nth term, T (n) = a + ( n - 1 ) d.

where, a = first term = 1

and d = common difference = -8 - 1 = -17 - (-8) = -9.

Therefore, the fifth term is given as;

T (5) = 1 + ( 5 - 1 ) -9

= 1 + (4 × -9)

= 1 - 36

= -35.

On this note, the fifth term of the sequence as required is; -35.

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please solve theta
csc^2 theta=cot theta+3

Answers

The value of θ will -45° or 26.56°

What are trigonometric identities?

Trigonometric Identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation.

Given that, cosec²θ = cotθ + 3

Solving for θ,

∵ cosec²θ = cot²θ+1

∴ cot²θ+1 = cotθ + 3

cot²θ-cotθ-2 = 0

Factorizing and solving, we get

(cotθ+1)(cotθ-2) = 0

cotθ+1 = 0

cotθ = -1

θ = -45°

or, cotθ-2 = 0

cotθ = 2

θ = 26.56°

Hence, The value of θ will -45° or 26.56°

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In a company, 80% of the workers are men. If 780 people work for the company who aren't men, how many workers are there in all? Use pencil and paper. Show two different ways that you can solve this problem.

There are [enter your response here] workers in all.

Answers

Answer:

3900

Step-by-step explanation:

20%=1/5

780 is 20%

780x5 equals total since 20% 80% is 3120


Write an equation that represents the line.
Use exact numbers.

Answers

answer : y = 4/5x - 22/5

y = mx + b

get m or slope (aka "rate" or "speed")

(fun fact : see how the graph is a straight line? a lot of calculus is trying to get the rate or speed or slope of a curved graph)

(-3,-6) (2,-2)

(y2 - y1)/(x2-x1)

-2 + 6/2 + 3

m = 4/5

(if you make the 2 points a triangle bottom is 5 and the right side is 4)

line formula

y - y1 = m (x - x1)

y + 6 = 4/5 ( x + 2 )

y = 4/5x + 8/5 - 6

y = 4/5x + 8/5 - 30/5

y = 4/5x - 22/5

side note : since the graph doesnt go thru (0,0) the graph is NOT PROPORTIONAL

If k is a negative integer, which of these is DEFINITELY NEGATIVE? A. k* (k-1) * (k - 2) B. k* (k+1) C. k* (-50) D. (50-k)​

Answers

Answer:

only A ans bellow

Step-by-step explanation:

let k= -4

A. k * (k - 1) * ( k - 2)

= -4 * (-4 -1) * ( -4 -2)

= -4* (-5) * (-6)

= 20*-6

= -120

B. k * ( k+1)

= -4 * ( -4+1)

= -4 * (-3)

= + 12

C. k * (-50)

= -4 * (-50)

= + 200

D . (50 - k)

= 50 - (-4)

= 50 + 4

= + 54

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if k is negative then k(k-1)(k - 2) will be definitely negative.

What is Number system?

A number system is defined as a system of writing to express numbers.

Given that k is a  negative integer.

We need to find which of the given options are defnitely negative.

Let us consider k as -3.

k(k-1)(k - 2)

-3(-3-1)(-3-2)

-3(-4)(-5)=-60

Which is negative.

k(k+1)=-3(-3+1)=6 +ve

k (-50)=-3(-50)=150 +ve

(50-k)​=50-(-3)=53 +ve.

Hence, if k is negative then k(k-1)(k - 2) will be definitely negative.

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Joseph is signing up for a gym membership with a one-time fee to join and then a monthly fee to remain a member. Let CC represent the total cost of the gym membership over t months. A graph of CC is shown below. Write an equation for CC then state the slope of the graph and determine its interpretation in the context of the problem.

Answers

Answer:

The equation for the total cost of the gym membership over t months is CC = Jo + M * t, where Jo represents the one-time fee to join, M represents the monthly fee to remain a member, and t represents the number of months for which the membership is valid.

The slope of the graph is M, the monthly fee to remain a member. The interpretation of the slope in the context of the problem is that it represents the cost per month of remaining a member of the gym.

a line with a slope of 2 passes through the points (10,8) and (w,6). what is the value of w?

Answers

Answer:

w = 9

Step-by-step explanation:

Use a slope formula to solve. Subtract the y's put that on top and subtract x's and put that on the bottom. This calc should equal 2 that was given.

(8-6)/(10-w) = 2

2/(10-w) = 2

Cross-multiply.

2 = 2(10-w)

Distributive property

2 = 20 - 2w

Add 2w

2 + 2w = 20

Subtract 2

2w = 18

divide by 2

w = 18/2 = 9

Or you can logic it out...8-6 is 2 on top. Need a 1 on the bottom (bc 2/1 is 2) 10-9 is 1 for on the bottom. w = 1

(93 points) Eloise bought 2 boxes of crackers to share with her friends. Her friends ate 12 of the first box and 34 of the second box.

A. 1/2 box

B. 2/3 box

C. 3/4 box

D. 1 1/3

Answers

Answer:

The answer is C, 3/4 of a box

identify the value of f(x) and x from the given coordinates

Answers

Answer:

1

Step-by-step explanation:

For function f(x), the average rate of change from x = a to x = b is:

average rate of change = (f(b) - f(a))/(b - a)

Here we have:

f(a) = f(-3) = -2.88

f(b) = f(2.5) = 2.62

average rate of change = (2.62 - (-2.88))/(2.5 - (-3)) = 1

There are 30 giraffe and 6 penguin at the zoo. Which tatement correctly compare the two quantitie?

Answers

To compare the two quantities, divide the number of giraffes by the number of penguins There are 5 times as many giraffes as penguins at the zoo.

To compare the two quantities, you need to divide the number of giraffes by the number of penguins.

30 giraffes / 6 penguins = 5

This means that there are 5 times as many giraffes as penguins at the zoo.

There are 5 times as many giraffes as penguins at the zoo. To compare the two quantities, divide the number of giraffes by the number of penguins (30/6 = 5). This means that there are 5 times more giraffes than penguins at the zoo.

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A system of equations consists of a line s of the equation y = x – 5 and a line t that passes through the points (0, 2) and (8, –4). Answer the questions about line t to write the equation.

What is the slope of line t?

–0.75
What is the y-intercept of line t?

2
What is the equation in slope-intercept form of line t?

y = –0.75x + 2

Answers

The line 't' is y = -0.75x + 2 which has a slope of negative 0.75 and the y-intercept is 2.

What is a linear equation?

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The line t that passes through the points (0, 2) and (8, -4) is given as,

(y - 2) = [(- 6 - 2) / (8 - 0)](x - 0)

y - 2 = - 0.75x + 0

y = -0.75x + 2

The line 't' is y = -0.75x + 2 which has a slope of negative 0.75 and the y-intercept is 2.

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a company wants to encrypt a document containing important passwords. to do this, the sum of two positive numbers will need to be minimized. if the product of both numbers is 47, what is the minimum sum?

Answers

The requried, "a" and "b" are positive numbers, the minimum sum (a + b) is 13.711.

To find the minimum sum of two positive numbers whose product is 47, we can use the concept of the arithmetic mean-geometric mean inequality (AM-GM inequality).

The AM-GM inequality states that for any two positive numbers, the arithmetic mean (average) is always greater than or equal to the geometric mean. Mathematically, it can be expressed as:

AM ≥ GM

For two positive numbers "a" and "b," the arithmetic mean is (a + b) / 2, and the geometric mean is √(ab).

Given that the product of the two numbers is 47 (ab = 47), we want to find the minimum value of their sum (a + b).

Using the AM-GM inequality:

(a + b) / 2 ≥ √(ab)

Substitute ab = 47:

(a + b) / 2 ≥ √47

Now, let's solve for the minimum sum (a + b):

a + b ≥ 2(√47)

a + b ≥ 2 * √(47)
a + b ≥  13.711.        

Since "a" and "b" are positive numbers, the minimum sum (a + b) is 13.711.

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pool workers conducted a chi-square goodness-of-fit test at the 5% significance level. the chi-square value is 1.3892 and the p-value is 0.7081. what can the pool workers conclude?

Answers

The pool workers can conclude that there is not a statistically significant difference between the expected and observed results.

The chi-square value is 1.3892 and the p-value is 0.7081 The p-value of 0.7081 is greater than the 5% significance level, meaning that the null hypothesis can not be rejected.

This means that the difference between the expected and observed results is not statistically significant, and the observed results are likely due to random chance. This means that there is not a significant difference in the observed results from the expected results, and the null hypothesis is accepted.

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find the number a such that the limit exists. lim x→−2 4x2 + ax + a + 12 x2 + x − 2

Answers

The limit exists and equals -4 when a = 28.

How to illustrate the limit?

From the information, we want to find the number a such that the limit exists. lim x→−2 4x² + ax + a + 12 divided by x² + x − 2.

It should be noted that this will be illustrated as:

(4x² + ax + a + 12) / (x² + x − 2)

We will substitute x = -2 into the value of x in the Illustration. This will be:

(16 - 2a + a + 12) / (4 - 2 - 2)

16 - 2a + a + 12 = 0

-a = -28

a = 28

Using lhopital rule, we'll find the derivative. This will be:

8x + a / 2x + 2

Substitute x = -2

(-16 + 28) / (-4 + 1)

= 12 / -3

= -4

Therefore the limit exists and equals -4 when a = 28.

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Complete question

find the number a such that the limit exists. lim x→−2 4x² + ax + a + 12 divided by x² + x − 2

[tex]\sqrt{x} \sqrt{x} 100\\[/tex]

Answers

Answer:

100 isn't under the root, so the roots over the x cancel and you have 100x as the answer

Step-by-step explanation:

100 isn't under the root, so the roots over the x cancel and you have 100x as the answer

What is the solution to this system of linear equations?
2x + y = 1
3x - y = -6

Answers

Answer:

x = -1

y = 3

Step-by-step explanation:

2x + y = 1

3x - y = -6

Let's find x first by adding both equations

5x = -5

x = -1

Now put -1 in the spot of the variable x

2(-1) + y = 1

-2 + y = 1

y = 3

Which graph represents function f?
f(x) = 2|x − 1|– 3

Answers

Answer:

graph D

Step-by-step explanation:

if x = 0

y = 2 |-1| - 3

y = 2 (1) - 3

y = 2 - 3

y = -1


A (0, -1)


if x = 1

y = 2 |1-1|  - 3

y = 2 (0) - 3

y = -3


B (1,-3)

select the correct answer from each drop down menu

choices: the rate of function eight is (greater than), (less than), (equal to) the rate of change a function b

(neither function is ), (only function b is) , (only function a is) , (both functions are) increasing.

The y intercept of function a is (less than) , (greater than), (equal to) the y-intercept of function B

whatever is in the parentheses are the choices. please help

Answers

The rate of change of function A is greater than the rate of change of function B.

The y-intercept of function A is less than the y-intercept of function B.

How to calculate the rate of change of the function?

The rate of change is also called the slope of a linear equation and is defined as the rate of change of y-values divided by the corresponding change in x-values.

For function A, we are told that the line passes through the points (2, 3) and (-1, -3). The rate of change is gotten from the formula;

Rate of change = (y₂ - y₁)/(x₂ - x₁)

Rate of change = (-3 - 3)/(-1 - 2)

Rate of change = -6/-3

Rate of change = 2

For function B, we are given that the equation of the line is;

y = ¹/₂x + 2

Now, formula for equation of a line in slope intercept form is;

y = mx + c

where ;

m is slope and c is y-intercept

Thus, slope is 1/2 and y-intercept is 2

For function A, we can find the y-intercept as;

3 = 2(2) + c

c = 3 - 4

c = -1

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Select the correct answer from each drop-down menu. which formulas return true, if the value in cell b4 is 12 and the value in c4 is 29? and return true, if the value in cell b4 is 12 and the value in c4 is 29.

Answers

the correct answer from each drop-down menu. which formulas return true,.if the value in cell b4 is 12 and the value in c4 is 29.: A. =B4=12 AND C4=29

The correct answer is A. =B4=12 AND C4=29, as this is the only formula that returns true if the value in cell b4 is 12 and the value in c4 is 29.

Both B. =(B4=12) AND (C4=29) and D. =(B4+C4)=41 are correct, but they do not fit the given criteria.

C. =B4+C4=41 does not return true for the given values, as 12 + 29 does not equal 41.

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8.
Are the two ratlos below proportional? *
5
15
6' 18
Mark only one oval.
a. No, because the unit rates are not equal.
b. Yes, because the unit rates are the same.
c. No, because the rates are the same.
d. Yes, because the unit rates are not equal.
2 points

Answers

Made possible via methods. In light of this, 5, 6, 15, and 18 are in proportion. The same unit rates prove that.

Rates and proportions are they equivalent?

A ratio, on the other hand, is the comparison of the sizes of two values, whereas a proportion is a part, share, or quantity in relation to an overall total. Each of the three measures has unique characteristics, and a rate is just one number divided by another.

The same units apply to proportions, or not?

Due to the consistency of the units and their equivalent, each ratio compares the same units—inches and feet—and is therefore similar. Compare two ratios using the same units when using proportions.

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a cylindrical water tank with its circular base parallel to the ground is being filled at the rate of 4 cubic feet per minute. the radius of the tank is 2 feet. how fast is the level of the water in the tank rising when the tank is half full? give your answer in feet per minute.

Answers

In the given cylinder we know that it takes the water around 3.14 minutes to rise 1 ft.

What is a cylinder?

One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid.

It is regarded as a prism with a circle as its base in basic geometry.

In several contemporary fields of geometry and topology, a cylinder can alternatively be characterized as an infinitely curved surface.

So, we know that:

The rate at which water is being filled is 4 ft³.

The radius of the cylinder is 2 ft.

Now, the time in which the level of water in the tank rises when the tank is half full:

Area of cylinder: πr²

πr² =  12.566 ft³

Next, multiply 4 by 12.566 to get how quickly the water is rising:

12.566 ft³/4 ft³/min = 3.14 m

According to this, a foot of water rises every roughly 3.14 minutes, or 1/3.14 - 0.318 ft/min, or 3.82 in/min.

Therefore, in the given cylinder we know that it takes the water around 3.14 minutes to rise 1 ft.


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Establish the identity.
1+ tan^2 (-0) = sec^2 0
Which of the following four statements establishes the identity?

pls help asap i can’t pass this class without passing this test :(

Answers

The correct statement that establishes the identity is the third one: "The reciprocal of the cosine of an angle is equal to the secant of the angle."

Here's how you can prove this using the other three statements:

"The tangent of an angle is equal to the sine of the angle divided by the cosine of the angle."

"The reciprocal of the sine of an angle is equal to the cosecant of the angle."

"The reciprocal of the cosine of an angle is equal to the secant of the angle."

"The reciprocal of the tangent of an angle is equal to the cotangent of the angle."

To prove the identity, we can start by substituting the first statement into the equation on the left side of the identity:

$1 + \tan^2 (-0) = 1 + \left( \frac{\sin (-0)}{\cos (-0)} \right)^2 = 1 + \frac{\sin^2 (-0)}{\cos^2 (-0)}$

Next, we can use the fourth statement to write the right side of the identity in terms of the cotangent:

$1 + \frac{\sin^2 (-0)}{\cos^2 (-0)} = 1 + \frac{1}{\cot^2 (-0)} = \frac{1}{\cot^2 (-0)}$

Now we can use the second statement to write the right side of the identity in terms of the cosecant:

$\frac{1}{\cot^2 (-0)} = \frac{1}{\frac{1}{\sin^2 (-0)}} = \csc^2 (-0)$

Finally, we can use the third statement to write the right side of the identity in terms of the secant:

$\csc^2 (-0) = \frac{1}{\sec^2 (-0)} = \sec^2 (-0)$

Therefore, the third statement establishes the identity.

Please help! Its algebra!

Answers

Step-by-step explanation:

don't panic. just read carefully and write equations for every relation described in the text.

perimeter = 34 cm = side 1 + side 2 + side 3

side 1 = 2×side 3

side 3 = (side 1) / 2

side 2 = (side 1) + 4

now we use the last 2 equations in the first :

34 = side 1 + ((side 1) + 4) + (side 1)/2

68 = 2×(side 1) + 2×((side 1) + 4) + side 1

68 = 2×(side 1) + 2×(side 1) + 8 + side 1

68 = 5×(side 1) + 8

60 = 5×(side 1)

side 1 = 60/5 = 12 cm

side 2 = (side 1) + 4 = 12 + 4 = 16 cm

side 3 = (side 1)/2 = 12/2 = 6 cm

you see ? it is all just straight forward. no mystery.

the only trick is to find forms of the various equations to have only one variable in the main equation. like we did here with side 1 and side 3.

please help me with this

Answers

Answer: The first one is equivlent because you move the variable to the left collect like terms and then divide both terms.

Step-by-step explanation:

What is x+3y ≥ 3
Help?

Answers

Answer: x

3

3

y

Step-by-step explanation:

You know distance and speed and want to find the time

You know time and distance and want to find the speed

You know speed and time and want to find the distance

Answers

Answer:

time=speed÷distance

speed=distance×time

distance=speed ÷time

Step-by-step explanation:

from the answers we get a relationship between speed,distance and time.there by when with two you can find the other

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____ is a computer-based network that triggers actions by sensing changes in the real or digital Multiple Choice O An app An intelligent deviceO An interlinked smartphone grid O A smart systemO A sensory track find the 25th, 50th, and 75th percentile from the following list of 32 data. please enter exact answers. the company sold 25,000 units in the east region and 10,000 units in the west region. it determined that $250,000 of its fixed selling and administrative expense is traceable to the west region, $150,000 is traceable to the east region, and the remaining $96,000 is a common fixed expense. the company will continue to incur the total amount of its fixed manufacturing overhead costs as long as it continues to produce any amount of its only product. prepare a contribution format segmented income statement that includes a total column and columns for the east and west regions. if victims wish to recoup their losses following a crime, they must rely on: group of answer choices a. substantive criminal law. b. procedural criminal law. c. real estate law. d. civil law. a client is taking antiprotozoal medications to prevent a relapse of plasmodium vivax malaria. the nurse is assessing the client during a scheduled follow-up appointment. what assessment finding suggests an increased risk for hepatotoxicity during antimalarial therapy? A direct result of the conquest of Tenochtitln by Hernn Corts in 1521 was thea. expulsion of Jews and Muslims from Spainb. establishment of Portuguese trade routes around Africac. fall of the Aztec Empired. conquest of the Kush Kingdom a production company is interested in collecting information on the impact of an educational documentary on everyone that watched it at the film festival. which statement is true deborah tannen notes that when women state their opinions, they often tag them with a question at the end of the sentence. 5350 divided by Equals 5.35 As Ruchira is packing her apartment while preparing to move in with her new husband, Biren, she reflectson the first time he saw her artwork.(1) He'd moved close to the wall and was standing very still. (2) It took her a moment to figure out that hewas examining her brushstrokes. (3) (But only artists did that. (4) Was he a closet artist, too?) (5) Finally hemoved back and let out a long, incredulous breath, and it struck her that she had been holding hers aswell. (6) "Tell me about your work," he said.(7) This was hard. (8) She had started painting two years ago, and had never talked to anyone about it. (9)Even her parents didn't know. (10) When they came for dinner, she removed the canvases from the walland hid them in her closet. (11) She sprayed the room with Eucalyptus Mist and lit incense sticks so theywouldn't smell the turpentine. (12) The act of painting was the first really risky thing she had done in herlife. (13) Being at the gallery, she knew how different her work was from everything in there, or in theglossy art journals. (14) Her technique was crude-she hadn't taken classes and didn't intend to. (15) Shewould probably never amount to much. (16) Still, she came back from work every evening and paintedfuriously. (17) She worked late into the night, light-headed with the effort to remember. (18) She stoppedinviting people over. (19) She made excuses when her friends wanted her to go out. (20) She had to forceherself to return their calls, and often she didn't. (21) She ruined canvas after canvas, slashed them infrustration and threw them into the Dumpster behind the building. (22) She wept till she sa a blurrybrightness, like sunspots, wherever she looked. (23) Then, miraculously, she got better. (24) Sometimesnow, at 2:00 or 3:00, her back muscles tight and burning, a stillness would rise around her, warm andvaporous. (25) Held within it, she would hear, word for word, the stories her grandmother used to tell.From Chitra Banerjee Divakaruni, The Unknown Errors of Our Lives. C2001 by Chitra Banerjee Divakaruni.QuestionAs used in sentence 16, "furiously" most nearly meansintenselyO viciouslyirritablyO vengefully The firm's problem Consider a competitive firm that produces bots. Labor (L) and capital (K) are the only two inputs of production; each unit of labor is paid the market wage (w), and each unit of capital is rented at the rental price of capital (r). Output (Y) is therefore a function of labor and capital, or Y = f (K, L), and is sold at the market price (P). The goal of this firm is to maximize profit given the price of bots, the wage rate, the rental rate of capital, and production technology by choosing its labor and capital inputs. Fill in the following equations with the firm's profit maximization problem: Profit Revenue - Labor Cost - Capital Cost Labor Cost + Capital Cost - Revenue Profit-maxi Revenue - Labor Cost iring an additional unit of labor will affect profit. To do this, the firm can compare the change in revenue from hiring the cost of that extra worker. The additional output produced by an extra unit of labor is equal to the Revenue - Labor Cost - Capital Cost marginal p h bot sells for the market price (P), the change in revenue from hiring an additional worker is Revenue - Capital Cost w Fill in the following equations with the firm's profit maximization problem: Profit = Revenue - Labor Cost - Capital Cost Pf (K, L) WL rK Pf (K, L) WL rK Profit-maxi rmine how hiring an additional unit of labor will affect profit. To do this, the firm can compare the change in revenue from hiring wL+ rK Pf (K, L) bor against the cost of that extra worker. The additional output produced by an extra unit of labor is equal to the marginal p Because each bot sells for the market price (P), the change in revenue from hiring an additional worker is Pf(K, L) WL in cost is Pf(K, L) rK W Firms will continue to hire workers until the change in profit is Given this condition, which of the following equations correctly Profit-maximizing firms must determine how hiring an additional unit of labor will affect profit. To do this, the firm can compare the change in revenue from hiring an additional unit of labor against the cost of that extra worker. The additional output produced by an extra unit of labor is equal to the marginal product of labor (MPL). Because each bot sells for the market price (P), the change in revenue from hiring an additional worker is and the change in cost is W P MPL F ntinue to hire workers until the change in profit is Given this condition, which of the following equations correctly Y P profit-maximizing labor choice of the firm? PXY MPL PL = ? W W PX MPL PL = MPL MPL III Profit-maximizing firms must determine how hiring an additional unit of labor will affect profit. To do this, the firm can compare the change in revenue from hiring an additional unit of labor against the cost of that extra worker. The additional output produced by an extra unit of labor is equal to the marginal product of labor (MPL). Because each bot sells for the market price (P), the change in revenue from hiring an additional worker is and the change in cost is W I W Firms will continue to hire workers until the rofit is Given this condition, which of the following equations correctly describes the profit-maximizing labor choice W X Y MPL = P W MPL = W W X MPL W= MPL Given this condition, which of the following equations correctly Firms will continue to hire workers until the change in profit is describes the profit-maximizing labor choice of the firm? positive MPL: W negative OMPL= W equal to zero W = MPL P MPL = w XP Demonstrate your understanding of the previous concepts in the following example. Suppose the price of a bot is equal to $2, and the market wage rate is $12. Moreover, suppose the marginal product of labor for this firm is equal to the following: MPL = 14-L On the graph, use the blue line (circle symbol) to show the firm's demand for labor. Then, place the black point (plus symbol) on the graph to indicate the real wage and the profit-maximizing quantity of labor. Note: Dashed drop lines will automatically extend to both axes. ? 20 O 18 Labor 16 14 12 Real w, labor UNITS OF OUTPUT (Bots) PER UNIT OF LABOR 10 8 0 0 2 4 6 14 16 18 20 10 12 UNITS OF LABORPrevious question archaeologists can understand how artifacts, features, and sites formed using information from which of the following. the edwards's theater chain has studied its movie customers to determine how much money they spend on concessions. the study revealed that the spending distribution is approximately normally distributed with a mean of $4.11 and a standard deviation of $1.37. what spending amount corresponds to the top 87th percentile? data or the trends in data that may indicate the effectivess of security countermeasures or controls-technical and managerial-implemented in the organization are known as program measurements people who have an integrating conflict style are least likely to have which big five trait? t on october 1, 20a1, borah, inc., a calendar year-end firm, invested in a derivative designed to hedge the risk of changes in fair value of certain assets, currently valued at $1.5 million. the derivative is structured to result in an effective hedge. however, some ineffectiveness may result. on december 31, 20a1, the fair value of the hedged assets has decreased by $350,000; the fair value of the derivative has increased by $325,000. borah should recognize a net effect on 20a1 earnings of: the first suggestion that chromosomes may physically exchange segments came from the microscopic identification of show the balanced chemical equation of methane with the heat of reaction added to the right side because it is an exothermic reaction. Precalc wohoo help would rlly appreciate it Match each term to its definition.A. anabolismB. biochemical pathwayC. catabolismReactions that result in the breakdown of large biomoleculesC