I REALLY NEED THIS TO PASS SOMEONE PLEASE TRY AND HELP

solve this triangle. Round to the nearest tenth

I REALLY NEED THIS TO PASS SOMEONE PLEASE TRY AND HELP Solve This Triangle. Round To The Nearest Tenth

Answers

Answer 1

Answer:

Im pretty sure its the third one

Step-by-step explanation:

It all depends on the square root to find the nearest tenth and rounding it all up.


Related Questions

Look at the figure shown. Which angle is obtuse?
Angle CDA.
Angle BAD.
Angle CBA.
Angle DAB.
A
60
B
120
120
C
60
D

Answers

The angle that is an obtuse angle (that is, greater than 90° but less than 180°) is 120°. The correct option is B. 120°

What is an obtuse angle?

An obtuse angle is an angle that is greater than 90° but less than 180°. Thus, if x is an obtuse angle, the range of values for x are

90° < x < 180°

From the given question, we are to determine the angle which obtuse.

In the given figure, to determine the angle which is obtuse, we will determine the angle that is greater than 90° but less than 180°.

The angle that is greater than 90° but less than 180° is 120°.

Thus,

The obtuse angle is the angle that measures 120°

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if A C B, then A n B = A U B

1) sometimes
2) never
3) always

Answers

if A C B, then A n B = A U B is always true

How to determine if A C B, then A n B = A U B

The statement "if A C B, then A n B = A U B" can be rephrased as "if A is a subset of B, then the intersection of A and B is equal to the union of A and B".

Every element of A is also an element of B. Therefore, the intersection of A and B contains all the elements of A.

On the other hand, the union of A and B contains all the elements of A and all the elements of B. Since A is a subset of B, all the elements of A are already included in B, so the union of A and B is just equal to B.

Therefore, we have:

A n B = A (since all the elements of A are in both A and B)

A U B = B (since A is a subset of B)

So A n B = A U B = B, which means that the original statement "if A C B, then A n B = A U B" is true

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Find the volume of a right circular cone that has a height of 11.9 ft and a base with a radius of 16.3 ft. Round your answer to the nearest tenth of a cubic foot.

Answers

The volume of a right circular cone which has a height of 11.9 ft and a base with a radius of 16.3 ft as required is;

What is the volume of the right circular cone?

As evident in the task content; the volume of a right circular cone a height of 11.9 ft and a base with a radius of 16.3 ft is to be determined.

Recall, the volume of the cone is;

V = (1/3) × πr²h

V = (1/3) × π × 16.3² × 11.9

V = 3310.9 ft³.

Ultimately, the volume of the right circular cone is; 3310.9 ft³.

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Answer:

3310.9

Step-by-step explanation:

Describe los Tipos de ángulos que se forman cuando divides un círculo en 4 partes iguales









Answers

The angles that you get when a circle is divided into 4 equal parts, would be four 90 degree angles.

How to describe the angles ?

The reason these angles are called 'right angles' is because they create an exact 90-degree angle, signifying one fourth of a complete circle. Every specific angle is named as a 'quadrant,' as it covers a quarter or a quadrant of the circle.

These four perpendicular angles stand side by side - having in common not just one diameter of the circle but also a shared vertex, which is at the center of the circle. Together, they share uniformly the circle into four unique sections - each turning toward a distinct quadrant of the circle parallel to their placement.

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The approximate areas of Nebraska and Massachusetts are listed below:
Nebraska: 2 x 105 square kilometers
Massachusetts: 2.73 x 104 square kilometers
What's the difference between the areas of the two states? Express your answer using
either standard notation or scientific notation.

Answers

The distance between the areas of the two states is A = 1.727 x 10⁵ km²

Given data ,

Let the area of Nebraska = 2 x 10⁵ km²

Let the area of Massachusetts = 2.73 x 10⁴ km²

The difference between the areas of Nebraska and Massachusetts A =  the area of Nebraska - the area of Massachusetts

On simplifying the exponents , we get

A = 2 x 10⁵ km² - 2.73 x 10⁴ km²

Taking the common factor , we get

A = 10⁴ ( 20 - 2.73 )

A = 10⁴ ( 17.27 )

A = 1.727 x 10⁵ km²

Hence , the area is A = 1.727 x 10⁵ km²

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In the United States between 1910 and 1994, the amount of currency in circulation M ( in billions of dollars) can be approximated by the function M = 2.08 * (1.06) ^ t where t represents the number of years since 1910. Determine the amount of currency in circulation in the year 1980. (round to the nearest hundredth).
A.3.32
B.122.88
C.220.06
D.2.65

Answers

Answer:

B. 122.88

Step-by-step explanation:

Since t is the number of years since 1910, we can find the t value we need for the equation by subtracting 1910 from 1980:

t = 1980 - 1910 = 70

Now, we can plug in 70 for t to find the amount of currency in 1980:

[tex]M(t)=2.08(1.06)^t\\M(70)=2.08(1.06)^7^0\\M(70)=122.8779348\\M(70)=122.88[/tex]

Thus, the amount of currency in 1980 according to the model was $122.88 billion

Helppp me please what is the formula for the carton 1/2*base of triangle*height of prism*height of prism ?

Answers

The volume of the triangular prism in the diagram is 10.5 in³

Calculating the volume of a triangular prism

From the question, we are to calculate the volume of the the given prism.

The given prism is a triangular prism.

Volume of a triangular prism = Area of triangle × Height of prism

Thus,

Volume of the triangular prism = 1/2 × Base of triangle × Height of triangle × Height of prism

From the given diagram,

Base of triangle = 2 in

Height of triangle = 1.5 in

Height of prism = 7 in

Volume of the triangular prism = 1/2 × 2 in × 1.5 in × 7 in

Volume of the triangular prism = 10.5 in³

Hence,

Volume of the triangular prism is 10.5 in³

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The table below shows the lengths and weights of six dolphins at an aquarium. Use the data from Pax and Snowflake to create a linear model that predicts the weight (y) of a dolphin given its length (x). Which dolphin's weight differs most from the value predicted by this model?

Answers

The dolphin's weight that differs most from the value predicted by this model is JoJo's (31 lb of difference)

Let's elaborate the model this way:

Snowflake's length - Pax's length = 8.2 - 7.6 = 0.6 ft

Snowflake's weight - Pax's weight = 549 - 519 = 30 lb

Ratio = 30/0.6 = 50 lb/ft

This means that for every foot of length, the dolphin has a variable weight of 50 lb.

However, if we multiply the ratio by the actual length of the two dolphins, we will have these results:

Snowflake = 50 × 8.2 = 410

Pax = 50× 7.6 = 380

Snowflake = Actual weight - Ratio× Length = 549 - 410 = 139

Pax = Actual weight - Ratio × Length = 519 - 380 = 139

The common difference is 139.

Therefore, the linear model that predicts the weight (y) of a dolphin given its length (X) is:

y = 139 + 50x

Now, let's use the linear equation or model to calculate the weight of the remaining four dolphins, as follows:

Blaze  y = 139 + 50 × 6.8 = 479 ⇒ difference of 9 lb (488 - 479)

JoJo   y = 139 + 50 × 5.8 = 429 ⇒ difference of 31 lb (460 - 429)

Corky   y = 139 + 50 ×8.4 = 559 ⇒ difference of 2 lb  (559 - 557)

Shadow  y = 139 + 50 × 7.4 = 509 ⇒ difference of 8 lb  (509 - 501)

Hence, the dolphin's weight that differs most from the value predicted by this model is JoJo's (31 lb of difference)

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The table below shows the lengths and weights of six dolphins at an aquarium. Use the data from Pax and Snowflake to

create a linear model that predicts the weight (y) of a dolphin given its length (X). Which dolphin's weight differs most from th

value predicted by this model?

Name

Snowflake

Shadow

Corky

Pax

JoJo

Blaze

Length (ft)

8.2

74

8.4

7.6

5.8

6.8

Weight (lb)

549

501

557

519

460

488

Blaze

JOJO

Corky

Shadow

please show work asap thankyou so much

Answers

The net sales, =$20.98

The Goods available for sales= $2,045

The total cost of Goods sold=$1,955

Gross profit =$1,934.02

Net income = $1,395.98

How to determine the net sales from the last month's business income statement?

The operating income (sales) = $7,240

The return on sales (ROS) = $345

The net sales (revenue generated) = ?

But ROS = operating income/net sales

Net sales = 7240/345;

= $20.98

The goods available for sale = beginning inventory+ new purchase = $725+$1320 = $2,045.

The total cost of Goods sold = Beginning inventory+goods available for sale - end inventory.

= 725+2,045- 815

= 2770-815

= $1,955

The gross profit = cost of goods sold (COGS) - total revenues.

= $1,955-$20.98

= $1,934.02

Net income = total operating expenses - gross profit

operating expenses = 1,750+1000+280+150+150 = $3,330

gross profit = $1,934.02

Net income = 3,330-1,934.02 = $1,395.98

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I need help on number 6

Answers

x=11. if you add all the given degrees up, you have 320, 360 is needed to be a full circle. 4 x 11= 44-4= 40

Write the equation for an exponential function, in the form ya x b. whose graph passes through the coordinate points (2, 12) and (3, 24).

Answers

The calculated equation for the exponential function is y = 3(2)ˣ

Calculating the equation for the exponential function

From the question, we have the following parameters that can be used in our computation:

Points = (2, 12) and (3, 24)

By definition, as exponential function is represented as

y = abˣ

Substitute the known values in the above equation, so, we have the following representation

ab² = 12

ab³ = 24

So, we have

b = 2

This means that

a(2)³ = 24

So, we have

a = 3

Recall that

y = abˣ

So, we have

y = 3(2)ˣ

Hence, the equation for the exponential function is y = 3(2)ˣ

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mrs. watson is buying vintage records for a friend at a local records shop. Thre price of a record is based on its condition. The table shows the total cost of x number of records for each condition.

Answers

The equation for total cost of buying and shipping the records is

76.4x + 80

We have,

She buys 3 in good condition

So, the cost for 3 good condition

= 3 (10.5x)

= 31.5 x

and, She buys 1 in Fair condition

So, the for 1 fair condition

= 5x

and, She buy 2 new condition then the price is

= 39.9 x

So, the equation for total cost of buying and shipping the records is

= 31.5x + 5x + 39.9x + 8

= 76.4x + 8

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We often use the phrase "to the power of" when talking about exponents. For example, x¹3 is
referred to as x to the power of 13. Why do you think that they would name it like this? How does
increasing the exponent of a number increase its "power"?
Hint: Use a number as an example. (for instance 2) if you keep increasing the power, what happens
to the answer? (i.e. compare 2¹, 2^2, 2^3, 2^4,..., 2^13, 2^14,... until you see the answer you are looking
for!)

Answers

In mathematics, the expression "to the power of" pertains to the exponent, signifying how many times a key number is to be multiplied by itself.

What is the exponents about?

Expressing this idea in English can be done well by using the term "to the power of." To show this, 2 raised to the third power can be interpreted as 2 multiplied by itself three times, resulting in 8.

Therefore, the possible reason behind using the word "power" is probably due to the fact that when the exponent rises, the outcome number is wide, either being greater or smaller, made on the base being above or below 1. This implies that the figure holds more significant value.

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What is the base of the following natural logarithm?
In(x)
O 1
O 10
O e

Answers

The base of the natural logarithm ln(x) expression is 10

What is the base of the natural logarithm?

From the question, we have the following parameters that can be used in our computation:

ln(x)

The base of the above expression is not stated

The general rule of logarithm is that when the base of the expression is not stated, then the base is 10

If the base of the expression is stated, then the expression would take the form

lnₐ(x), where the base is represented with the variable a

This means that the base of the natural logarithm ln(x) expression is 10

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An executive for a large company received gross pay of $200,000 for the year 2018. Determine the total amount of FICA tax that was paid on behalf of the employee. Round your answer to the nearest cent. Do NOT round until you calculate the final answer.

Answers

The total amount of FICA tax that was deducted from the executive's paychecks for the year 2018 is $10,860.80.

What is the total amount of FICA tax?

The FICA tax is imposed on both employees and employers to fund Social Security and Medicare which are federal programs that provide benefits for retirees, the disabled and children of deceased workers.

The Social Security tax will be calculated on the maximum taxable earnings of $128,400:

= $128,400 x 6.2%

= $7,961.20

The Medicare tax will be calculated on the entire earnings:

= $200,000 x 1.45%

= $2,900.

The total FICA tax will be:

= Social Security tax + Medicare tax

= $7,960.80 + $2,900

= $10,860.80.

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Complete the ratio table.

Answers

Answer:

55

70

Step-by-step explanation:

Hope this helps! Pls give brainliest!

Answer:

55 and 70

Step-by-step explanation:

5÷2=2.5

20÷8=2.5

45÷18=2.5

so

22×2.5=55

and

28×2.5=70

I need help with this please

Answers

Answer: a. d. f.

Step-by-step explanation:

Use the distance and slope formula to prove that qaudlateal ABCD IS A PARLLAGRAM

Answers

Answer:79

Step-by-step explanation:

Explain how decimal place value is like place value with whole numbers. Use pictures or words to explain your thinking.

Answers

The tenths place is represented by the first digit following the decimal. The hundredths place is represented by the digit that follows the decimal.
Up until there are no more digits, the remaining ones keep the place values filled in.

What is the square root of ab²?
O ab
Ob√a
Oa²b²
Ob²

Answers

Answer:

b[tex]\sqrt{a}[/tex]

Step-by-step explanation:

using the rule of radicals

[tex]\sqrt{ab}[/tex] = [tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] , then

[tex]\sqrt{ab^2}[/tex]

= [tex]\sqrt{a}[/tex] × [tex]\sqrt{b^2}[/tex]

= [tex]\sqrt{a}[/tex] × b

= b[tex]\sqrt{a}[/tex]

Let sin(2x) – sin(x) = 0, where 0 ≤ x < 2π. What are the possible solutions for x? Left-brace StartFraction pi Over 6 EndFraction, StartFraction 5 pi Over 6 EndFraction Right-brace Left-brace StartFraction pi Over 3 EndFraction, StartFraction 5 pi Over 3 EndFraction right-brace Left-brace StartFraction pi over 6 EndFraction, StartFraction pi Over 2 EndFraction, StartFraction 5 pi Over 6 EndFraction, StartFraction 3 pi Over 2 EndFraction right-brace

Answers

The possible solutions for x for the equation sin(2x) – sin(x) = 0 will be (π/3, 5π/3). Then the correct option is B.

Given that:

sin(2x) – sin(x) = 0

Simplify the equation, then the value of 'x' is calculated as,

sin(2x) – sin(x) = 0

sin(2x) = sin(x)

2 sin x cos x = sin x

cos x = 1/2

cos x = cos (π/3, 5π/3)

x = π/3, 5π/3

The possible solutions for x for the equation sin(2x) – sin(x) = 0 will be (π/3, 5π/3). Then the correct option is B.

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graph the following linear inequalities: y < -2+7

Answers

The graph of the inequality is added as an attachment

How to determine the graph

From the question, we have the following parameters that can be used in our computation:

y < -2 + 7

The above expression is an inequality that implies that

The value of y is less than the sum of -2 and 7

Next, we plot the graph

See attachment for the graph of the inequality

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Abe purchased a candle at the candle store. The candle is nine inches long and the packaging states the candle burns down at the rate of 1/2 an inch per hour. Write a function to determine the length of the candle, y, after burning for x number of hours.

Answers

The function to determine the length of the candle, y, after burning for x number of hours is y = 9-x/2

Given that, a candle is nine inches long and the packaging states the candle burns down at the rate of 1/2 an inch per hour.

We need find function to determine the length of the candle, y, after burning for x number of hours.

Since, the melting rate of the candle is 1/2 per hour,

So, the function will be =

y = 9-x/2

Hence, the function to determine the length of the candle, y, after burning for x number of hours is y = 9-x/2

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Express the area of the entire rectangle. Your answer should be a polynomial in standard form. An area model for a rectangle that has a height of x plus two and a width of x plus six. The rectangle is broken into four rectangles to isolate each term in the height and the width. The top left rectangle has a height of x and a width of x. The top right rectangle has a height of x and width of six. The bottom left rectangle has a height of two and a width of x. The bottom right rectangle has a height of two and a width of six.

Answers

The area of the entire rectangle as polynomial is x^2 + 8x + 12

Expressing the area of the entire rectangle as polynomial

From the question, we have the following parameters that can be used in our computation:

Height = x + 2; Width = x + 6

Broken rectangles

Height = x; Width = xHeight = x; Width = 6Height = 2; Width = xHeight = 2; Width = 6

The area of the rectangle is the product of the dimensions

Adding the heights and the width of the individual rectangles, we have

Height = x + 2; Width = x + 6

So, the area is

Area = (x + 2)(x + 6)

Expand

Area = x^2 + 8x + 12

Hence, the area expression is x^2 + 8x + 12

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If 5, x, y, and 40 are in geometric progression find x and y respectively​

Answers

The values of x  and y in the geometric progression are 10 and 20

Finding x and y in the geometric progression

From the question, we have the following parameters that can be used in our computation:

5, x, y, and 40

To calculate the values of x and y, we have

x/5 = 40/y

Cross multiply

So, we have

xy = 200

Set x = 10

So, we have

10y = 200

This gives

y = 20

So, we have

10/5 = 40/20 = 2 --- true

Hence, x is 10 and y is 20

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The vertices of SRT are S (1, 4), R (2, 2) and T (1, 3). A reflection across the line _________ [ (A) x = 4, (B) x = 6, (C) y = –x + 5,(D) y = –x + 6] and then across the line _________ [ (A) y = 6, (B) y = 8, (C) y = –x + 10, (D) y = –x + 12] is the same as a translation of 4 units to the right and 4 units up because the lines are _________ [ (A) congruent, (B) parallel, (C) perpendicular, (D) similar].

Answers

The given reflection transformation is a rigid transformation, such that the dimensions are preserved

The statements that are true about the image of triangle ABC following a reflection Bout the the line y = 2·a are;

AB = RS

ΔABC ≅ ΔRST

m∠BAC ≅ m∠SRT

Reasons:

The given parameters are;

Triangle ΔABC is reflected across the line y = 2·x

Given that a reflection is a rigid transformation, we have;

The distance between two points on a preimage is the same as the distance between the corresponding points on the image;

Therefore;

ΔABC is congruent to ΔRST by Side-Side-Side SSS, rule of congruency, such that we have;

AB ≅ RS, BC ≅ ST, and AC ≅ RT

m∠BAC ≅ m∠SRT

m∠BCA ≅ m∠STR

m∠BAC ≅ m∠SRT

Therefore;

The true statements are;

AB = RS

ΔABC ≅ ΔRST

Therefore;

m∠BAC ≅ m∠SRT given that ΔABC ≅ ΔRST

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complete question:

Triangle ABC is reflected across the line y=2x to map onto triangle RST. Select all statements that are true.

Question 3 options:

AB=RS

AB=2RS

ΔABC~ΔRST

△ABC≅ΔRST

m∠BAC=m∠SRT

m∠BAC=2m∠SRT

In the following diagram, ABCDABCD is a square. The coordinates of the vertices A,B,CA,B,C and DD are (3,3),(8,3),(8,8)(3,3),(8,3),(8,8) and (3,8)(3,8) respectively.

The square is dilated from the origin by a factor of 1111 to give A′B′C′D′A′B′C′D′.

What are the coordinates of point C′C′? (NEED THIS ASAP)

Answers

Answer:

Step-by-step explanation:

To dilate the square by a factor of 1111 from the origin, we need to multiply each coordinate by 1111.

The coordinates of point C are (8,8). So, to find the coordinates of point C' after dilation, we can simply multiply each coordinate by 1111:

x-coordinate of C' = 1111 * 8 = 8888

y-coordinate of C' = 1111 * 8 = 8888

Therefore, the coordinates of point C' are (8888, 8888).

new car is purchased for 18700 dollars. The value of the car depreciates at
14.25% per year. To the nearest year, how long will it be until the value of the
car is 3000 dollars?

Answers

The minimum time required to depreciate the value of the car is 12 years.

Let us assumed the time to be t. Representing the formula for calculation of time-

Final value = Principal value × [tex] {(1 - rate of depreciation)}^{t} [/tex]

Keeping the values in formula to find the time period

3000 = 18700 × [tex] {(1 - 14.25%)}^{t} [/tex]

Solving the expression

[tex] {(0.8575)}^{t} [/tex] = 3000/18700

Cancelling zeroes common in numerator and denominator

3000/18700 = [tex] {(0.8575)}^{t} [/tex]

Taking log on both sides of the equation

t log 0.8575 = 30/187

Keep the value

t = log 0.8575 30/187

t = 12 years

Hence, it will take 12 years for value depreciation.

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What is the style of William Holman Hunt's The Awakening Conscience (1853)?

Pre Raphaelite

Impressionism

Nabis

Realism

Answers

Answer:

The style of William Holman Hunt's The Awakening Conscience (1853) is Pre-Raphaelite.

What is the solution to the given linear-quadratic system: y = x + 5 and y = x² + 5?

Answers

Answer: 1 over 6

Step-by-step explanation:

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Identify the key factors that influence the export involvement levels of born-global firms:. run-off-the-mill products global orientation of decision makers market conditions financial and tangible resources 3) Find the linearization L(x) of the function at a. f(x)= cosx, a= pi/2 What does George mean when he says " I haven't any country?!?!?!??! 04.05 Ecological Tolerance Lab Worksheet Student Name: Annalise Clark Time Estimate: 60 minutes Pre-Activity Questions: Use information from the lesson to answer these questions. Answer in complete sentences. What conditions can impact the ecological tolerance of a species? How does island biogeography decrease ecological tolerance? Data: Trial Blue Island Red Island Green Island Yellow island 1 2 3 4 5 Calculations: Calculate the mean value for each island and record it in the data table. To calculate mean, add all the values of the trials and divide the value by the number of trials, which is five. Please show your work. Example: Trial One: 3 beans Trial Two: 4 beans Trial Three: 5 beans Trial Four: 7 beans Trial Five: 2 beans Mean = 3 + 4 + 5 + 7 + 2 = 21/5 = 4.2 Blue Island Red Island Green Island Yellow Island Unless Otherwise Noted All Content 2021 Florida Virtual School Mean Making Connections: Use your lesson and the results of your activity to answer the questions. Answer questions in complete sentences. Which islands had the most successful migrations? Explain why. How does a successful immigration rate impact the biodiversity of an island? How would the migration of generalist species onto the green island affect specialist species living on the island? Based on your data, which islands would you select as wildlife refuges? Explain your reasoning. Did the lab activity follow the island biogeography model? Why or why not? A 50-foot long irrigation sprinkler line rotates around one end. The sprinkler moves through anarc of 240 in 1.45 hours. Find the speed of the moving end of the sprinkler in feet per minute.Round your answer to the nearest tenth. Find the sector area Select the correct answer.Which sentence from the text provides an example of bandwagon appeal? A. "Out of the experience of and extraordinary human disaster that lasted too long, must be born a society of which all humanity will be proud." (paragraph 2) B. "The national mood changes as the seasons change." (paragraph 5) C. "Each time one of us touches the soil of this land, we feel a sense of personal renewal." (paragraph 5) D. "The moment to bridge the chasms that divide us has come." (paragraph 12) What is a referee's role in sports? 1. Should we have a Balanced Budget amendment? Are you for or against an amendment and why? Please discuss the consequences in your answer and provide data to support your position.2. Should we go back to the Gold standard? Why or why not?3. How does fiscal policy play a role in deficit building? Negative reinforcement helps control a person's behavior bySelect one:a. rewarding useful behavior.b. punishing negative behavior.c. encouraging a behavior by being removed.d. discouraging a behavior by being removed. if larry exercises the provisions in the corporate charter to protect his stake, his investment value in the firm will become Abiotic factors that affect population growth and demographics are also referred to as which of the following?A. density-dependent factorsB. density-independent factorsC. density-unrelated factorsD. density-diversity factors Select the corect answer.Which equation matches the function shown in the graph?3-2-1-0--14-2--3-FINO A.2y3 cos (+)OB. y = 3 cos (z)OC. yOD. 3/2T 5 3x3 sin (z-7)sin (x-x) + 3 shayra wants to reference a journal article published in 2008 by kim, sherman, and taylor for her social psychology paper. the sentence she wants to use is as follows:when people perceive that those from another culture engage in actions that are not concordant with the norms and expectations of their own culture, they often unjustly regard the difference as maladaptive.which option is an acceptable way to paraphrase this sentence? A misplacement of punctuation or spacing in a command during programming that causes the program to stop running is most likely which type of error? What are the signs and symptoms of decreased Blood Pressure in the nonprogressive/compensatory stage? What is the difference between oral apraxia and dysarthria? What if I make a spelling mistake or a capitalization error in the code? {{c1::Material culture}} is the objects that are involved in a certain way of life The area of a chalkboard is 24 square feet. The perimeter is 20 feet. What are the dimensions of the board?