In the given figure, l ∥ m and n are a transversal. If ∠1=80° and ∠5=100°,
find the measure of <2 , ∠3, ∠4.

Please give brief explanation

In The Given Figure, L M And N Are A Transversal. If 1=80 And 5=100,find The Measure Of &lt;2 , 3, 4.Please

Answers

Answer 1

The value of angle ∠5 will be equal to 120°.

What are lines and angles?

Straight lines with little depth or width are present. You will learn about a variety of lines, including transversal, intersecting, and perpendicular lines.

A figure called an angle is one in which two rays originate from the same point. In this area, you might also encounter contrasting and related viewpoints.

Given that In the given figure, l ∥ m and n are transversal and the angles are ∠1=80° and ∠5=100°.

First, calculate angle 2,

∠1 = ∠2  = 80 ( By alternate interior angles)

Calculate the angle ∠4,

∠4 = 180 - 80 - 40

∠4 = 180 - 120

∠4 = 60°

Calculate the angle ∠5,

∠5 = 180 - 60

∠5 = 120

Therefore, the value of angle ∠5 will be equal to 120°.

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Related Questions

Simplify the expression:
2(2f+5) =

Answers

Answer:

4f+10

Step-by-step explanation:

multiply the 2 to both the numbers in the parenthesis. 2 times 2f is 4f and 2 times 5 is 10

Can anyone write the equation of this graph?

Answers

The equation of the graph in the figure is f(x) = |x - 3| + 5

How to find the equation of the graph line?

Given that the graph is an absolute value graph

We start by calculating the vertex of the graph

In this case, the graph has it minimum point located at the coordinate (3, 5)

This coordinate can then be interpreted as

(h, k) = (3, 5)

As a general rule, the general representation of the equation of an absolute value function is f(x) = |x - h| + k

Substitute the known values in the above equation

So, we have the following equation

f(x) = |x - 3| + 5

Hence, the equation of the graph is f(x) = |x - 3| + 5

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L, M and N are points on a circle, centre O.
QMT is the tangent at M

(1) find LNOM
(2) find LNMQ

Please help me guys it urgent it would really make my day.

Answers

The size if the angle NOM is 54.

What is angle?

An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.

What is tangent of circle?

A Tangent of a Circle is a line that touches the circle’s boundary at exactly one point. The tangential point is the place where the line and the circle meet.

Given,

M and N are points on a circle.

QMT is the tangent

O is the center.

angle NOM = 2 angle NLM

NOM = 2(27)

= 54.

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wilma can mow a lawn in 40 minutes. vanessa can mow the same lawn in 120 minutes. how long does it take for both wilma and vanessa to mow the lawn if they are working together?

Answers

It takes 13 minutes 20 seconds for both wilma and vanessa to mow the lawn if they are working together.

A lawn can be mowed by Wilma in 40 minutes. In one hour, Vanessa can cut the same lawn in 120 minutes.

1/120 + 1/40 = 1/T

multiply by 40T;

3T = 40

T = 40/3

  = 13 1/3 minutes

  = 13 minutes 20 seconds

It takes 13 minutes 20 seconds for both wilma and vanessa to mow the lawn if they are working together.

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Solve for an angle in right triangles

I just need the answer :)

Answers

Answer:

19.47

Step-by-step explanation:

Answer:

[tex]m\angle A \approx 19.47 \textdegree[/tex]

Step-by-step explanation:

Utilize the trigonometric ratio sine.

[tex]\sin(m\angle A) = \dfrac{2}{6}[/tex]

[tex]\sin(m\angle A) = \dfrac{1}{3}[/tex]

[tex]m\angle A = \sin^{-1}\left( \dfrac{1}{3} \right)[/tex]

[tex]m\angle A \approx 19.47 \textdegree[/tex]

a license plate consists of 2 letters followed by 4 digits. how many license plates are possible if the 1st digit cannot be 0, and letters and digits may repeat? a) 4,100,625 b) 6,760,000 c) 4,435,236 d) 5,625,000 e) 6,084,000 f) none of the above.

Answers

The possible number of license plates is 6084000 .

We have to make a 6 word license plate in which first two are letters and remaining four are digits.

conditions are :

1. letters and digits can repeat themselves

2. 1st digit can't be 0.

taking into account these conditions

we know total letters are 26 and total digits are 10 ( 0,1,2,3,4,5,6,7,8,9)

Now if we divide number plate in 6 columns where first two are filler by letters and rest four by digits so

1st column can be filled in ways = 26

2nd column can be filled in ways = 26

3rd column can be filled in ways = 9 ( as zero is not allowed )

4th column can be filled in ways = 10

5th column can be filled in ways = 10

6th column can be filled in ways = 10

therefore, total number of ways = 26x26x9x10x10x10

                                                      = 6084000 ways

The possible number of license plates is 6084000 .              

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help help help help help help ​

Answers

When equation f(x) = 3x + 4 is transformed to h(x) = f(x + 3) and plotted on the graph, both the lines of the equations are parallel to each other.

What are graph equations?Equations with graphs as unknowns are known as graph equations in graph theory. The concept of isomorphism is one of the key issues in graph theory.Different graph equations may be used to express the aforementioned graphs.

So, the equations are graphs are:

Given equation: f(x) = 3x + 4Which is transform to equation: h(x) = f(x + 3)

Now, graph both equations as follows:

Both equations are parallel to each other.(Refer to the graph attached below)

Therefore, when equation f(x) = 3x + 4 is transformed to h(x) = f(x + 3) and plotted on the graph, both the lines of the equations are parallel to each other.

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How do you find the x for both of these problems?

Answers

Considering the figure the required angle is solved using the vertical angle theorem. The values are

14. 42 degrees and 16. 20 degrees

How to determine the required angle

The problem is solved considering this theorems

vertical angle theorem

According to this theorem, when two straight lines cross, they create two sets of linear pairs and the vertical opposite angles are equal.

solution for the missing angle

x + 70 + 60 = 180 sum of angles of a triangle

x = 50

Using vertical angle theorem

? + 88 + 50  = 180 sum of angles of a triangle

? = 180 - 88 - 50

? =  42

solution for the missing angle

x + 75 + 30 = 180 sum of angles of a triangle

x = 75

Using vertical angle theorem

? + 88 + 75  = 180 sum of angles of a triangle

? = 180 - 85 - 75

? =  20

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HELP ITS DUE IN A LITTLE BIT!!!

Answers

Answer:

Step-by-step explanation:

Yes it does

10 and 15

Answer:

A. the independent and dependent variables are the number of miles and total fee (y = 2.8 + 3.5x)

B. the domain is 0 <= x <= 20 and  range is 2.8≤x≤20

Step-by-step explanation:

Describe in words where cube root of 24 would be plotted on a number line.


100 points and brainliest

Answers

Answer: the square root of twenty-four would be plotted (A) between 4 and 5, but closer to 5 on a number line.

Step-by-step explanation:

after collecting the historical data from a process of filling coca-cola bottles, it was found that the variance in the filling process is constant. however, clogs in the machine often affect the average volume. the historical standard deviation is 5 ml. in filling 250 ml bottles, a sample of 20 bottles found an average of volume of 246 ml. create a 95% confidence interval for the average volume of coca-cola in a bottle. can you conclude from your results that the manufacturer needs to adjust the equipment to meet the standard?

Answers

The manufacturer needs to adjust the equipment to meet the standard with the margin of error of 2.34.

Define the term margin of error?

The calculated number known as the margin of error is added to and removed from the mean value to get the resulting confidence interval. The confidence interval expands as the margin of error does.

Alpha value = 0.05Standard deviation = 5Sample size = 20Sample average = 246

Calculate the 95% confidence interval's margin of error based on the aforementioned data.

α = 0.05

n = 20

s = 5

The following is the formula to determine the margin of error:

E = T(n-1) ×s/√n

The t-distribution table is used to determine the value of tn-1 at 19 degrees of freedom.

Replace the values in the formula above.

E = 2.093 ×5/√20

Thus, its margin of error is 2.34 as a result.

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what is the smallest positive integer $n$ such that the rightmost three digits of $n!$ and $(n 1)!$ are the same?

Answers

The smallest positive integer n will be 10 .

To find : the smallest positive integer n such that the rightmost digits of  n ! and ( n + 1 ) ! are same .

Since ,

putting n = 10 gives

n ! = 10 ! = 3628800

and ( n + 1 ) ! = 39916800

Last three digits ( rightmost digits ) ie. 800 are same .

Hence , n = 10 is the required answer ,

Therefore , the smallest positive integer is n = 10 such that the rightmost digits of  n ! and ( n + 1 ) ! are same .

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If x²y - 3x = y³ – 3, then at the point (-1,2), dy/dx=

Answers

now, the assumption in this implicit differentiation is that "y" is really a function in x-terms, whilst "x" is just a simple variable

[tex]x^2y-3x=y^3-3\implies \stackrel{product~rule}{\left( 2xy + x^2\cdot \cfrac{dy}{dx} \right)}-3=\stackrel{chain~rule}{3y^2\cdot \cfrac{dy}{dx}} \\\\\\ 2xy-3=3y^2\cdot \cfrac{dy}{dx}-x^2\cdot \cfrac{dy}{dx}\implies 2xy-3=\cfrac{dy}{dx}(3y^2-x^2) \\\\\\ \left. \cfrac{2xy-3}{3y^2-x^2}=\cfrac{dy}{dx} \right|_{(-1,2)}\implies \cfrac{2(-1)(2)-3}{3(2)^2-(-1)^2}\implies -\cfrac{7}{11}[/tex]

A cell phone provider offers a plan that costs ​40$ per month plus ​0.10$ per text message sent or received. A comparable plan costs ​50$ per month but offers unlimited text messaging. Complete parts a. and b. below.

a. How many text messages would have to be sent or received in order for the plans to cost the same each​ month?

In order for the plans to cost the​ same,
enter your response here text messages would have to be sent or received.
​(Simplify your answer. Type an integer or a​ decimal.)

Answers

answer:

100 text messages.

$50-$40 = $10

$10/$0.1 = 100

100 text messages

please help. ill give brainliest

Answers

Answer:

X=30

Step-by-step explanation:

[tex](4x + 30) + (2x - 30) = 180 \\ 4x + 2x + 30 - 30 = 180 \\ 6x = 180 \\ x = 30[/tex]

Answer:

x = 30

Step-by-step explanation:

We are told that:

• m∠A =  (4x + 30)°

• m∠B = (2x - 30)°,

and that these two angles are supplementary to each other.

When two angles are supplementary to each other, it means that they add up to 180°.

Therefore:

∠A + ∠B = 180°

⇒ (4x + 30)°  +  (2x - 30)° = 180°

⇒ 4x + 30 + 2x - 30 = 180

⇒ 4x + 2x + 30 - 30 = 180      [Combining like terms]

⇒ 6x = 180

⇒ [tex]\frac{6}{6}x = \frac{180}{6}[/tex]     [Dividing both sides of the equation by 6]

x = 30

The sum of two numbers is 12. The difference of the same two numbers is -4. Wht is the smaller number?

Answers

Answer:

The smaller number is 4.

Step-by-step explanation:

X and Y are the two numbers

x+y=12

x-y=-4

Subtract these two equations

(x+y=12)

-(x-y=-4)

—————-

2y=16

y=8

Plug it in to any equation:

x+y=12

x+8=12

x=4

Which of the following equations have infinitely many solutions?
Choose all answers that apply:
Choose all answers that apply:

(Choice A)
A
-6x+35=-6x-35−6x+35=−6x−35minus, 6, x, plus, 35, equals, minus, 6, x, minus, 35

(Choice B)
B
-6x+35=-6x+35−6x+35=−6x+35minus, 6, x, plus, 35, equals, minus, 6, x, plus, 35

(Choice C)
C
6x+35=-6x+356x+35=−6x+356, x, plus, 35, equals, minus, 6, x, plus, 35

(Choice D)
D
6x+35=-6x-356x+35=−6x−356, x, plus, 35, equals, minus, 6, x, minus, 35

Answers

The equation which has infinitely many solutions include the following: B. -6x + 35 = -6x + 35

What are infinitely many solutions?

In Mathematics, an equation is said to have an infinitely many solution when the left hand side and right hand side of the equation are the same or equal.

This ultimately implies that, an equation would have infinitely many solutions when both sides of the equal sign are the same, and both the slope and intercept for the two lines are the same.

In this scenario, we can reasonably and logically deduce that the following equations satisfy the condition for an equation which has infinitely many solutions:

-6x + 35 = -6x - 35 (False).

-6x + 35 = -6x + 35 (True).

6x + 35 = -6x + 35 (False).

6x + 35 = -6x - 35 (False).

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Complete Question:

Which of the following equations have infinitely many solutions?

Choose all answers that apply:

A. -6x + 35 = -6x - 35

B. -6x + 35 = -6x + 35

C. 6x + 35 = -6x + 35

D. 6x + 35 = -6x - 35

Solve for X:
1/2x + 1/3x = 10

Answers

Answer:

Step-by-step explanation:

weknr f not sure

Answer:

12

Step-by-step explanation:

1/2x+1/3x=10

We simplify by making common denominator and adding them (if you don’t know how to do that please tell me)

3/6x+2/6x=10

5/6x=10

Now divide 5/6 on both sides

5/6x=10

/5/6. /5/6

x=10*6/5

x=60/5

x=12

Hopes this helps please mark brainliest

What is the total volume of both boxes if s equals 8 inches

Answers

The total volume of both cubed boxes, combined, is of:

612 cubic inches.

What is the volume of a cube?

The volume of a cube of side length s is given by the side length s cubed, as shown by the formula presented as follows:

V = s³.

In this problem, the boxes are given as follows:

Cubed box with side length of s = 8 inches.Cubed box with a volume of 100 cubic inches.

The volume of the box with side length 8 inches is given as follows:

V = 8³ = 512 cubic inches.

(measure is in inches, hence the cubed measure is in cubic inches).

The total volume is given by the sum of the volumes of the two boxes, hence:

Total volume = 512 cubic inches + 100 cubic inches = 612 cubic inches.

Missing Information

The image showing the cubes is given at the end of the answer.

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f(x) = x + 2
g(x) = 3x
Work out the value of gf (4).

Answers

The value of gf(4) is 18

What is Function?

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

Given,

f(x) = x + 2

g(x) = 3x

Now we need Function of a function

i.e. g[f(x)]

Then on g(x) we have to replace the x with f(x)

Thus,

g[f(x)] = 3(x + 2)

         = 3x + 6

Now by evaluating at

x = 4 i.e.

gf(4) = 3(4) + 6

gf(4) = 12 + 6

gf(4) = 18

Hence, The value of gf(4) = 18

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Container A has 200 L of water, and is being filled at a rate of 6 liters per minute. Container B has 500 L of water, and is being drained at 6 liters per minute. How many minutes, m, will it take for the two containers to have the same amount of water?

Answers

It will take 25 minutes for the two containers to have the same amount of water .

In the question ,

it is given that ,

water present in container A = 200L

water present in container B = 500L

rate at which the water is filling in container A= 6 liter/minute

rate at which the water is draining in container B = 6 liter/minute

let the time taken = m minutes ,

So , According to the question ,

the equation representing the situation is  

200 + 6m = 500 - 6m

Simplifying further , we get

6m + 6m = 500 - 200

12m = 300

m = 300/12

m = 25

Therefore , It will take 25 minutes for the two containers to have the same amount of water .

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sam rolls 3 standard fair dice. that probability that the three numbers rolled on the dice are the sides of a triangle is , where are relatively prime positive integers. what is the value of ?

Answers

The required probability for three numbers rolled on the dice are the sides of a triangle is 31/36.

What is probability?

The area of mathematics known as probability studies potential outcomes of events as well as their relative probabilities and distributions. It is based on the likelihood that something will occur. The justification for probability serves as the main foundation for theoretical probability.

Here,

When three dice are rolled, there are 63=216 possible outcomes, or triplets (x, y, z).

Once more, in a triangle, any two sides added together are larger than the third side, or (x+y)>z.

As a result, 186 outcomes or triplets are possible and satisfy this property.

Hence, the required probability is 186/216=31/36.

The required probability is 31/36 for three dice rolls to produce triangle sides.

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Determine which integer will make the inequality 5x + 6 ≤ 2x + 15 false.

S:{−2}
S:{5}
S:{2}
S:{−5}

Answers

Answer:

the correct she answer should be 5

Step-by-step explanation:

31 <= 25 is false

The solution set for the given inequality is  {.......-4, -3, -2, -1, 0, 1, 2, 3}, so the for x=5 the inequality is false. Therefore, the correct answer is option B.

The given inequality is 5x+6≤2x+15.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Here, the inequality can be solved as follows

5x+6≤2x+15

Subtract 6 on both the sides of the inequality, we get

5x+6-6≤2x+15-6

5x≤2x+9

Subtract 2x on both the sides of the inequality, we get

5x-2x≤2x+9-2x

3x≤9

Divide 3 on both the sides of the inequality, we get

x≤3

Here, solution set is {.......-4, -3, -2, -1, 0, 1, 2, 3}

So, the for x=5 the inequality is false.

Therefore, the correct answer is option B.

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Given g(x)=-x-4g(x)=−x−4, solve for xx when g(x)=10g(x)=10.

Answers

The solution for x in the function when the function g(x) = 10 is 4

How to determine the solution for x in the function?

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

g(x)=x-4

To make the equation legible, we need to rewrite it

So, we have the following representation

g(x) = x - 4

Also from the question, we have

g(x) = 10

This means that we calculate x when g(x) = 10

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

10 = x - 4

So, we have the following equation

x - 4 = 10

Add 4 to both sides of the equation

So, we have the following representation

x - 4 + 4 = 10 + 4

Evaluate the equation

x = 14

Hence, the solution is 14

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Sandy bought an outboard motor for a total selling price of $420 in Maine, which has a 7% sales tax rate. Calculate the sales tax.

Answers

Answer

you do 420x0.7= 29.40

Answer:

The sales tax is 29.4

Step-by-step explanation:

Just divide in half until you reach 5 and then calculate the other 2 percent of it and add the 2 percent back onto it.

Solve x² + 5x - 14 = 0

Answers

By solving  the equation  x² + 5x - 14 = 0 get the value of x is 2 or -7.

Given,

In the question:

To solve the equation:

x² + 5x - 14 = 0

Now, According to the question:

x² + 5x - 14 = 0

Split the middle term into two terms :

x² - 2x + 7x  - 14 = 0

Factor the first two terms and the last two terms separately

x(x - 2) + 7 (x -2) = 0

Factor out

(x - 2) (x + 7) = 0

Apply Zero Product Property

x - 2 = 0 or x + 7 = 0

x = 2 or x = -7

Hence, By solving  the equation  x² + 5x - 14 = 0 get the value of x is 2 or -7.

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The sum of the ages of pam,dion, and their three children, in years, is 5x - 99. where x is dion's age. pam is five years younger than dion. what is the usm of the ages of their children?

Answers

The sum of the ages of the children would be 3x - 94 years.

We have the total sum of the ages of pam ,dion and their children  

as 5x - 99

here , x is the age of Dion .

we see , pam is five years younger than Dion , so

age of Pam = x - 5

Now as the sum of all the ages = 5x - 99

therefore ,

Age of Dion + Age of Pan + Age of children = 5x - 99

x + x - 5 + Age of children = 5x - 99

2x - 5 + Age of children = 5x - 99

therefore ,

Age of children = 3x - 94

So  the age of their children would be 3x - 94 years

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What is the value sine?
5/12
5/13
12/13
13/5

Answers

Answer:

(C.) 5/13

Step-by-step explanation:

The sine proportion is opposite / hypotenuse

Given the reference angle, the side measuring 5 units is the opposite side and the side measuring 13 units (and opposite of the right angle) is the hypotenuse

Thus, sine is 5/13

Which is not true about a direct porprtion

Answers

The equation of the line in slope - intercept form will be -

y = (4/5)x + 5

Writ the general equation of a Straight line?

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

At [c] = 0 -

y = mx

We have a directly proportional relation.

The general equation of a straight line is -

[y] = [m]x + [c]

At [c] = 0, y = mx

m = y/x

where [m] acts as a constant of proportionality.

So -

y = mx : represents direct proportionality between [y] and [x]. Its graph is a straight line.

Therefore, y = mx : represents direct proportionality between [y] and [x]. Its graph is a straight line.

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Please help with slope question

Answers

The change in y is 12 and the change in x is 3 so 12/3 is 4 so the slope is 4

choose any 2 points on the graph

To calculate the slope use the formula:

slope = y (point 2)-y (point 1)/x (point 2)-x (point1)

substitute the choses points in

calculate your awnser

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When I saw my grandmother ordering gardening supplies online, it struck me that the days of brick-and-mortar shops might be doomed. Not that my grandmother is a dinosaur, mind you. She is a wizard with the remote, uses social media to stay in touch with her friends, and sends text messages with ease. However, she is certainly not of a generation that grew up with computers or the Internet. Her purchase got me thinking about the early days of online shopping, when people were anxious about ordering merchandise from the Internet. What if the items never arrived? Was putting all my personal information online safe? Should I really disclose my credit card information to some unknown entity? Is this online company legitimate? And last but not least, who would buy something without seeing it first? But my grandmothers transaction made it clear: online shopping has become as commonplace as brushing your teeth.What is the cultural context of this passage?The reading takes place in a past generation. The narrator is a grandmother who shares her thoughts about online shopping.The reading takes place in the early days of online shopping. The story is set in a doomed brick-and-mortar shop.The reading takes place in a past generation. The narrator is a grandmother who shares her thoughts about online shopping.The reading takes place in modern times. The narrator considers her beliefs about the cultural changes regarding shopping online. 1.explain why a polar aprotic solvent is used for this reaction? what is the polar aprotic solvent that is used? what is a type of body plan in which an animal's body is divided into nearly identical units? multiple choice question. Under what conditions do consumers bear the full burden of an excise tax levied onthe producer? what is the temperature of 0.43 mol of xe gas contained in a 2.65 l container at 3.77 atm? question 7 options: while eating out, mike and joe each tipped their server 22 dollars. mike tipped 10\% of his bill and joe tipped 20\ % of his bill. what was the difference, in dollars between their bills? Suppose you are the campaign manager for one of the presidential candidates in 1800. Create a campaign song for your candidate. Your song can be to the tune of Hail, Columbia, Fair and Free Elections, or any other tune you choose. Your song must: clearly describe the Federalist or the Republican vision for the United States. contain at least two reasons why your candidate should be elected. use language that reflects the passionate feelings held by Federalists or Republicans. brice co. purchases land in order to drill oil. this oil field would be classified as a(n) on the balance sheet. compared to traditional goods, digital goods have: group of answer choices higher copying costs. higher marginal costs. higher inventory costs. higher delivery costs. lower marginal costs of production. john is a 67-year-old male who recently suffered a stroke, which affected his ability to walk. over a series of months in physical therapy, john is able to walk again. which psychological concept best describes the biological reason he regained his motor ability? Which factor contributed to colonel james fannin's decision to surrender to general jos de urrea? question 1 options: urrea's army received reinforcements. sam houston sent a letter ordering the surrender. fannin's wife asked him to end the fighting. urrea promised him 1,000 dollars in gold if he gave up. if the rate on one-year treasury strips currently is 6 percent, what is the repayment probability for each of the following two securities? assume that if the loan is defaulted, no payments are expected. what is the market-determined risk premium for the corresponding probability of default for each security? one-year aa-rated zero-coupon bond yielding 9.5 percent. one-year bb-rated zero-coupon bond yielding 13.5 percent. In the diagram below, GH is parallel to DE. If FH is 5 more than GF, DF:and FE = 48, find the length of GF. Figures are not necessarily drawn to scalState your answer in simplest radical form, if necessary.Answer: GF = 1. Design and implement a class dayType that implements the day of the week in a program. The class dayType should store the day, such as Sun for Sunday. The program should be able to perform the following operations on an object of type dayType: a. Set the day. b. Print the day. c. Return the day. d. Return the next day. e. Return the previous day. f. Calculate and return the day by adding certain days to the current day. For example, if the current day is Monday and we add 4 days, the day to be returned is Friday. Similarly, if today is Tuesday and we add 13 days, the day to be returned is Monday. Add the appropriate constructors.2. Also, write a program to test various operations on this class .