The equation of the **parallel line **will be y = (2/3)x - 8/3.

Let the **equation **of the line be ax + by + c = 0. Then the equation of the parallel line that is **parallel **to the line ax + by + c = 0 is given as ax + by + d = 0.

The **equation **of the line is given below.

y - 4 = 2/3 (x - 3)

The **equation **of the line that is **parallel **to the given line will be written as,

y = (2/3)x + c

The equation of the line that **passes **through (1, -2), then we have

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

- 2 = 2 /3 + c

c = - 8 / 3

Then the equation of the **parallel line **will be y = (2/3)x - 8/3.

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What is x? Because I don’t know g how to work it out

**Answer:**

45 degrees

**Step-by-step explanation:**

The 4 angles of a quadrilateral will add to 360.

We know 1 of them (angle B) is 90 degrees.

We can set up an equation to solve the others.

2x+3x+x+90 = 360

Now solve for x.

Start by combining the x terms together.

6x+90 = 360

6x = 360-90

6x = 270

(6x/6) = 270/6

x = 45 degrees

Check back to see if that makes sense and if the equation equals 360 when x is 45:

2x+3x+x+90 = 360

2(45)+3(45)+45+90=360.

Gillian's Restaurant has an ice-cream counter where it sells two main products, ice cream and frozen yogurt, each in a variety of flavors. The restaurant makes one order for ice cream and yogurt each week, and the store has enough freezer space for 115 gallons total of both products.

A gallon of frozen yogurt costs $0.75 and a gallon of ice cream costs SO.93, and the restaurant budgets $90 each week for these products. The manager estimates that each week the restaurant sells at least twice as much ice cream as frozen yogurt. Profit per gallon of ice cream is $4.15. and profit per gallon of yogurt is $3.60.

a. Formulate a linear programming model for this problem.

b. Solve this model by using graphical analysis

The constraints involve three variables (Y, I, and Z), it is not feasible to graphically represent the entire **Feasible region** in three dimensions.

The linear **programming model **for decision variables, objective function, and constraints.

Decision Variables:the number of gallons of frozen yogurt purchased each week as Y and the number of gallons of ice cream purchased each week as I.

Objective Function:

The objective is to maximize the** total profit.** The profit from frozen yogurt can be calculated as 3.60Y, and the profit from ice cream can be calculated as 4.15I. Thus, the objective function is:

Maximize Profit: Z = 3.60Y + 4.15I

Constraints:

1. Budget constraint: The total cost of frozen yogurt and ice cream should not exceed the weekly budget of $90.

Cost Constraint: 0.75Y + 0.93I ≤ 90

2. Freezer space **constraint**: The total gallons of frozen yogurt and ice cream should not exceed the available freezer space of 115 gallons.

Space Constraint: Y + I ≤ 115

3. Ice cream sales constraint: The weekly ice cream sales should be at least twice the frozen yogurt sales.

Ice Cream Sales Constraint: I ≥ 2Y

4. Non-negativity constraint: The number of gallons for both products cannot be negative.

Non-negativity Constraint: Y ≥ 0, I ≥ 0

The model using graphical analysis, we can plot the constraints on a graph and find the feasible region. Then, we can evaluate the objective function at each corner point of the feasible region to determine the optimal solution.

Since the constraints involve three variables (Y, I, and Z), it is not feasible to graphically represent the entire feasible region in three dimensions.

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A square piece of sheet metal (24 in x 24 in)

is used to make an open box (no lid). Equal

squares are cut out of each corner, and the

edges are folded up to make the box.

What is the maximum volume, V, of the box?

The **maximum volume **of the box is 864 cubic inches.

Let side **length **of the square cut from each corner is x inches.

After cutting the squares from each corner, the **remaining dimensions **of the sheet metal will be:

Length: 24 - 2x inches

Width: 24 - 2x inches

Height: x inches

So, the **volume **of the **box **

V = (24 - 2x) (24 - 2x) x

V = x(24 - 2x)²

To find the **maximum **volume, we can take the **derivative **of V with respect to x, set it to zero, and solve for x:

dV/dx = (24 - 2x)² - 2x(24 - 2x) = 0

4x² - 96x + 576 = 0

**Solving **the quadratic equation,

x = 6 and x = 12.

We can **substitute **x = 6 into the volume equation to find the maximum volume:

V = 6(24 - 2(6))²

V = 6(12)²

V = 6 x 144

V = 864 cubic inches

Therefore, the **maximum volume **of the box is 864 cubic inches.

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The first shelf of one bookcase is 2 inches off the ground. The second shelf is 1’5” above the first the third shelf is 1’3” above the second and the fourth shelf is 1’2” above the third. The top shelf is 1’4” above the fourth how high off the ground is the top shelf.

**answer: 5'6"**

**step by step: 1'5"+2"=1'7"+1'3"=3'0"+1'2"=4'2"+1'4"=5'6"**

In Algebra, a minus symbol [-] will represent two things, an operation of subtraction and a negative number, depending on where it's placed.

(a) True

(b) False

**Answer:**

It is true that in algebra minus symbol represent two things

**Step-by-step explanation:**

And it is true that it depend on where it placed such as

8-2 this minus indicate the substraction of two terms

-3 this show that the number has negative quantity

What is the value of x *

7+5x

47°

The answer is going to be 8

Answer: X = 8

Step-by-step explanation:

47 - 7 = 40

40 / 5 = 8

x = 8

Can someone please answer and provide an explanation for these problems?

The values of x for the **tangent** segments to the **circles** are: (25). x = 2 and (26). x = 4

A theorem of **tangents** to a circle states that if from one exterior point, two tangents are drawn to a **circle** then they have equal tangent segments.

(25). 2x - 1 = x + 1 {equal tangent segments}

2x - x = 1 + 1 {collect like terms}

x = 2

(26). 2x - 4 = x {equal tangent segments}

2x - x = 4 {collect like terms}

x = 4

Therefore, the values of x for the **tangent** segments to the **circles** are: (25). x = 2 and (26). x = 4

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The distribution of monthly charges for cellphone plans in the United States is approximately normal with a mean of $62 and a standard deviation of $18. What percentage of plans have charges that are less than $83.60?

About 88.49% of **cellphone **plans have charges that are less than $83.60.

To determine the **percentage **of plans that have charges less than $83.60, we need to find the **z-score** (z) using the given mean and standard deviation, and then look up the corresponding area under the normal distribution curve.

z = (x – μ) / σ

where x = 83.60, mean, μ = 62 and standard deviation, σ = 18

Thus, the z-score of $83.60 is:

z = (83.60 - 62) / 18 = 1.2

Using a standard **normal distribution** table, we can find that the area to the left of z = 1.20 is 0.8849 or 88.49% (check image attached).

Therefore, about 88.49% of **cellphone** plans have **charges** that are less than $83.60.

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Can someone help me? Write a rule for nth term of the arithmetic sequence with a1=7 and the common difference is 3

**Answer:**

[tex]a_n=3n+4[/tex]

**Step-by-step explanation:**

If the common difference is d=3 and the first term is a₁=7, then we can create an arithmetic sequence:

[tex]a_n=a_1+(n-1)d\\a_n=7+(n-1)(3)\\a_n=7+3n-3\\a_n=3n+4[/tex]

8 +[13-(2+1] =

20

18

-3

**Answer: false**

**Step-by-step explanation:**

find the center and radius by completing the square x2+6x+y2-16y-8=0

center- (-3,-8) radius- (3)

Consider the experiment of selecting a playing card from a deck of 52 playing cards. Each card corresponds to a sample point with a

1

52

probability.

(a)

List the sample points in the event an ace is selected.

S = {x | x is a card from the deck that is not a club a spade or a diamond}

S = {x | x is a card from the deck but not king, jack, or queen}

S = {1 of clubs, 1 of diamonds, 1 of hearts, 1 of spades}

S = {ace of clubs, ace of diamonds, ace of hearts, ace of spades}

S = {king of clubs, king of diamonds, king of hearts, king of spades}

If Each card corresponds to a sample point with a 1/52 **probability** then the **sample** points in the event an ace is selected is S = {ace of clubs, ace of diamonds, ace of hearts, ace of spades}

In a standard deck of 52 playing cards, there are four aces.

Each ace corresponds to a different suit: clubs, diamonds, hearts, and spades.

So, when we talk about the event of selecting an ace, we are referring to the act of **choosing** one of these four specific cards from the deck.

The sample points in the event "an ace is selected" are the individual cards that match this criteria.

Therefore, the **sample** points in this event are:

S = {ace of clubs, ace of diamonds, ace of hearts, ace of spades}

These four cards are the possible outcomes when we **randomly** select a single card from the deck, focusing only on the event of selecting an ace.

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Answer this and I'll get you Brainlest!

The **total cost **of the meal if the **meal** costs $50 is $60

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

**Tip percent **= 20%

From the question, we can use any value as the cost of the **meal **

So, we can use the following

Meal cost = $50

So, we have

**Tip amount **= Tip percent * Meal cost

This gives

Tip amount = 20% * 50

Tip amount = 10

Next, we have

Total meal cost = Tip amount + Meal cost

This gives

Total meal cost = 10 + 50

Evaluate

Total meal cost = 60

Hence, the **total cost **of the meal is $60

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D

(x+2)(x+6)=0

In the problem shown, to conclude that x+2=0 orx+6=0, one must use the:

O zero product property

O division property

O transitive property

O multiplication property

H

OI

**Answer:**

zero product property

**Step-by-step explanation:**

To conclude that x+2=0 or x+6=0 from the equation (x+2)(x+6)=0, one must use the zero product property.

The zero product property states that if the product of two factors is equal to zero, then at least one of the factors must be equal to zero. In this case, if (x+2)(x+6)=0, it means that the product of (x+2) and (x+6) is zero. Therefore, we can conclude that either (x+2) = 0 or (x+6) = 0, based on the zero product property.

Cual es la sucesión aritmética de 3,8,13,18,23

**Equation** [1] : a(n) = 3 + (n - 1)5 represents the step where he made the mistake.

We have,

A mathematical** expression** is made up of terms (constants and variables) separated by mathematical operators. A mathematical **equation** is used to equate two expressions.** Equation** modelling is the process of writing a mathematical verbal **expression** in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have a student who used the explicit formula a[n] = 5+3(n-1) for the **sequence** 3,8,13,18,23,...to find the 12th term.

The given **sequence **is -

3 , 8 , 13 , 18 , 23, ..

Here -

d = 8 - 3 = 13 - 8 = 5

a = 3

a(n) = a + (n - 1)d {for arithmetic **sequence**}

a(n) = 3 + (n - 1)5 ...Eq[1]

a(n) = 3 + 5n - 5

a(n) = 5n - 2

Therefore, **Equation **[1] : a(n) = 3 + (n - 1)5 represents the step where he made the mistake.

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complete question:

A student uses the explicit formula an= 5+3(n-1) for the sequence 3,8,13,18,23,...to find the 12th term. Explain the error the student made.

Please help urgent thank you

If he wants an **average **of 84, he needs to get at least 93 points.

Remember that the **average **value between 3 values A, B, and C is:

(A + B + C)/3

Here we know that the first two scores are 76 and 83 points, let's say that the** third score** is x, if we want to have an average of 84 or more, then we need to solve:

(76 + 83 + x)/3 = 84

159 + x = 252

x = 252 - 159

x = 93

So he needs to get at least 93 points in the next exam.

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when y is directly proportional to x. When x= 2.5, y=20. what is the value of y when x= 22?

If it’s proportional that means you can put it in a ratio

Y:X

20:2.5

8:1

176:22

Y:X

20:2.5

8:1

176:22

evaluate 6a +4b -3c when a=4 , b=7 , and c=-2 (a) 26 (b) 16 (c) 46) (d) 58

**Answer:**

(d) 58

**Step-by-step explanation:**

Let's start with the equation:

6a+4b-3c

Now, since we got the values of a, b, and c, we can just plug them into the equation:

6(4)+4(7)-3(-2)

24+28+6=58

So the answer is d) 58

Which expressionis equivalent to 60m-2n6/5m-4n-2 for all values of m and n where the expression is defined?

The **expression **that is equivalent to [tex]\\\\\frac{60m^-2n^6\\}{5m^-4 n^-2}[/tex] for all values of m and n where the 5m-4n-2 expression is defined is [tex]12m^{2} n^{8}[/tex]

In mathematics, an expression or** mathematical expression** can be described as the finite combination of symbols which is been analyzed and well-formed according by following some set of rules which could be varies base on the kind of the symbol as ll as the operation that are involved in the expression and it s been done depending on the context so that another expression can be gotten.

This is given as [tex]\\\\\frac{60m^-2n^6\\}{5m^-4 n^-2}[/tex]

Then we have it defined by; [tex]12m^{2} n^{8}[/tex]

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2. Six months after John William becomes a shareholder, Peixotto Media announces

its first shareholder meeting. Because the co-presidents will be making some very

important announcements about decisions that will be voted upon by the

shareholders, John William attends. He finds that of the 20,000 shares that have

been offered so far, the shareholders who attend the meeting own 6,000 of them.

a. The co-presidents propose adding a new member to the company's board of

directors. The shareholders are allowed to vote on this matter. What percentage of

the total vote will John William control? (2 points)

b. The company's co-presidents announce that Peixotto Media will be issuing

another offering of stock, this time in the amount of 50,000 shares. Given his

preemptive rights as an existing shareholder, how many shares of this stock is John

William entitled to purchase before the offering is made to the public? (3 points)

John William is entitled to** purchase** 15,000 shares before the offering is made to the public.

a. To calculate the percentage of the total vote John William will control, we need to find the proportion of shares he owns out of the total shares represented at the meeting.

John William owns 6,000 shares out of the 20,000 shares offered so far. Therefore, the **proportion** of shares he owns is 6,000/20,000, which simplifies to 3/10 or 0.3.

To convert this proportion to a percentage, we multiply by 100:

Percentage of the total vote = 0.3 * 100 = 30%

Thus, John William will control 30% of the total vote at the. **shareholder meeting. **

b. Preemptive rights allow existing shareholders to purchase new shares before they are offered to the public. To determine the number of shares John William is entitled to purchase, we need to calculate the proportion of his **current ownership**.

John William owns 6,000 shares out of the total shares offered so far, which is 20,000. Therefore, his ownership proportion is 6,000/20,000, or 3/10.

If Peixotto Media plans to issue 50,000 new shares, John William's entitlement would be:

Entitlement = (3/10) * 50,000 = 15,000 shares.

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What is the value of i 20+1

1

-1

i

-i

the value of 20+1 should be one bc thats what it equals

Which type of retirement account is an investment option for ANY young person?

a. traditional IRA

b. pension

c. 401(k)

d. social security

The type of** retirement account **is an** investment** option for ANY young person is 401(k). option C

A 401(k)** retirement account **is described as an option for investing money, created and arrangement for youths with access to any lucrative job that pays a reasonable amount of money.

This retirement account creates room for individuals to contribute a portion of their tax income towards retirement savings, and also contributes to grow **tax-deferred** until withdrawal.

However, pensions are employer-funded retirement plans and may be unavailable to all young individuals

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Which equation is the inverse of y = x² - 36?

Oy=± √√x +6

Oy=+√√x+36

O y=+√√x +36

Oy=+√√x²+36

**Answer:**

**Step-by-step explanation:**

**Answer: B **y = ±[tex]\sqrt{x+36}[/tex]

**Step-by-step explanation:**

To find the inverse of any equation. Switch the x and the y then solve for y.

y = x² - 36 >switch variables

x = y² - 36 >add 36 to both sides

x+36=y² >take square root of both sides

y = ±[tex]\sqrt{x+36}[/tex]

B

A student is establishing the A.A criterion for the similarity of triangles [MN and [QR. The student writes LMLN ~ ZQLR What other information can the student use to establish the AA criterion?

The other information can the student use to establish the AA criterion is Angle LMN **congruent **angle LQR or angle LMN **congruent **angle LRQ

The student can use the following **information **to establish the AA **criterion**:

These two angles **correspond **to the two **angles **in the other triangle (LQR or LRQ) that are **not congruent **to the angle already known to be congruent (angle QLR).

Therefore, the AA **congruent **for similarity can be **congruent **.

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lin's family needs to travel 325 miles to reach her grandmother's house at 377 miles what percentage have they completed

Lin's family has completed approximately 86.15% of the total **Distance **to her grandmother's house.

The percentage of the distance Lin's family has completed, the ratio of the distance they have **traveled **to the total distance.

The distance traveled is 325 miles, and the total distance to Lin's grandmother's house is 377 miles.

To calculate the percentage, we can use the following formula:

**Percentage **= (Distance Traveled / Total Distance) * 100

Plugging in the values, we have:

Percentage = (325 / 377) * 100

= 0.8615 * 100

= 86.15

Therefore, Lin's family has completed approximately 86.15% of the **total **distance to her grandmother's house.

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3. In a cooking class, Martin pours 500 milliliters

of broth into a pot. He then adds 1,500 milliliters

of water to the broth. How much total liquid is in

the pot?

A. 1 liter

B.

2 liters

C.

3 liters

D. 5 liters

C

**Answer:The correct answer is C. 3 liters.**

**Step-by-step explanation:**

To determine the total amount of liquid in the pot, we need to add the volume of the broth and the volume of the water.

The broth has a volume of 500 milliliters, and the water has a volume of 1,500 milliliters. Adding these together, we get:

500 mL + 1,500 mL = 2,000 mL

Since there are 1,000 milliliters in a liter, we can convert the volume to liters:

2,000 mL ÷ 1,000 = 2 liters

Therefore, the total amount of liquid in the pot is 2 liters.

What is the length of this circle?

The **length** of **arc** **length** s is 1152π² or 11358.26.

We have,

The **arc length** of a **circle** can be calculated using the formula:

Arc Length = 2πrθ/360

Where:

π is a mathematical constant approximately equal to 3.14159.

r is the radius of the circle.

θ is the central angle subtended by the arc, measured in degrees.

The **arc** **length** of a **circle** can be written as:

s = angles/360 x 2πr _______(1)

Now,

r = 4 cm

Angle = (2/5)π

Now,

Substitute in (1).

s = angles/360 x 2πr

s = (2/5)π/360 x 2π x 4

s = 2π x 72 x 2π x 4

s = 4π² x 288

s = 1152π²

or

s = 11358.26

Thus,

The **length** of **arc** **length** s is 1152π² or 11358.26.

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A rectangle has an area of 114cm squared and a perimeter of 50 cm. What are its dimensions

**Answer:**

width = 6

length = 9

**Step-by-step explanation:**

Perimeter = 2(length + width) or P = 2(l + w)

2(l + w) = 50

l + w = 25

l = 25 - w

Area = length x width or A = lw

lw = 114

Substitute l = 25 - w into the lw = 114

(25 - w)w = 114

25w - w^2 = 114

-w^2 + 25w - 114 = 0

=> w^2 - 25w + 114 = 0

we have x = [-b ± √(b^2 - 4ac)] / 2a

w = [-(-25) ± √((-25)^2 - 4(1)(114)))] / 2(1)

w = [25 ± √(625 - 456)] / 2

w = [25 ± √(169)]/2

w = [25 ± 13]/2

w = [25 + 13]/2 = 38/2 = 14

or

w = [25 - 13]/2 = 12/2 = 6

if width = 14, length = 25 - 14 = 11

then area = 14 x 11 = 154, this is incorrect answer

if width = 6, length = 25 - 6 = 19

then area = 6 x 19 = 114, this is correct answer

Haru recorded how long his bus ride to school took for `16` days.

Here are the values of the quartiles.

About how many rides would you expect to be less than `6.5` minutes long?

The number of **rides **that one would expect to be **less than** `6.5` minutes long is 4 rides.

To determine the **number **of rides, we will first begin by classifying the quartiles. There are 4 quartiles that each constitute 25% of the ride timing.

The number of rides that one would expect to be less than 6.5 minutes can be gotten by finding 25% of 16, the total days recorded. This is 1/4 * 16 = 4. So, the number of rides that will be less than 6.5 minutes will be 4 rides.

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Which data set has a variation, or mean absolute deviation, similar to the data

set in the given dot plot?

50 51 52 53 54 55 56 57 58 59 60 61

Ο Α.

OB.

O C.

D.

4612

15 17 19

0123

8 9 1011

55 57 59 61 63 65

Option C (15 17 19) has a similar mean **absolute** **deviation** to the data set in the given dot plot.

The informational collection in the given speck plot has a mean of roughly 55 and a **moderately** little scope of values, with most of the information bunched around the mean. An informational index with a comparable mean outright deviation would have a **comparative** degree of variety in the information values.

Out of the given choices, the informational index that has a variety like the given informational collection is choice C: 15 17 19. This informational collection has a **mean** of roughly 17 and a little scope of values, with most of the information bunched around the mean.

The mean outright deviation of this informational collection is around 1.63, which is like the mean outright deviation of the given informational collection. Choice A (50 51 52 53 54 55 56 57 58 59 60 61) has a bigger scope of values and a bigger mean outright deviation contrasted with the given informational **collection**.

Choice B (4612) and Choice D (8 9 1011 and 55 57 59 61 63 65) have altogether unique mean qualities and scopes of values, and consequently their mean outright deviations are not quite the same as the given informational collection.

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Which is an indicator of a false ID?a.raised letters on the faceb.ghost image of the photographc.bar code on the backsided.card is too thick
An experiment is performed to determine to determine the molar mass of a solid unknown monoprotic acid (HA) by titration with a standardized NaOH solution. A) What measurements must be made to determine the number of moles of NaOH used in the titration? B) Write a mathematical expression to be used in determining the number of moles used to reach the endpoint of the titration. C) How can you use the information in B) to determine the moles of acid, HA? D) To determine the molar mass of the acid what should be measured about the acid before the titration? E) Write the mathematical expression to calculate the molar mass of the acid. F) Draw the apparatus to be used in this titration indicating what is going to be in each part of the apparatus. G) If the original solid acid was not completely dry before the experiment, would the results be different? In which way? Explain. H) If the original procedure called for dissolving the acid in 25.0 mL , but 35.0 mL were accidentally used, how would the results be affected? Explain.
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Part 4. Watch the signer sign ASL statements. Fill in the blanks with missing pronouns orpossessive pronoun(s). (translation)1.__ don't like __ book.2. __ like __.3. What is __ name?4. Are __ excited to learn sign language?5. It's nice to meet __two of them__.
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why does mullett make this argument?
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10. Johnny completes the bicycle ride across the country with the final velocity of 10 m/s andacceleration 2 ms within 3s. Calculate the initial velocity.
which human activity has a negative impact on animal populations
I know I should know this but my teacher is really bad at teaching so Im still having trouble. Does anyone know this?? Directions: After reading both the American Declaration of Independence and French Declaration of the Rights of Man, fil in this Venn Diagram with similarities and differences that you noticed.Then after I do similarities and differences I need to do these questions 1. What is the purpose of each of these documents?2. Which aspects of the Enlightenment are reflected in these two documents?3. How does the Declaration of the Rights of Man define liberty? Do you agree or disagree with this definition?4. Using this definition, are Americans denied their liberty in any sense today?
What does knowing a while well mean? Context: But he knows a while well, and longs for the clang of the bell.Poem- Recess by Maria Hummel
What is the formula for a balloon?