Sherbrooke, Quebec is 210 miles from Boston, MA. A train leaves Boston at noon and arrives in Sherbrooke at 4:40 PM. On the return trip to Boston, the train travels 50.4 mph. How many times greater (or less) is the train’s speed on the return trip to Boston than on the trip to Sherbrooke?

The regular-size granola bar is 1 1/3 inches longer than the snack-size granola bar.

The regular-size granola bar has a volume of 4 cubic inches, while the snack-size bar has a volume of 3 cubic inches.

Since both bars have the same width and height, we can use the formula for the volume of a rectangular prism to find the length of each bar:

Regular-size bar: V = lwh = 4 cubic inches, w = 1 inch, h = 3/4 inch

l = V/wh = 4/(1 × 3/4) = 16/3 inches

Snack-size bar: V = lwh = 3 cubic inches, w = 1 inch, h = 3/4 inch

l = V/wh = 3/(1 × 3/4) = 4 inches

Therefore, the regular-size granola bar is (16/3 - 4) = 4/3 inches longer than the snack-size granola bar.

This can also be written as the mixed number 1 1/3 inches.

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Answer:  [tex]\frac{1}{3}[/tex]  (One third)

Step-by-step explanation: There are 3 numbers below 8. So 3 is the denominator as there are 3 different options to choose. There is only 1 six so, it is the numerator.

The Second Linearly Independent solution of the differential equation is:

y = c₁x⁷ + c₂(Ax¹⁰ + Bx⁻¹¹)

When solving a second-order linear differential equation of the form

x²y'' - 42y = 0, it is important to find two linearly independent solutions to fully describe the general solution. The first solution is given as y₁=x⁷.

To find the second linearly independent solution, we can use the method of reduction of order.

Let y₂ = u(x)y₁(x), where u(x) is a function to be determined.

Then we have y₂' = u(x)y₁'(x) + u'(x)y₁(x) and y₂'' = u(x)y₁''(x) + 2u'(x)y₁'(x) + u''(x)y₁(x).

Substituting y₂ and its derivatives into the original differential equation, we have:

x²(u(x)y₁''(x) + 2u'(x)y₁'(x) + u''(x)y₁(x)) - 42u(x)y₁(x) = 0

Dividing by x²y₁(x), we get:

u''(x)/u(x) + 2/x[u'(x)/u(x)] - 42/x² = 0

Let v(x) = u'(x)/u(x), then v'(x) = u''(x)/u(x) - (u'(x))²/(u(x))². Substituting v(x) into the above equation, we have:

v'(x) + 2/xv(x) - 42/x² = 0

This is now a first-order linear differential equation that can be solved using an integrating factor. Letting mu(x) = x², we have:

(x²v(x))' = 42

Solving for v(x), we get:

v(x) = 21/x + C/x²

where C is an arbitrary constant. Substituting back to u(x), we get:

u(x) = Ax³ + Bx⁻⁻¹⁸

where A and B are constants. Therefore, the second linearly independent solution is

y₂ = (Ax³ + Bx⁻¹⁸)x⁷ = Ax¹⁰ + Bx⁻¹¹

Hence, the general solution of the differential equation is:

y = c₁x⁷ + c₂(Ax¹⁰ + Bx⁻¹¹)

where c₁ and c₂ are arbitrary constants

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For the "regression-line",  Ŷ = -6 + 0.41(X), the predicted value,

(a) when X=25 is 4.25,

(b) when X=50 is 14.50,

(c) when X=75 is 24.75.

The "Regression-Line", is Ŷ = -6 + 0.41(X), we can make predictions for the value of Y (the dependent variable) for different values of X (the independent variable).

(a) To predict the value of "Y" when X = 25, we substitute 25 into the regression line equation:

Ŷ = -6 + 0.41(25)

Ŷ = -6 + 10.25

Ŷ = 4.25

So, the predicted value of Y when X = 25 is 4.25.

(b) To predict the value of Y when X = 50, we substitute 50 into the regression line equation:

Ŷ = -6 + 0.41(50)

Ŷ = -6 + 20.50

Ŷ = 14.50

So, the predicted value of Y when X = 50 is 14.50.

(c) To predict the value of Y when X = 75, we substitute 75 into the regression line equation:

Ŷ = -6 + 0.41(75)

Ŷ = -6 + 30.75

Ŷ = 24.75

So, the "predicted-value" of Y when X = 75 is 24.75.

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The correct answer is [tex]\dfrac{16\pi }{9}[/tex]

The area of a shaded region is [tex]\sf \dfrac{n\pi r^2}{360}[/tex]

So, applying the formula [tex]\sf \dfrac{n\pi r^2}{360}[/tex]

[tex]\sf =\dfrac{160\pi r^2}{360}=\dfrac{160\pi (2^2)}{360} =\dfrac{160\times\pi \times4}{360} =\dfrac{16\pi }{9}[/tex]

Hence the area of shaded region is [tex]\dfrac{16\pi }{9}[/tex]

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Since the p-value is less than 0.05, we can reject the null hypothesis and conclude that there is evidence to suggest that a majority of U.S. adults wear a helmet when they ride their bike.

The randomization distribution will show the proportion of people who wear helmets in each of the 1000 samples.

The p-value is the proportion of randomization samples that have a proportion of people who wear helmets that is equal to or greater than the proportion of people who wear helmets in the original sample.

In this case, the p-value is 0.04. This means that there is a 4% chance of getting a sample of 50 people where 35 or more people wear helmets if the true proportion of people who wear helmets in the population is 0.5.

Since the p-value is less than 0.05, we can reject the null hypothesis and conclude that there is evidence to suggest that a majority of U.S. adults wear a helmet when they ride their bike.

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The angle measure of LJK is 27 degrees

Following the triangle sum theorem, we have that the sum of the interior angles of a triangle is 180 degrees

Also, we need to know that the sum of angles on a straight line is 180, then, we have;

<JLK = 180 - <LKM = 180 - (8x - 19)

Then, substitute the value, we have that;

<JKL + < JLK + < KJL = 180

Then,

3x - 16 + (180 - (8x - 19)) + 2x + 15 = 180

expand the bracket, we have;

3x - 16 - 8x - 19 + 2x + 15 = 0

add the like terms

-3x + 18 = 0

collect the terms

-3x = -18

x = 6

Then, the angle LJK = 2x + 15 = 2(6) + 15 = 27 degrees

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14. The measure of angle ABC is 90⁰.

15. The measure of angle CED is 43⁰.

16. The measure of angle BDE is 47.5⁰.

17. The measure of angle CBD is 43⁰.

18. The measure of arc AD is 94⁰.

19. The measure of angle BCE is 47.5⁰.

20. The measure of angle ABD is 47⁰.

21.  The measure of arc ABC is 180⁰.

The measure of the missing angles is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

The measure of angle ABC is calculated as follows;

m∠ABC = 90⁰ (since line AC is the diameter)

The measure of angle CED is calculated as follows;

m∠CED = ¹/₂ (arc CD) (interior angle of intersecting secants)

m∠CED = ¹/₂ (86⁰) = 43⁰

The measure of angle BDE is calculated as follows;

m∠BDE= ¹/₂ (arc BE) (interior angle of intersecting secants)

m∠BDE = ¹/₂ (95⁰) = 47.5⁰

The measure of angle CBD is calculated as follows;

m∠CBD = ¹/₂ (arc CD) (interior angle of intersecting secants)

m∠CBD = ¹/₂ (86⁰) = 43⁰

The measure of arc AD is calculated as follows;

arc ABC = 180 (sum of angles in a semi circle)

arc ADC = 180 (sum of angles in a semi circle)

arc ADC = arc AD + arc CD

180 = AD + 86

AD = 94⁰

The measure of angle BCE is calculated as follows;

m∠BCE= ¹/₂ (arc BE) (interior angle of intersecting secants)

m∠BCE = ¹/₂ (95⁰) = 47.5⁰

The measure of angle ABD is calculated as follows;

m∠ABD = ¹/₂ (arc AD) (interior angle of intersecting secants)

m∠ABD = ¹/₂ (94⁰) = 47⁰

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Answer:

x = 5.7

Step-by-step explanation:

Use the pythagorean theorem, which says a^2+b^2 = c^2 where c is the hypotenuse (longest side of a right triangle, always opposite the 90 degree right angle).

7^2 + x^2 = 9^2

49 + x^2 = 81

x^2 = 32

now take the square root of both sides

x = 5.65685424949

Round to the nearest tenth.

x = 5.7

Answer:

5.7

Step-by-step explanation:

x^2 + 7^2 = 9^2

x^2 + 49 = 81

x^2 = 81 - 49

x^2 = 32

x = the square root of 32

x = 5.657

round to the nearest tenth

x = 5.7

a) The rate of slower train is 110 km/hr

b) The speed of faster train is 112 km/hr

Given data ,

When two objects are moving towards each other, their combined rate is equal to the sum of their individual speeds.

So, the rate of the slower train as x km/hr. Since the faster train is traveling 12 km/hr faster, its rate will be ( x + 12 ) km/hr.

The combined rate of the two trains is x + (x + 12) = 2x + 12 km/hr.

We know that the trains travel a total distance of 696 km and meet in 3 hours. Using the formula distance = speed × time, we can set up the following equation:

(2x + 12) × 3 = 696

Simplifying the equation:

6x + 36 = 696

Subtracting 36 from both sides:

6x = 660

Dividing both sides by 6:

x = 110

Hence , the rate of the slower train is 110 km/hr, and the rate of the faster train is 110 + 12 = 122 km/hr.

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John William will receive a total dividend of $43.70.

The value of John William's investment in Peixotto Media, including dividends, is $3,216.95.

a. John William owns a total of 125 + 312 = 437 shares in Peixotto Media. If the company is paying a cash dividend of 10 cents per share, then John William's total dividend income will be:

437 shares x $0.10 per share = $43.70

Therefore, John William will receive a total dividend of $43.70.

b. If John William owns 437 shares in Peixotto Media and the current stock price is $7.25 per share, then the value of his investment in the company (excluding dividends) is:

437 shares x $7.25 per share = $3,173.25

If we add the dividend income of $43.70 to this value, then the total value of John William's investment in Peixotto Media is:

$3,173.25 + $43.70 = $3,216.95

Therefore, the value of John William's investment in Peixotto Media, including dividends, is $3,216.95.

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The standard form (SF), center (C) and radius (R) are given as follow: (13) SF:  (x + 4)² + (y - 3)² = 50, Center: (-4, 3), R: √50 (14) SF: (x - 2)² + (y - 6)² = 169, C: (2, 6), R: 13 (15) SF: (x + 7)² + (y + 5)² = 1, C: (-7, -5), R: 1 (16) SF: (x - 8)² + y² = 225, C: (8,0), R: 15 (17) SF: (x - 12)² + (y - 2)² = 63, C: (12, 2), R: √63 (18) SF: (x - 5)² + (y + 4)² = 100 , C: (5, -4), R: 10

The general form of a circle is given as:

       (x - h)² + (y - k)² = r²

where:

        (h, k) represents the center of the circle

       r represents the radius.

Now we can use the above information to solve the following questions:

13. x² + y² + 8x - 6y - 25 = 0

Rearranging the equation:

x² + 8x + y² - 6y = 25

Completing the square for x terms:

(x² + 8x + 16) + y² - 6y = 25 + 16

Simplifying:

(x + 4)² + (y² - 6y) = 41

(x + 4)² + (y² - 6y + 9) = 41 + 9

(x + 4)² + (y - 3)² = 50

Center: (-4, 3)

Radius: √50

14. x² + y² - 4x - 12y - 129 = 0

Rearranging the equation:

x² - 4x + y² - 12y = 129

Completing the square for x terms:

(x² - 4x + 4) + y² - 12y = 129 + 4

Simplifying:

(x - 2)² + (y² - 12y) = 133

(x - 2)² + (y² - 12y + 36) = 133 + 36

(x - 2)² + (y - 6)² = 169

Center: (2, 6)

Radius: 13

15. x² + y² + 14x + 10y + 73 = 0

Rearranging the equation:

x² + 14x + y² + 10y = -73

Completing the square for x terms:

(x² + 14x + 49) + y² + 10y = -73 + 49

Simplifying:

(x + 7)² + (y² + 10y) = -24

(x + 7)² + (y² + 10y + 25) = -24 + 25

(x + 7)² + (y + 5)² = 1

Center: (-7, -5)

Radius: 1

16. x² + y² - 16x - 161 = 0

Rearranging the equation:

x² - 16x + y² = 161

Completing the square for x terms:

(x² - 16x + 64) + y² = 161 + 64

Simplifying:

(x - 8)² + y² = 225

Center: (8, 0)

Radius: 15

17. x² + y² = 24x + 4y - 85

Rearranging the equation:

x² - 24x + y² - 4y = -85

Completing the square for x and y terms:

(x² - 24x + 144) + (y² - 4y + 4) = -85 + 144 + 4

Simplifying:

(x - 12)² + (y - 2)² = 63

Center: (12, 2)

Radius: √63

18. x² + y² - 9x + 2y = x - 6y + 59

Rearranging the equation:

x² - 9x - x + y² + 2y + 6y = 59

Combining like terms:

x² - 10x + y² + 8y = 59

Completing the square for x and y terms:

(x² - 10x + 25) + (y² + 8y + 16) = 59 + 25 + 16

Simplifying:

(x - 5)² + (y + 4)² = 100

Center: (5, -4)

Radius: 10

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The required angles (corresponding, vertical and alternate) in relation to the Parallel lines are attached accordingly.

Parallel lines are coplanar infinite straight lines that do not cross at any point in geometry. Parallel planes are planes that never intersect in the same three-dimensional space.

When two parallel lines cross by any other line (i.e. the transversal), corresponding angles are generated in matching corners or corresponding corners with the transversal.

When two parallel lines are sliced by a transversal, the resulting alternate exterior angles are congruent, according to the Alternate Exterior Angles Theorem.

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It would cost [tex]$8,100[/tex] to rent the safety deposit box for 15 years at a rate of [tex]$45[/tex] per month.

The total cost of renting a safety deposit box for 15 years, we need to first determine the total number of months in 15 years.

Since there are 12 months in a year, the total number of months in 15 years is:

15 years x 12 months/year = 180 months

So, if the safety deposit box costs [tex]$45[/tex] per month to rent, then the total cost of renting the box for 15 years would be:

180 months x [tex]$45[/tex]/month = [tex]$8,100[/tex]

We must first ascertain the entire number of months in 15 years in order to compute the total cost of renting a safety deposit box for 15 years.

Since there are 12 months in a year, there are a total of 180 months in 15 years: 15 years multiplied by 12 months per year.

In this case, if the monthly rental fee for the safety deposit box is [tex]$45[/tex] and the rental period is 15 years, the total cost would be calculated

180 months x [tex]$45[/tex]/month = [tex]$8,100[/tex]

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ΔAOB will be neither isosceles nor a right angled triangle.

Given,

In Parallelogram ABCD diagonals bisect at the point O.

Parallelogram and its properties:

Hence from the above properties it is clear that the triangles formed will neither be isosceles nor a right angled triangle.

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The arrangement of the side length of the triangles from the least to the greatest is DF <  DE < EG <  EF <  GF.

The arrangement of the lengths of the triangle from the least to the greatest is determined as follows;

The size of the length of a triangle increases as the size of the angle opposite to the length increases.

That is the greater the size of the angle opposite the side length of a triangle, the greater the size of the side length of the triangle.

From the given diagram, we can arrange the size of the side length of the triangle as follows;

angle D = 180 - (57 + 58 )

angle D = 65⁰ (this is opposite to length EF)

So the arrangement of the side length of the triangles are;

length DF < Length DE < length EG < length EF < length GF

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For calculating the percentage of discount, we can use the formula:

Percentage of discount = (Discount amount / Original price) * 100

We have given that the discounted price is Birr 51,000 and the discount amount is Birr 9,000,we need to find the original price.

Original price = Discounted price + Discount amount

Original price = 51,000 + 9,000 = 60,000 Birr

Now, we can calculate the percentage of discount:

Percentage of discount = (9,000 / 60,000) * 100 = 15%

Hence, the percentage of discount for the four-door model is 15%.

Asia is larger than North America by approximately 8.0 x 10⁶ square miles.

The difference in area between Asia and North America is calculated as follows;

Difference in area = Area of Asia - Area of North America

Difference in area  = 1.74 x 10⁷ mi² - 9.4 x 10⁶ mi²

The difference in the area between Asia and North America is calculated as

= 1.74 x 10⁷ mi² - 9.4 x 10⁶ mi²

= 8.0 x 10⁶ mi²

Thus, The difference in area between Asia and North America is 8.0 x 10⁶ mi².

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The circumference of the circle whose diameter is 2x + 2 is (44x + 44)/7

The formula for the circumference of a circle is 2πr

r = radius of the circle

Diameter of circle = radius  of circle × 2

The radius of the circle = ( diameter of the circle ) / 2

The radius of circle = (2x+2)/2

Taking 2 commons from 2x + 2

we get 2( x + 1 )

The radius of circle = 2(x+1)/2

The radius of the circle = x + 1

Circumference =  2 × 22/7 × (x+1)

Circumference = 44(x+1)/7

Circumference = (44x + 44)/7

Or in the form of π circumference can be written as (2x + 2)π

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Answer:

this is what i found for ya:3

Step-by-step explanation:

In mathematics, specifically abstract algebra, an integral domain is a nonzero commutative ring in which the product of any two nonzero elements is nonzero. ... Noncommutative integral domains are sometimes admitted.

Answer:

That's the meaning of of integers in math and algebra: Whole numbers. No fractions allowed! Integers are counting numbers, and they include 0. ... In other words, integers can be negative, but they can't be fractional. Any number with a fraction – and that includes decimal fractions – is not an integer.

Step-by-step explanation:

The value of angle LAF in the intersecting chords is determined as  104⁰.

The value of angle LAF is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

Also this theory states that arc angles of intersecting secants at the center of the circle is equal to the angle formed at the center of the circle by the two intersecting chords.

m∠LAF = ¹/₂ (arc LF + arc YS)

From the diagram, we have arc LF = 160⁰ and YS = 48⁰

m∠LAF = ¹/₂ (160 + 48)

m∠LAF = 104⁰

Thus, the value of angle LAF is calculated by applying intersecting chord theorem.

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The solution to the function h(x) = 2x² - x - 1 is given by the graph attached which is a positive quadratic graph.

A quadratic graph represents a quadratic equation in the form:

   y = ax² + bx + c,

where a, b, and c are constants.

The graph of a quadratic equation is a curve called a parabola.

The general shape of a quadratic graph depends on the value of the coefficient "a." If "a" is positive, the graph opens upward, and if "a" is negative, the graph opens downward.

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Answer:9/41

SOH = opposite over hypotenuse

Step-by-step explanation:

The lines intersect at only one specific point (-5, 9)

The correct answer is: There is one unique solution (-5, 9).

When two straight-line equations intersect at a point, it means that there is one unique solution to the system of equations. In this case, the point of intersection is (-5, 9), which indicates that the system has a single solution. This means that there is a unique set of values for the variables that satisfy both equations simultaneously.

If the system had no solution, it would mean that the two lines are parallel and will never intersect. However, since the lines in the given system intersect at (-5, 9), it implies that there is a solution.

Alternatively, if the system had infinitely many solutions, it would mean that the two equations represent the same line. In this case, the lines intersect at every point along their entire length, resulting in an infinite number of solutions. However, the fact that the lines intersect at only one specific point (-5, 9) indicates that there is one unique solution to the system of equations.

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The values are given as:

a. Mean = 19

Median = 20

Mode = 22

Standard deviation = 7.2

Range  = 24

b. Mean = 75

Median  =  80

Mode  = 90

Standard deviation  = 16

Range = 100

The three measures of central tendency include;

The measures of dispersions are;

From the information given, if 4 is added to all the measures, we get;

Mean = 15 + 4 = 19

Median = 16 + 4 = 20

Mode = 18 + 4 = 22

Standard deviation = 3.2 + 4 = 7.2

Range = 20 + 4 = 24

If the values are multiplied by 5

Mean = 15(5) = 75

Median = 16(5) =  80

Mode = 18(5) = 90

Standard deviation = 3.2(5) = 16

Range = 20(5) = 100

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The best estimate of the number of centimeters (cm) in 1 yard is; Yard ⇒ feet ⇒ inches ⇒ centimeters

If we have to determine the number of centimeters in 1 yard, the best way is;

Here we convert  yard to feet = 1 yard = 3 ft

Then, we convert ft to inches = 1 ft = 12 inches

                                                  3 ft = 3 × 12 = 36 inches

Now, we convert inches to centimeters = 1 inch = 2.54 cm

                                            36 inches = 36 × 2.54 = 91.44 cm

Therefore, the best path is Yard to feet to inches to centimeters

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The factored form of the polynomial [tex]x^4 - x^3 - 5x^2 - x - 6[/tex] is:

[tex](x - 2)(x^3 + x^2 - 3x - 7)[/tex]

We have,

To factor the polynomial [tex]x^4 - x^3 - 5x^2 - x - 6,[/tex]

we can look for its roots and express it as a product of linear factors.

First, let's check if there are any rational roots using the rational root theorem.

The possible rational roots can be found by taking the factors of the constant term (-6) and dividing them by the factors of the leading coefficient (1).

The factors of -6 are: ±1, ±2, ±3, ±6

The factors of 1 are: ±1

The possible rational roots are: ±1, ±2, ±3, ±6

By testing these values, we find that x = 2 is a root of the polynomial.

Using synthetic division, we can divide the polynomial by (x - 2) to find the quotient.

The quotient is [tex]x^3 + x^2 - 3x - 7.[/tex]

Now, we can continue factoring the quotient.

The polynomial x³ + x² - 3x - 7 does not have any rational roots.

We can try factoring it by grouping or using other factoring methods, but in this case, it does not factor nicely into linear factors.

Therefore,

The factored form of the polynomial [tex]x^4 - x^3 - 5x^2 - x - 6[/tex] is:

[tex](x - 2)(x^3 + x^2 - 3x - 7)[/tex]

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Answer:

7/100 w postaci dziesiętnej to 0,07.

3 5/10 w postaci dziesiętnej to 3,5.

Answer:

CaCL2 + KL → KCL + CaL2

Step-by-step explanation:

To balance a chemical equation, enter an equation of a chemical reaction and press the Balance button. The balanced equation will appear above.

Use uppercase for the first character in the element and lowercase for the second character. Examples: Fe, Au, Co, Br, C, O, N, F.

Ionic charges are not yet supported and will be ignored.

Replace immutable groups in compounds to avoid ambiguity. For example, C6H5C2H5 + O2 = C6H5OH + CO2 + H2O will not be balanced, but XC2H5 + O2 = XOH + CO2 + H2O will.

Compound states [like (s) (aq) or (g)] are not required.

You can use parenthesis () or brackets [].Li + Ag = Li + Ag

KOH + KMnO4 + H2SO4 = KOH + KMnO4 + H2SO4

C6H6O + KOH = C6H7KO2

CUO + HNO3 = CU(NO3)2 + H2O

C4H6O4 + KOH = C2K2O4 + C2H6O2

Zn + Sr(OH)2 = Sr + Zn(OH)2

Al + Pb(No3)2 = Al(No3)3 + Pb

HNO3 + Zn = Zn(NO3)2 + H2

ZnO + CH3COOH + H2O + Al2O3 = Zn(CH3COO)2*2H2O + Al2O3

BeO + Zn(OH)2 = Be(OH)2 + ZnO

CH3COOK + CH3Br = CH3COOCH3 + KBr

Pb(NO3)2 + HBr = PbBr2 + NHO3