Let G be a group and a ∈ G. Show that o(a) = o(a-1)
(this should include both the finite and infinite order cases).

Answer:

1.5 inches of stell will make 1 spring

Step-by-step explanation:

If 450 inches of steel are used to make 300 springs, we can simply divide the inces by the spring count to obtain a unit of inches/(1 spring).

(450 inches of steel)/(300 springs) = (1.5 inches of steel)/)1 spring)

6% of the students surveyed said that their favorite music is Country music. This may be due to its classic sound, relatable lyrics, and lifestyle connection.

Number is an abstract concept used to describe a quantity, or amount, of something. It is used in mathematics to quantify things, such as in counting, measuring, and representing data. Numbers are used to describe the size, quantity, or position of objects or people in space or time. They are also used to classify, classify, and identify items in a variety of fields. Numbers can be used to represent ideas and concepts, such as in equations, formulas, and other mathematical operations.

Six students represents 6 out of 100 students, so the percent of students who said that their favorite music is Country music is 6%. Rap, Pop, and Latin music each represent 12% of the students, for a total of 36%. The remaining 64% of the students may have chosen other genres, or did not answer the question.

The popularity of Country music among the students may have several explanations. First, Country music is often considered to be a classic genre, and the students may have grown up with the music and developed an appreciation for it. Second, many Country music songs have lyrics that are easy to relate to, which can resonate with the students. Finally, Country music is often associated with a certain lifestyle, and the students may be drawn to its image.

In conclusion, 6% of the students surveyed said that their favorite music is Country music. This may be due to its classic sound, relatable lyrics, and lifestyle connection.

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The after-tax cost of the tennis racket is $101.70.

To calculate the after-tax cost of the tennis racket, we first need to find the sale price of the racket, then add on the HST.

Step 1: Find the sale price of the racket. To do this, we need to find 25% of $120, then subtract that amount from the original price.

25% of $120 = 0.25 × $120 = $30

Sale price = $120 - $30 = $90

Step 2: Add on the HST. To do this, we need to find 13% of the sale price, then add that amount to the sale price.

13% of $90 = 0.13 × $90 = $11.70

After-tax cost = $90 + $11.70 = $101.70

Therefore, the after-tax cost of the tennis racket is $101.70.

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Answer:

1: x=2

Step-by-step explanation:

Do you know the pythagorean theorem?

a2 + b2 = c2

1) We will square all the sides:

2[tex]\sqrt{2}[/tex] -squared- 2(4)=8

x squared= [tex]x^{2}[/tex]

[tex]x^{2} +x^{2} =2x^{2} =8[/tex]

[tex]2x^{2} =8[/tex]

[tex]x^{2} =4[/tex]

x=2

2: [tex]\sqrt{3}[/tex] we will square to make 3

same with x to [tex]x^{2}[/tex]

and y to [tex]y^{2}[/tex]

3+[tex]x^{2}[/tex]=[tex]y^{2}[/tex]

Since the ratio of the sides is 1: 2: 3

Imma continue typing later srry gtg

Answer: From the passage, we can conclude that Tuan has had a strenuous basketball workout and has also done an hour's worth of weight-training exercises, which suggests that he has had a physically demanding day. Additionally, it is mentioned that he is experiencing some tiredness towards the end of the day, which is not uncommon after such an active day. Therefore, we can conclude that Tuan is experiencing physical fatigue or tiredness due to his physical activity.

Step-by-step explanation:

A = 5,700,000 bacteria

The equation for the amount of bacteria present after one hour is A = 5,000,000 + 5,000,000(0.14%) bacteria. After factoring, the equation is A = 5,000,000(1 + 0.14%) bacteria. Using the given percent, the equation is A = 5,000,000(1 + 0.0014) bacteria. Finally, the answer is A = 5,700,000 bacteria.

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Answer:

He bought more turkey

Step-by-step explanation:

Simple way is to check how close both numbers are to a whole number or convert to fraction

0.75 =75/100

0.57= 57/100

The result of multiplying (x+5)^(2) using the rule for the square of a binomial is x^(2) + 10x + 25.

To multiply using the rule for the square of a binomial, we can use the formula (a+b)^(2) = a^(2) + 2ab + b^(2). In this case, a = x and b = 5, so we can plug these values into the formula:

(x+5)^(2) = (x)^(2) + 2(x)(5) + (5)^(2)

Simplifying the right side of the equation gives us:

(x+5)^(2) = x^(2) + 10x + 25

Therefore, the result of multiplying (x+5)^(2) using the rule for the square of a binomial is x^(2) + 10x + 25.

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2. The exact value of sin (185° - 65°) is (√3/2)(cos (65°)) - (1/2)(sin (65°)).

3. The exact value of tan 255° is (1/√3 - √3)/2.

The sine function has a range of values between -1 and 1, and it is a periodic function that repeats every 2π radians or 360 degrees.

We can use the difference identity for sine to find the exact value of sin (185° - 65°):

sin (185° - 65°) = sin 185° cos 65° - cos 185° sin 65°

Since sin (180° + x) = -sin x and cos (180° + x) = -cos x to simplify the expression:

sin (185° - 65°) = sin (120°) cos (65°) + cos (120°) sin (65°)

= (√3/2)(cos (65°)) + (-1/2)(sin (65°))

= (√3/2)(cos (65°)) - (1/2)(sin (65°))

Therefore, the exact value of sin (185° - 65°) is (√3/2)(cos (65°)) - (1/2)(sin (65°)).

Here,

tan 255° = tan (225° + 30°)

Using the tangent sum identity, we get:

tan (225° + 30°) = (tan 225° + tan 30°)/(1 - tan 225° tan 30°)

Since tan 225° = tan (225° - 180°) = tan (-45°) = -1 and tan 30° = (√3)/3, we can substitute these values:

tan 255° = (-1 + (√3)/3)/(1 + 1/√3)

Simplifying the denominator by rationalizing the denominator, we get:

tan 255° = (-1 + (√3)/3)/(√3 + 1)

Multiplying the numerator and denominator by (√3 - 1), we get:

tan 255° = [(-1 + (√3)/3)(√3 - 1)]/[(√3 + 1)(√3 - 1)]

= [(√3 - 1 - 1 + 1/√3)]/(2)

= [√3 - 2 + 1/√3]/2

= (1/√3 - √3)/2

Therefore, the exact value of tan 255° is (1/√3 - √3)/2.

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John owes his mom R1041.6 after 2 years

To find out how much John owes his mom after 2 years, we need to calculate the interest on the loan. The formula for calculating interest is I = Prt, where I is the interest, P is the principal, r is the annual interest rate, and t is the time in years.

In this case, the principal is R840, the annual interest rate is 12% (or 0.12), and the time is 2 years. Plugging these values into the formula, we get:

I = (R840)(0.12)(2) = R201.6

So the interest on the loan is R201.6.

To find out the total amount John owes his mom, we need to add the interest to the principal:

Total amount owed = Principal + Interest = R840 + R201.6 = R1041.6

Therefore, John owes his mom R1041.6 after 2 years.

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The volume of the rectangle is 120 cubic yards

It is important to note that the formula for calculating the volume of a rectangle is expressed as;

V = lwh

Given that the parameters are;

From the information given, we that;

Area = 15 square yards

That is, length and width

Then,

Volume = 15(8)

multiply the values

Volume = 120 cubic yards

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The sum of A, B, and C is : A = [1, 3], B = [3, 11], C = [13, 4], ABC = [1+3, 3+11, 13+4] = [4, 14, 17]. Therefore, ABC is equal to [4, 14, 17].

To explain in more detail, A represents the set of numbers [1, 3], B the set of numbers [3, 11], and C the set of numbers [13, 4]. Adding all the elements of each set together gives the sum of A, B, and C as [4, 14, 17]. Adding along with mentioning the values together by putting commas in between them is a way to represent the values.

The representation of  set of numbers is always crucial in determining the value of entire set. In computation we add and then multiply the values given inside the set. In order to get a computed value of the set.

A = [1 3), B = 3 11, and c = 13 4. ABC can be computed by the given formula: ABC = AB + BCAB = 1 * 3 + 3 * 4 + 13 * 0 = 3 + 12 + 0 = 15 BC = 3 * 11 + 4 * 1 + 0 * 13 = 33 + 4 + 0 = 37. So, ABC = AB + BC = 15 + 37 = 52. Therefore, the value of ABC is 52.

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The two variables move in opposite directions.

For a relationship that has a negative slope, there is an inverse relationship between the independent and dependent variables. This means that as the value of the independent variable increases, the value of the dependent variable decreases, and vice versa. In other words, the two variables move in opposite directions.

For example, suppose we have a dataset that shows the relationship between the number of hours of study and the score on a test.

If the slope of the line of best fit is negative, this means that as the number of hours of study increases, the score on the test decreases. This negative relationship indicates that the more time a student spends studying, the lower their score on the test is likely to be.

It is important to note that a negative slope does not necessarily imply a causal relationship between the variables. There may be other factors that affect the relationship between the variables, and further analysis is needed to determine the nature of the relationship.

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a) The sales of the cooking club will be $80, while the expenditures will be $80 when the number of cakes sold will cover their expenditures (break-even point).

b) The number of cakes that the members of the cooking club will sell at the street fair at this point (break-even point) is 10.

The break-even point is the sales units that will equate to the expenditures.

At the break-even point, there is no profit or loss because the total sales revenue equals the total costs (fixed and variable).

The selling price per unit = $8

The fixed cost for a booth at the fair = $20

The variable cost price per unit = $6

Contribution margin per unit = $2 ($8 - $6)

The break-even point in units = Fixed Cost/Contribution margin per unit

= 10 units ($20/$2)

Total sales revenue at the break-even point = $80 ($8 x 10)

Total variable cost = $60 ($6 x 10)

Total fixed and variable costs = $80 ($20 + $60)

Thus, at the break-even point, the cooking club will have sold 10 units making revenue to equal the total costs.

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Answer:

8183

Step-by-step explanation:

Plug in calculator

500(1+0.15)^20

Answer:

Для применения метода деления отрезка пополам нужно использовать тот факт, что функция x^3 + 2x + 4 непрерывна на всей числовой оси. Кроме того, нужно заметить, что функция монотонно возрастает на всей числовой оси, так как ее производная 3x^2 + 2 всегда положительна.

Начнем с интервала [a, b], где a = -2 и b = 0. Тогда значение функции в точке a равно -4, а значение функции в точке b равно 4. Значит, на этом интервале есть хотя бы один корень уравнения x^3 + 2x + 4 = 0.

Посередине интервала [a, b] находим точку c = (a + b) / 2 = -1. Значение функции в точке c равно 1, то есть на интервале [c, b] нет корней уравнения.

Затем выбираем интервал [a, c] и повторяем процесс. Находим точку d = (a + c) / 2 = -1.5. Значение функции в точке d равно -1.375, то есть на интервале [d, c] есть корень уравнения.

Продолжаем делить отрезки пополам и находить корни, пока не достигнем требуемой точности. Например, следующая точка будет e = (d + c) / 2 = -1.25. Значение функции в точке e равно 0.234375, то есть на интервале [e, c] есть корень уравнения.

Таким образом, метод деления отрезка пополам дает корень уравнения x^3 + 2x + 4 = 0 на интервале [-1.25, -1.125], который можно записать в виде x ≈ -1.1875 (с точностью до Ɛ=0,01).

The two supplementary angles where one angle measures 6° more than the other one are 87°  and 93°.

Two angles are said to be supplementary if the sum of the two angles is 180 degrees. One way to avoid confusion in these definitions is to note that s comes after c in the alphabet and 180 is greater than 90. 

Solution according to the information in the question:

Let, "x" be one of the two supplementary angles

then, the other angle will be "x+6" according to the question.

As we know sum of two supplementary angles is 180 degrees, so

x +(x+6)=180

⇒2x + 6 = 180

⇒2x = 180 - 6

⇒2x = 174

⇒x = 174/2

⇒x = 87°

∴ The other angle = x +6 = 87 +6 = 93°

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The measure of the angle being discussed is 84° and the measure of its supplementary angle is 96°. This is because the measure of the angle being discussed is 6° more than the measure of its supplementary angle.

A supplementary angle is two angles whose sum is 180 degrees. These angles do not have to be adjacent or even in the same plane, but their sum must always equal 180 degrees.

If the angle being discussed is 6° more than the measure of its supplementary angle, then the measure of the angle being discussed is 84° (180° - 6° = 84°). Therefore, the measure of the angle being discussed is 84° and the measure of its supplementary angle is 180° - 84° = 96°.

To further explain the relationship between the two angles, the supplementary angle is the measure of the angle that completes the 180° angle when combined with the angle being discussed. This means that the measure of the supplementary angle is the 180° minus the measure of the angle being discussed. In this case, the measure of the angle being discussed is 84° and thus, the measure of its supplementary angle is 180° - 84° = 96°.

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The concrete cost for the pillar was $37,879.52.

Velocity is a quantity that indicates how quickly and in which direction a point is moving. A point always moves in a direction that is tangent to its path; for example, a circular path's direction at any instant is perpendicular to a line connecting the point to the circle's centre (a radius). The magnitude of the velocity (or speed) is the rate at which the point moves along its path in time.

If a point moves a certain distance along its path in a given time interval, its average speed is equal to the distance moved divided by the time taken. A train travelling 100 kilometres in two hours, for example, has an average speed of 50 kilometres per hour.

The cylinder's radius is equal to its diameter divided in half, or 12/2, or 6 metres.

The cylinder's volume is determined by:

[tex]V = pi * r^2 * h[/tex]

[tex]V = 3.14 * 6^2 * 4[/tex]

V equals 452,16 cubic metres

The price of the concrete is $82 per cubic metre, making the overall price:

$82 * 452.16 = $37,879.52

Hence, the pillar's concrete expense came to $37,879.52.

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The derivative of f(x) = (1 + x4 - 1/x)5/3 using the chain rule is (5/3)(1 + x4 - 1/x)2/3(4x3 + 1/x2).

To find the derivative of f(x) = (1 + x^4 - 1/x)^5/3 using the chain rule, we need to use the following steps:

1. Identify the inner function and the outer function. In this case, the inner function is 1 + x^4 - 1/x and the outer function is ( )^5/3.
2. Find the derivative of the outer function with respect to the inner function. This is done by using the power rule: (5/3)( )^2/3.
3. Find the derivative of the inner function with respect to x. This is done by using the power rule and the quotient rule: 4x^3 + 1/x^2.
4. Multiply the derivative of the outer function and the derivative of the inner function together to get the derivative of the original function: (5/3)(1 + x^4 - 1/x)^2/3(4x^3 + 1/x^2).

Therefore, the derivative of f(x) = (1 + x^4 - 1/x)^5/3 using the chain rule is (5/3)(1 + x^4 - 1/x)^2/3(4x^3 + 1/x^2).

Here is the answer formatted in HTML:

To find the derivative of f(x) = (1 + x4 - 1/x)5/3 using the chain rule, we need to use the following steps:

Therefore, the derivative of f(x) = (1 + x4 - 1/x)5/3 using the chain rule is (5/3)(1 + x4 - 1/x)2/3(4x3 + 1/x2).

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The value of the angles in the parallel line is 34 degrees.

When parallel are cut by a transversal line, angle relationships are formed such as corresponding angle, alternate interior angles, alternate exterior angles, linear angles, vertically opposite angles etc.

Therefore, the angle 5 can be found using the angle relationship.

Hence,

m∠1 ≅ m∠5(corresponding angles)

Corresponding angles are congruent to each other.

Therefore,

m∠5 = 34 degrees

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The angle opposite to the side length c is given as follows:

θ = 53º.

The Law of Cosines is a trigonometric formula that relates the lengths of the sides of a triangle to the cosine of one of its angles. It is also known as the Cosine Rule.

The Law of Cosines states that for any triangle with sides a, b, and c and angle C opposite to side c, the following equation holds true:

c^2 = a^2 + b^2 - 2ab cos(C)

The parameters for this problem are given as follows:

a = 122.5, b = 58.2, c = 164.5.

Hence the measure of angle θ is given as follows:

c^2 = a^2 + b^2 - 2ab cos(θ)

164.5² = 122.5² + 58.2² - 2 x 122.5 x 58.2 x cos(θ)

14259cos(θ) = 8666.76

cos(θ) = 8666.76/14259

θ = arccos(8666.76/14259)

θ = 53º.

The angle is opposite to the side length C.

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The value of the expression a + 4 when a = 7 is 11.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

We are given that;

Function= a+4

Now,

By algebra

If a = 7, then we can substitute this value into the expression a + 4 to get:

=a + 4

= 7 + 4

= 11

Therefore, by algebra the answer will be 11.

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The complete question is;

Evaluate the expression a+4 when a=7?

According to the triangle's "angle sum property," a triangle's interior angles add up to 180°.

Take a triangle ABC; to demonstrate the triangle's above-mentioned, angle sum property draw a line PQ parallel to its BC side.

PAB + BAC + QAC Equals 180 degrees.

(1)

PQ||BC and AB, AC, and AB, AC are transversals, therefore QAC = ACB (a pair of alternate angle)

Moreover, PAB = CBA (a pair of alternate angle)

When QAC and PAB's values are substituted in equation (1), ACB + BAC + CBA = 180°.

As a result, a triangle's interior angles sum up to 180°.

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

b because i did it

The comparison of textbooks is History textbooks > Science textbooks. The mass of the stacks of textbook differ by 0.15 kilograms.

Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.

a × b means that a is added to itself b times or b is added to itself a times.

Given that,

Mass of science textbook = 1.15 kilograms

Mass of 4 science textbooks = 4 × 1.15 kilograms

                                                = 4.6 kilograms

Mass of a history textbook = 950 grams = 0.95 kilograms

Mass of 5 history textbooks = 5 × 0.95 kilograms

                                              = 4.75 kilograms

Part A :

History textbooks > Science textbooks

Part B :

Mass of History textbooks - Mass of science textbooks = 4.75 - 4.6

                                                                                            = 0.15 kilograms

Hence the history textbooks are 0.15 kilograms more.

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It is difficult to predict the future of financial services and whether or not we will reach full decentralization. However, there are several factors to consider when analyzing the potential for full decentralization of financial services.

First, it is important to consider the role of government regulation in the financial sector. Currently, banks and other financial institutions are heavily regulated in order to protect consumers and ensure the stability of the financial system. It is unclear how government regulation would fit into a fully decentralized financial system, as there would be no central authority to oversee and regulate transactions.

Second, while cryptocurrencies and other decentralized financial services offer many benefits, there are also potential risks and drawbacks. For example, the lack of regulation and oversight can make it easier for fraud and other illegal activities to occur. Additionally, the volatility of cryptocurrencies can make them a risky investment for consumers.

Finally, it is important to consider the role of trust in the financial system. Banks and other financial institutions have built up trust with consumers over time, and it may be difficult for a fully decentralized financial system to achieve the same level of trust without some form of central oversight.

In conclusion, while the decentralization of financial services offers many benefits, there are also potential risks and challenges that must be considered. It is difficult to predict if we will ever reach full decentralization of financial services, but it is clear that there are several factors that will play a role in determining the future of the financial system.

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The supplied statement indicates that there is a mistake in the D set of conditional probabilities.

Students do not "lose their inherent liberty of speech or thought now at schoolhouse gate," according to a 1969 Supreme Court decision. This also holds true for other essential rights.

Given collection of related objects

A (6, 8) (-6, 8)

B (1, 1) (-1, 1)

C (0, 3) (0, 3)

D (3, 2) (3, -2)

Finding the set with an erroneous refraction to across y axis is necessary.

The value of y mostly in point (x,y) will remain the same when a point is mirrored across the y axis, or the sign of the x value will be altered to the opposite. For example, with a point (x,y), the reflection across the y axis will also be (-x,y)

Point A: Y is the same, but the symbol of x is now the opposite.

Point B: The y is the same, but the sign of the x has been altered to the opposite.

Point C: y and x are both zero.

Point D-y is not the same, and the sign of x has not been altered to the opposite.

Hence, there is a mistake in set D.

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1... The coefficient of correlation between X and Y is 0.87, indicating that the linear relationship between the variables is close.

2.... The forecasted sales volume is 410.5 + C thousand Euro.

1) To calculate the correlation coefficient and make conclusions about the closeness of the linear relationship, you can use the formula for the coefficient of correlation (r): r = (∑XiYi - n*Xm*Ym) / √((∑Xi2 - n*Xm2) * (∑Yi2 - n*Ym2)), where n is the number of observations (10 in this case), Xm is the mean of X (24.9 in this case), and Ym is the mean of Y (150 in this case). Calculating, we get: r = (39423 - 10*24.9*150) / √((6557 - 10*24.92) * (237366 - 10*1502)) = 0.87.

2) To find the linear regression from variable Y to the X, you can use the formula for the coefficient of determination (b): b = (∑XiYi - n*Xm*Ym) / (∑Xi2 - n*Xm2). Calculating, we get: b = (39423 - 10*24.9*150) / (6557 - 10*24.92) = 8.21. Therefore, the linear regression equation is Y = 8.21X + C. To forecast the sales volume if the investment volume is planned to be 50 thousand Euro, substitute 50 in the equation and calculate: Y = 8.21*50 + C = 410.5 + C.  

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a) The equation that can be used to determine the total cost, y, for a tickets ordered in a transaction is y = 15.50x + 2.25

b) The number of movie tickets sold is x = 10 tickets

Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.

It displays the similarity of the connections between the phrases on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are examples of the parts of an equation. When creating an equation, the "=" symbol and terms on both sides are necessary.

Given data ,

Let the total cost of the movie be represented as y

Let the number of tickets sold be x

Now , the cost of one movie ticket = $ 15.50

And , the cost of x tickets = $ 15.50x

The cost of the transaction = $ 2.25

So , the total cost y = cost of x tickets + cost of the transaction

On simplifying the equation , we get

y = 15.50x + 2.25   be equation (1)

b)

Let the number of tickets be x

Now , the total cost of the transaction is y = $ 157.25

So , y = 15.50x + 2.25

On simplifying , we get

157.25 = 15.50x + 2.25

Subtracting 2.25 on both sides , we get

15.50x = 155

Divide by 15.5 on both sides , we get

x = 10 tickets

Hence , the number of tickets sold is 10 tickets

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The complete question is attached below :

Part A

Which equation can be used to determine the total cost, y, for a tickets ordered in a transaction?

O y = 2.25x + 15.50

O y = 15.50x +2.25

x = 2.25y + 15.50

O = 15.50y +2.25

Part B

If the total cost of a transaction is $157.25, how many movie tickets were ordered?