Alexandra and Maris are playing a game where they guess how many sides the regular polygon the other is holding has. Alexandra says her regular polygon has exactly 12 lines of symmetry. Maris says her regular polygon has an angle of rotational symmetry of 24°. How many sides does each regular polygon have?

Complete question :

Formulate the hypothesis that can be used to test for a difference between the population mean minutes late for delayed flights by these two airlines. (Let μ1 = population mean minutes late for delayed Company A flights and μ2 = population mean minutes late for delayed Company B flights.)

(b) What is the sample mean number of minutes late for delayed flights for each of these two airlines?

(c) Calculate the test statistic. (Round your answer to three decimal places.)

What is the p-value? (Round your answer to four decimal places.)

Answers:

H0: μ1 − μ2 = 0

H1: μ1 − μ2 ≠ 0

Test statistic = - 0.314

Pvalue = 0.7550

Step-by-step explanation:

Mean, xbar = Σx / n

Standard deviation, s = √(Σ(x-xbar) / n-1)

Company A :

Sample size, n = 25

Mean, x1 = 50.6

Standard deviation, s1 = 26.57

Company B :

Mean, x2 = 52.82

Sample size, n2 = 20

Standard deviation, s2 = 20.02

Mean, xbar = Σx / n

Standard deviation, s = √(Σ(x-xbar) / n-1)

Company A :

Sample size, n = 25

Mean, x1 = 50.6

Standard deviation, s1 = 26.57

Company B :

Mean, x2 = 52.85

Sample size, n2 = 20

Standard deviation, s2 = 20.02

The hypothesis :

H0: μ1 − μ2 = 0

H1: μ1 − μ2 ≠ 0

The test statistic :

Test statistic:

t = (x1 - x2)/[√(s²p(1/n1 + 1/n2 )]

Pooled variance = s²p

s²p = ((n1-1)*s1² + (n2-1)*s2² )/(n1+n2-2)

s²p = (24*26.57^2) + (19*20.02^2) / 43

s²p = 571. 125

√(s²p(1/n1 + 1/n2) ;

√572.125(1/25 + 1/20) = 7.169

x1 - x2 ; 50.6 - 52.85 = - 2.25

Test statistic = - 2.25 / 7.169

Test statistic = - 0.314

Using the Pvalue from t score calculator :

Pvalue(-0.314, 43) = 0.755

Pvalue > α ; We fail to reject the Null

Step-by-step explanation:

\(b = k + \frac{l}{m} \\ b - k = \frac{l}{m} \\ m = \frac{l}{b - k} \\ thank \: you\)

Answer:

bout 7

Step-by-step explanation:

Answer:3.049533e+44 to be exact

Step-by-step explanation:

Answer:

p=32 p<32

Step-by-step explanation:

The reasonable range for the total cost of the tickets the groups

would pay  is {84, 126, 2163}.

The sets of all the x-coordinates and all the y-coordinates of ordered pairs, respectively, are the domain and range of a relation.

A function's domain and range are its constituent parts. A function's range is its potential output, whereas its domain is the set of all possible input values.

Given:

The Function modeled for the situation is

f(x) = 21 x where x is the number of tickets sold.

So, For x= 4 Tickets

Fare, F(x) = 21 x 4= $84

and, For x= 6 Tickets

Fare, F(x) = 21 x 6 = $126

and, For x= 103 Tickets

Fare, F(x) = 21 x 103 = $2163.

Hence, the range is {84, 126, 2163}.

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From a group of 15 randomly selected residents , the probability that at least thirteen of them shop at Walmart is 0.0271  .

6 out of 10 Niceville residents shop at Walmart

So, the probability of shopping at Walmart (p) is = 6/10 = 0.6

The probability of not shopping at Walmart is (q) = 1 - 0.6 = 0.4 .

The number of members in the group is(n) = 15 ;

We have to find the probability that, at least thirteen of them shop at Walmart

By the Binomial Probability Distribution,

we know that ; P(x = a) = ⁿCₐ×pᵃ×qⁿ⁻ᵃ

So , P(x ≥ 13) = P(x=13) + P(x=14) + P(x=15)

Substituting the values of a , n and p and q ,

We get ;

= ¹⁵C₁₃p¹³q² + ¹⁵C₁₄p¹⁴q¹ + ¹⁵C₁₅p¹⁵q⁰

= ¹⁵C₁₃(0.6)¹³(0.4)² + ¹⁵C₁₄(0.6)¹⁴(0.4)¹ + ¹⁵C₁₅(0.6)¹⁵(0.4)⁰

= 0.0219 + 0.0047 + 0.0004

= 0.0271

Therefore, the required probability is 0.0271

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Answer:

20

Step-by-step explanation:

percentage error = predictions - actual ÷actual × 100

error

\( \frac{82 - 52 \\ }{52} \times 100\)

=

20

Answer:

  (d)  P ≥ -40

Step-by-step explanation:

You want the solution to P/8 ≥ -5.

Multiply both sides of the inequality by 8.

  8(P/8) ≥ 8(-5)

  P ≥ -40

The probability of selecting a girl and a boy for the class committee can be calculated by considering the total number of outcomes and the number of favorable outcomes.

Identify the number of girls and boys in the class. In this case, there are 5 girls and 7 boys.

Determine the total number of students in the class. That is 5 + 7 = 12.

Determine the number of ways to select two students from the class.

Here we can use the combination formula, which is written as C(n, r), where n is the total number of items and r is the number of items to be chosen.

In our case, n = 12 (total number of students) and r = 2 (number of students to be selected).

C(12, 2) = 12! / (2!(12-2)!) = 66.

Determine the number of favorable outcomes.

In this case, we want to select one girl and one boy. We multiply the number of girls by the number of boys: 5 x 7 = 35.

To find the probability, we divide the number of favorable outcomes (35) by the total number of outcomes (66):

Probability = Number of favorable outcomes / Total number of outcomes = 35 / 66 = 5/6.

So, the probability of selecting a girl and a boy for the class committee is 5/6.

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Answer:

I don't think so

Step-by-step explanation:

The sum is the numbers added together and 3+1 -5 -8 -2+1=-10 so you did not get 5

No, Cameron will not win the game.

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

Given that;

A card game requires that you have a sum of 5 in order to win.

Now, Let us calculate the sum of the cards.

= 3 + 11 + (-5) + (-8) + (-2) + 1

= 0.

Since, the sum is not equal to 5,

Hence, Cameron will not win the game.

So, Cameron needs to draw more cards and hope that they add up to 5 to win the game.

Thus, Cameron will not win the game.

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======================================================

Work Shown:

A = event of losing $100

P(A) = probability event A occurs = 0.20

V(A) = net gain of event A happening = -100

B = event of gaining $30

P(B) = probability event B occurs =  0.80

V(B) = net gain of event B happening = 30

-----------------

E(X) = expected value

E(X) = P(A)*V(A) + P(B)*V(B)

E(X) = 0.20*(-100) + 0.80*(30)

E(X) = 4

The expected value is $4

This means the investor expects to get an average return of $4.

Answer:

Step-by-step explanation:

C = 3t - 1 + t^6

D = 2t + 7

2C - 2D

2(3t - 1 + t^6) - 2(2t + 7)

6t -2 + 2t^6 - 4t - 14

2t^6 + 2t - 16

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

C = 3t - 1 + t^6

D = 2t + 7

2C = 2 ( 3t - 1 + \(t^6\) )

2D = 2 (2t + 7)

The expression that equals 2C - 2D is

2t - 16 + 2\(t^6\).

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

C = 3t - 1 + t^6

D = 2t + 7

Now,

2C = 2 ( 3t - 1 + \(t^6\) )

2D = 2 (2t + 7)

Now,

2C - 2D

= 2 ( 3t - 1 + \(t^6\) ) - 2 ( 2t + 7 )

= 6t - 2 + 2\(t^6\) - 4t - 14

= 2t - 16 + 2\(t^6\)

Thus,

C = 3t - 1 + t^6

D = 2t + 7

2C = 2 ( 3t - 1 + \(t^6\) )

2D = 2 (2t + 7)

The expression that equals 2C - 2D is

2t - 16 + 2\(t^6\).

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Using the Venn diagram, each set and the number of elements in each set are:

a. U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12}

b. A = {1, 3, 4, 5, 6, 8}

c. B = {4, 5, 6, 7, 9, 11}

d. C = {6, 8, 9, 12}

e. A ∪ B = {1, 3, 4, 5, 6, 7, 8, 9, 11}

f. A ∩ B = {4, 5, 6}

A Venn diagram is a pictorial representation used to visualize the relationships between different sets of objects or concepts.

a.) U is the universal set. This implies it contains all the elements in the set. Thus:

U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12}

b.) A is all element (number) is set A (circle A). Thus:

A = {1, 3, 4, 5, 6, 8}

c.) B is all element is set B (circle B). Thus:

B = {4, 5, 6, 7, 9, 11}

d.) C is all element is set C (circle C). Thus:

C = {6, 8, 9, 12}

e.) A ∪ B is all element is sets A and B (circles A and B). Thus:

A ∪ B = {1, 3, 4, 5, 6, 7, 8, 9, 11}

f.) A ∩ B is all element is sets A and B (circles A and B) have in common. Thus:

A ∩ B = {4, 5, 6}

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Answer: 11/9 or 1 2/9 or 11 over 9

Step-by-step explanation:

Firstly, you need to know what a fraction is.

A fraction is a segment (part of) a whole. To express a fraction, you write the numerator over the denominator. A numerator is the top part of the fraction, and it shows how much it is out of. The denominator shows how much it is out of.

Example: \(\frac{1}{3}\)

That means it is 1 part out of 3 parts

Now you know what a fraction is, now let's add them.

Next, convert the word form into the number form:

2 over 3 is 2/3

plus is +

5 over 9 =is 5/9

Combine them:

2/3 + 5/9

Steps of the problem:

Firstly, you have to find the L.C.M (Lowest Common Multiple) of 3 and 9 because to add fractions, you need a common (same) denominator.

9 is the L.C.M of 3 and 9, as 9x1 = 9 and 3x3 = 9.

Mulitiply the numerator and denominator by 3:

2x3/3x3 = 6/9

Now, the equation is 6/9+5/9.

Add the numerators:

11/9

The answer is 11/9

If the question tells you to convert into a mixed number, then here's the following steps:

You have to find the highest number 11 goes into 9

It's 1.

Take the remainder (2) into the fraction:

2/9

Now, add 1 in front of it:

1 2/9

As a decimal, it is 1.2222222 (recurring).

If that helped you, please make me Brainliest!

Answer:

11 over 9 \((\frac{11}{9})\)

Step-by-step explanation:

A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.

To solve for \(\frac{2}{3} +\frac{5}{9}\), we need to first convert these fractions so that they share a common denominator.

A common denominator consists of two or more fractions that have the same denominator. This makes it easier to perform numeric equations, and to solve them.

If a common denominator just refers to 2 fractions having the same denominator, we can simply multiply the numerator and denominator of the fraction \(\frac{2}{3}\) by a number. To solve for that number, we can divide 9 by 3.

Now that we know that the number is 3, multiply both by 3.

Now the fraction looks like this: \(\frac{6}{9}\).

We can now change the expression to this:

When adding fractions with the same denominator, we can just add the 2 numerators and keep the common denominator the same.

Now just insert 11 in as the numerator:

Therefore 2 over 5 plus 5 over 9 is 11 over 9.

Answer:

(a+b) (a-b) =a^2 - b^2

In this question a=2, b=square root of 5

So 2*2=4 square root of 5 times square root of 5 is 5

4-5=-1

Answer:

I believe the answer is -1.

Step-by-step explanation:

So I distributed,

2 x 2 = 4

\(-\sqrt{5}\) x 2 = \(-2\sqrt{5}\)

\(\sqrt{5}\) x 2 = \(2\sqrt{5}\)

\(\sqrt{5}\) x \(-\sqrt{5}\) = -5

4 \(-2\sqrt{5}\) + \(2\sqrt{5}\) - 5 = ?

the radicals cancel out and 4 -5 = -1

Answer:

3.278 * 10 ^ 2

Step-by-step explanation:

To change a number to scientific notation you:

Move the decimal point to the left to make the number have 1 number before the decimal point.

From there you multiply by 10 to the power 2 the number of decimal points you moved.

So the answer is 3.278 * 10^2

HOPE IT HELPED

The cheapest price Sam would pay for 10kg of cake for the party is $5000 from Mega Mart.

To find the cheapest price Sam would pay for 10kg of cake for the party, we need to compare the prices of the available cakes and determine the most cost-effective option.

At Mega Mart, a 5kg cake costs $2500.

Therefore, the price per kilogram for this cake is:

Price per kilogram at Mega Mart = $2500 / 5kg = $500/kg.

At the same time, a 2kg chocolate cake costs $1200.

So, the price per kilogram for this cake is:

Price per kilogram for the chocolate cake = $1200 / 2kg = $600/kg.

Now, let's calculate the total price for 10kg of cake from each option:

Total price at Mega Mart for 10kg = $500/kg \(\times\) 10kg = $5000.

Total price for 10kg of chocolate cake = $600/kg \(\times\) 10kg = $6000.

Comparing the two options, we see that the Mega Mart cake is the more cost-effective choice.

Sam would pay a total of $5000 for 10kg of cake from Mega Mart, whereas the chocolate cake would cost $6000 for the same quantity.

Therefore, the cheapest price Sam would pay for 10kg of cake for the party is $5000 from Mega Mart.

In summary, Sam would pay the cheapest price of $5000 to purchase 10kg of cake for the party from Mega Mart.

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Answer:

Here, given

present population = 20000

according to question,

population gets double every 34 years

i.e P = 20000 × 2

= 40000

now,

P = 40000

T = 68-34 = 34

ie, again p is double

so, P = 40000×2

= 80000

Hence, the population after 68 years from now is 80000

Answer:

\(Gallons = 27.95\)

Step-by-step explanation:

Given

\(Gallons : Miles = 17:590\)

Required

Determine the number of gallon for 870 miles

To do this, we simply substitute 870 for miles in the ratio above

So, we have:

\(Gallons : 870= 17:590\)

Convert to fraction

\(\frac{Gallons}{870} = \frac{17}{590}\)

Multiply through  by 870

\(870 * \frac{Gallons}{870} = \frac{17}{590}*870\)

\(Gallons = \frac{17}{590}*970\)

\(Gallons = \frac{17*970}{590}\)

\(Gallons = \frac{16490}{590}\)

\(Gallons = 27.95\)

Answer:

Step-by-step explanation:

Assuming the system is solvable in the first place, create an augmented matrix of coefficients from the equations. Then put the matrix into reduced row echelon form.

Example is attached.

"Demonstrate by solving the following system."

You need to provide the system of equations.

Answer:

A chip of 16.59 ounces represents the 67th percentile for the bag weight distribution

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

\(\mu = 16.5, \sigma = 0.2\)

What chip amount represents the 67th percentile for the bag weight distribution

This is X when Z has a pvalue of 0.67, so X when Z = 0.44.

\(Z = \frac{X - \mu}{\sigma}\)

\(0.44 = \frac{X - 16.5}{0.2}\)

\(X - 16.5 = 0.44*0.2\)

\(X = 16.59\)

A chip of 16.59 ounces represents the 67th percentile for the bag weight distribution

Using the normal distribution concept, the chip amount which corresponds to the 67th percentile is 16.59

Using the concept of normal distribution :

The 67th percentile is defined as :

P(Z < 0.67) ; Using a normal distribution table, the corresponding Zscore value is 0.44

Substitute into the Zscore relation and solve for the score, X :

0.44 = (X - 16.5) / 0.2

Cross multiply

0.44 × 0.2 = (X - 16.5)

0.088 = X - 16.5

0.088 + 16.5 = X

X = 16.588

Therefore, the chip amount is 16.59.

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Answer: \(-3y^{2} +5x+2\)

Step-by-step explanation:

\(-3y^{2} +2x+2+3x\\2x+3x=5x\\\)

that is all that you can combine so it makes the answer \(-3y^{2} +5x+2\)

Answer:

Part A: $3,415.50

B: 11.34%

Step-by-step explanation:

Part A: $31,000 is within the values 10,276≤x≤41,175, so use f(x)=0.12x-205.50

Part B: For the effective tax rate, divide the amount in part A by the taxable income

Part C: Compare both the taxable income and the effective tax rate to the income domains given and the % multiplier. This one is mostly about how you describe the situation, so I'll leave that up to you.

To calculate the taxes owed on a taxable income of $31,000, we use the appropriate equation for the tax bracket it falls into and substitute the value of x. The effective tax rate is calculated by dividing the amount of taxes owed by the taxable income and multiplying by 100. The piecewise function represents the marginal tax rate chart by using different equations for each tax bracket.

Part A:

To calculate the amount of taxes owed on a taxable income of $31,000, we need to determine which tax bracket it falls into. Since $31,000 is greater than $10,275 but less than $41,175, it falls into tax bracket 2. To find the amount of taxes owed, we use the equation for tax bracket 2: f(x) = 0.12x - 205.50. Plugging in $31,000 for x, we get:

f(x) = 0.12 * 31000 - 205.50 = $3,574.50

Therefore, the amount of taxes owed on a taxable income of $31,000 is $3,574.50.

Part B:

To determine the effective tax rate, we divide the amount of taxes owed by the taxable income. Using the result from Part A (taxes owed = $3,574.50) and the taxable income of $31,000, we have:

Effective tax rate = (taxes owed / taxable income) * 100 = (3,574.50 / 31,000) * 100 ≈ 11.52%

Therefore, the effective tax rate on a taxable income of $31,000 is approximately 11.52%.

Part C:

The piecewise function represents the amount of taxes owed as a function of the taxable income. Each part of the function corresponds to a different tax bracket, with the equation for that tax bracket. The marginal tax rate chart is represented in the piecewise function by the different equations for each tax bracket. For example, the equation in part 1 of the function (f(x) = 0.10x) corresponds to the 10% marginal tax rate for the tax bracket $0-$10,275.

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a) The angle swept out  since kelsey started skiing: 1.1498 radians

b) The distance Kelsey skied:  3.334 km

In this question, we have been given Kelsey is skiing along a circular ski trail that has a radius of 2.9 km. she starts at the 3-o'clock position and travels in the ccw direction. kelsey stops skiing when she is 1.185 km to the right and 2.647 km above the center of the ski trail.

Consider the following figure for reference.

We need to find the angle θ and the distance kelsey skied (i.e., the arc length)

Here, the horizontal distance x = 1.185 km and the vertical distance y = 2.647 km

a. the tangent of angle θ would be,

tan(θ) = y/x

tan(θ) = 2.647/1.185

tan(θ) = 2.2337

θ = arctan(2.2337)

θ = 65.88°

θ = 1.1498 radians

b. The length of the arc is:

s = rθ

s = 2.9 * 1.1498

s = 3.334 km

Therefore, a) the angle swept out : 1.1498 radians

b) the distance Kelsey skied:  3.334 km

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Answer: Complain

Step-by-step explanation:

Gripe- express a complaint or grumble about something, especially something trivial.

Answer:

It should be complain, tell me if I'm wrong.

Step-by-step explanation:

I used context clues

Answer:

36 is d

Step-by-step explanation:

Answer:

Given that there are 21 flags, NOW using backward induction we can see that;

If there is only one flag left, whosoever picks up that particular  flag will lose. Therefore, 1 is loosing number.

Now if there are 2 flags left, whosoever's turn it is, can pick 1 flag and leave one for the opponent and win the game. Therefore, 2 is winning number. Similarly if there are 3 flags left then whosoever's turn it is can pick 2 flags and leave one for the opponent and can win the game. Hence 3 is winning number. Similarly when 4 flags left, 3 can be picked up and leave one for the opponent and win the game. So, 4 is also winning number.

Now, if there are 5 flags left, then no matter whichever number you choose among 1,2 or 3 you gonna leave other team with 4,3 or 2 respectively and all 3 are winning number. Therefore, 5 is loosing number.

Similarly, if you have 6,7,8 then by taking 1,2,3 respectively you can leaveyour opponent with number 5 and that is loosing number and you can win certainly. Therefore, 6,7,8 are also winning number.

Following above discussion, we see a pattern among the number that would make sure you win and with other numbers you loose.

we see after 1 if we go in positive direction on number line till 21 then every fourth number is loosing number because no matter what you choose you will leave your opponent with a winning number of flags and if your opponent knows and follows the optimal strategy can win. Therefore,

Loosing Numbers = 1,5,9,13,17 and 21

Winning Numbers = 2,3,4,6,7,8,10,11,12,14,15,16,18,19 and 20

a) STRATEGY

If you are a team that is stuck with any of loosing number that is 1,5,9,13,17 or 21 then no matter what strategy you follow you gonna loose. Therefore, there is n winning strategy in this situation given other team also knows the winning strategy

But if you have any of winning numbers at any point then you can follow the following strategy and can win

- 2 flags = pick up one flag and leave 1 for the opponent, win

- 3 flags = pick up 2 flags and leave 1 for the opponent, win

- 4 flags = pick up 3 flags and leave 1 for the opponent, win

- 6 flags = pick up one flag, then no matter what your opponent chooses you follow either strategy number 1,2 or 3 based on the number of flags left and win

- 7 flags = pick up 2 flags, then no matter what your opponent chooses you follow either strategy number 1,2 or 3 based on the number of flags left and win

- 8 flags = pick up 3 flags, then no matter what your opponent chooses you follow either strategy number 1,2 or 3 based on the number of flags left and win

- 10 flags = pick up one flag, then no matter what your opponent chooses you follow either strategy number 4,5 or 6 based on the number of flags left and win

- 11 flags =  pick up 2 flags, then no matter what your opponent chooses you follow either strategy number 4,5 or 6 based on the number of flags left and win

- 12 flags =  pick up 3 flags, then no matter what your opponent chooses you follow either strategy number 4,5 or 6 based on the number of flags left and win

- 14 flags =  pick up one flag, then no matter what your opponent chooses you follow either strategy number 7,8 or 9 based on the number of flags left and win

- 15 flags =  pick up 2 flags, then no matter what your opponent chooses you follow either strategy number 7,8 or 9 based on the number of flags left and win

- 16 flags =  pick up 3 flags, then no matter what your opponent chooses you follow either strategy number 7,8 or 9 based on the number of flags left and win

- 18 flags =  pick up one flag, then no matter what your opponent chooses you follow either strategy number 10,11 or 12 based on the number of flags left and win

- 19 flags = pick up 2 flags, then no matter what your opponent chooses you follow either strategy number 10,11 or 12 based on the number of flags left and win

- 20 flags = pick up 3 flags, then no matter what your opponent chooses you follow either strategy number 10,11 or 12 based on the number of flags left and win

b)

Since team moving first will have 21 flags left on ground and it is a loosing number, no matter which number it chooses to pick it is gonna loose as it will leave other team with winning number. So, they will be indifferent between choosing 1,2 or 3

c)

If first teams removes 1 flag then best strategy for second team would be to remove 3 flags and again leave first team with loosing number

similarly, If first teams removes 2 flags then best strategy for second team would be to remove 2 flags and again leave first team with loosing number

and If first teams removes 3 flags then best strategy for second team would be to remove only 1 flag and again leave first team with loosing number

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

You can find the intercepts by dividing the constant (1) by the coefficient of x (1) for the x-intercept, and the coefficient of y (-1) for the y-intercept.

Knowing the x-intercept is +1 and the y-intercept is -1 tells you the graphed line makes a triangle with the axes in the 4th quadrant. The attachment shows a graph of the equation.

Answer:

Hello your question is incomplete below is the complete question

Let R be a relation from A to B and S a relation from B to C.

(a) Prove that  . \(Dom(S \circ R) \subseteq Dom(R)\)

(b) Find a counterexample to show that we don’t always have equality.

answer : (b) Dom ( S o R ) = [ 1 ] and Dom ( R ) = [ 1, ∝ ]

              hence: Dom ( S o R ) ≠ Dom ( R )

Step-by-step explanation:

Note : R ⊆ A * B and  S ⊆ B * C

A) To prove that \(Dom(S \circ R) \subseteq Dom(R)\)

 we take note that : S o R ⊆ A x C

ATTACHED BELOW IS THE REMAINING PART OF THE SOLUTION

B) A counterexample to show that we don't always have equality

attached below is a assumptions and solution on how we arrived at the value below

Dom ( S o R ) = [ 1 ] and Dom ( R ) = [ 1, ∝ ]

hence: Dom ( S o R ) ≠ Dom ( R )