Choose the best multiple choice option below! Thanks in advance!

n = 2, in which case D2 is just the cyclic group of order 2, which is commutative.

n is a multiple of 4, in which case Dn is a product of two cyclic groups of order n/2, which are commutative.

A cyclic group is a mathematical group that is generated by a single element, which is called a generator. In other words, a cyclic group is a group in which all elements can be obtained by repeatedly applying the group operation to a single element.

Formally, a cyclic group is defined as a group G that has an element g such that every element of G can be written as a power of g. That is, for every element x in G, there exists an integer n such that x = gⁿ, where gⁿ denotes the product of g with itself n times.

The Dihedral group, denoted by Dn, is a group of symmetries of a regular n-gon. It has 2n elements and is not commutative in general, except for some special cases.

Group Dn has a presentation:

Dn = ⟨r, s | rⁿ = s² = (sr)² = e⟩

where r represents a clockwise rotation of 2π/n radians and s represents a reflection about a line through the center of the n-gon.

If n is odd, then the group Dn is not commutative, because rs is not equal to sr. This can be seen by considering the effect of the two operations on the vertices of the n-gon.

However, if n is even, then the group Dn is commutative in certain cases. Specifically, Dn is commutative if and only if the two generators r and s commute, i.e., if rs = sr. This happens when either:

n = 2, in which case D2 is just the cyclic group of order 2, which is commutative.

n is a multiple of 4, in which case Dn is a product of two cyclic groups of order n/2, which are commutative.

To know more about the dihedral group visit:

brainly.com/question/31461742

#SPJ1

The monthly installments are €761.94, the total amount paid is €809.68 , and the interest paid is €72,904.00 over 25 years. The principal pending at the end of year 10 is €136,148.95, and the interest paid in 10 years is €33,851.05. The amounts corresponding to the first 4 years are Year 1 - €166,105.68, Year 2 -  €162,059.00, Year 3 - €157,857.39, and Year 4 -€153,498.11

To find the amount of the monthly installments, we can use the formula

M = P * (r / (1 - (1 + r)⁻ⁿ))

where M is the monthly installment, P is the principal amount borrowed, r is the monthly interest rate, and n is the total number of monthly payments.

First, we need to convert the annual nominal interest rate to a monthly rate

r = 2.25% / 12 = 0.1875%

Next, we need to find the total number of monthly payments

n = 25 years * 12 months/year = 300 months

Using the formula, we get

M = 170,000 * (0.001875 / (1 - (1 + 0.001875)⁻³⁰⁰)) = €809.68 (rounded to the nearest cent)

The total amount paid over the 25 years would be:

Total amount paid = M * n = €809.68 * 300 = €242,904.00

The interest paid over those 25 years would be

Interest paid = Total amount paid - Principal amount borrowed = €242,904.00 - €170,000 = €72,904.00

To find the principal pending at the end of year 10, we can use the formula for the remaining balance on a loan

B = P * ((1 + r)ⁿ - [tex](1 + r)^t[/tex] / ((1 + r)ⁿ - 1)

where B is the remaining balance, P is the principal amount borrowed, r is the monthly interest rate, n is the total number of monthly payments, and t is the number of monthly payments made.

After 10 years, the number of monthly payments made would be

t = 10 years * 12 months/year = 120 months

The remaining number of monthly payments would be

n - t = 300 - 120 = 180 months

Using the formula, we get

B = 170,000 * ((1 + 0.001875)³⁰⁰ - (1 + 0.001875)^¹²⁰) / ((1 + 0.001875)³⁰⁰ - 1) = €136,148.95

To find the amount of interest paid in those 10 years, we can subtract the remaining balance from the original principal amount:

Interest paid = Principal amount borrowed - Remaining balance = €170,000 - €136,148.95 = €33,851.05

To find the amounts corresponding to the first 4 years of the loan amortization schedule, we can use an amortization schedule calculator or a loan amortization formula. Here are the amounts for the first 4 years

Year 1

Beginning balance: €170,000.00

Monthly payment: €809.68

Principal paid: €3,894.32

Interest paid: €6,594.51

Ending balance: €166,105.68

Year 2

Beginning balance: €166,105.68

Monthly payment: €809.68

Principal paid: €4,046.67

Interest paid: €6,442.16

Ending balance: €162,059.00

Year 3

Beginning balance: €162,059.00

Monthly payment: €809.68

Principal paid: €4,201.61

Interest paid: €6,287.22

Ending balance: €157,857.39

Year 4

Beginning balance: €157,857.39

Monthly payment: €809.68

Principal paid: €4,359.28

Interest paid: €6,129.55

Ending balance: €153,498.11

To know more about interest rate:

https://brainly.com/question/15089941

#SPJ1

The missing values of y in the exponential function are 6 and 1/36.

The missing part of the table is calculated as follows;

The exponential function is given as;

y = (1/6)×

when x = -2, the value of y is calculated as;

y = (1/6)⁻² = 36

when x = -1, the value of y is calculated as;

y = (1/6)⁻¹ = 6

when x = 2, the value of y is calculated as;

y = (1/6)² = 1/36

Learn more about exponential functions here: https://brainly.com/question/30241796

#SPJ1

In 2022, Tom will have approximately 157783.78 in his account.

Future Value (FV)

= Principal (P) * (1 + Interest Rate (R))^Number of Years (N)

In this case:

Principal (P) = $100

Interest Rate (R) = 3.5%  = 0.035

Number of Years (N)

= 2022 - 1759

= 263 years

Now we can plug in the values into the formula:

FV = $100 * (1 + 0.035)^263

FV ≈ $100 * 1577.837835196 (rounded to 9 decimal places)

FV ≈ $157,783.78 (rounded to 2 decimal places)

So, in 2022, Tom will have approximately 157783.78 in his account.

Read more on future values here:https://brainly.com/question/24703884

#SPJ1

The equation of the line that passes through  (3,-2) and is (a) parallel to the line is y = 3x - 11 and (b) perpendicular to the line is y = - 1 / 3 x - 2.

The equation of a line can be represented in different form such as slope intercept form.

The equation of a line in slope intercept form can be represented as follows:

y = mx + b

where

Hence, let's find the equation of a line passing through (3, -2) and is parallel to the line shown.

Parallel line have the same slope.

Hence,

m = -4 + 1 / 1 - 2

m = -3 / -1

m = 3

Therefore,

y = 3x + b

-2 = 3(3) + b

b = -2 - 9

b = -11

The equation is y = 3x - 11

Hence, let's find the equation of a line passing through (3, -2) and is perpendicular to the line shown.

The slopes of perpendicular lines are negative reciprocals of one another.

hence,

m = - 1 / 3

Therefore,

y = - 1 / 3 x + b

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

b = -2 + 1

b = -2

Therefore, the equation is y = - 1 / 3 x - 2.

learn more on equation here: https://brainly.com/question/29866344

#SPJ1

Step-by-step explanation:

so, overall, 63% will grow.

that means, every seed has a 63% chance to grow. in other words, the probabilty to grow is 0.63 (as 63% means 63 out of 100 = 0.63).

and a chance of

1 - 0.63 = 0.37

to not grow.

fewer than 8 out of 9 seeds means not 8 and not 9.

it is

1 - P(8) - P(9)

with P(x) means the probability that exactly x seeds out of the 9 grow/germinate.

the chance for a group of exactly 8 out of 9 seeds to grow is then the probabilty for 8 to grow and 1 not to grow :

0.63⁸ × 0.37 = 0.009181764...

but these are 8 seeds out of 9.

and we calculated the probability for only one possible grouping.

how many groups of 8 can we build out of 9 ?

as the sequence does not matter, and we cannot have repetitions (every seed can only count as 1), we have combinations

C(9, 8) = 9! / (8! × (9-8)!) = 9!/8! = 9

so, the total probability P(8) for exactly 8 seeds out of 9 to grow/germinate is

9 × 0.63⁸ × 0.37 = 9 × 0.009181764... = 0.082635875... ≈

≈ 0.083

now, the chance for a group of exactly 9 out of 9 seeds to grow is then the probabilty P(9) for all 9 to grow :

0.63⁹ = 0.015633814... ≈ 0.016

the probabilty that fewer than 8 out of the 9 will grow/germinate is

1 - 0.082635875... - 0.015633814... = 0.901730311... ≈

≈ 0.902

If you started driving 10 miles closer to the beach then you normally would, after 2 hours of driving, you are 130 miles away from home.

Assuming that the distance to the beach from your home is "d" miles, you normally drive "d - 10" miles before reaching the beach.

If you drive for 2 hours at 70 miles per hour, you will have traveled a total distance of:

distance = speed x time = 70 x 2 = 140 miles

However, this distance includes the 10 miles that you started closer to the beach than normal. Therefore, the distance you have traveled from your home is:

distance from home = 140 - 10 = 130 miles

To learn more about distance click on,

https://brainly.com/question/19908562

#SPJ1

Answer:

Step-by-step explanation

The first step is to add up all of the numbers to get the total budget.

Total Budget = 858 + 429 + 924 + 198 + 363 + 528 =3,300

Then to find the percentage for a certain category it is:

[tex]\frac{Budget Category}{Budget Total} times 100%[/tex]

So, 429 / 3300 x 100% = 0.13 x 100% = 13% Car Expense

Answer:

Step-by-step explanation

The first step is to add up all of the numbers to get the total budget.

Total Budget = 858 + 429 + 924 + 198 + 363 + 528 =3,300

Then to find the percentage for a certain category it is:

[tex]\frac{Budget Category}{Budget Total} times 100%[/tex]

So, 429 / 3300 x 100% = 0.13 x 100% = 13% Car Expense

Answer:

D. 67 square inches

Step-by-step explanation:

16 inches in diameter is an 8 inch radius. The area of a circle (the whole pizza) is

A = pi• r^2

= 3.14•8^2

= 64pi

= 200.96

The whole pizza is 200.96 square inches of pizza.

There are 12 pieces.

200.96 ÷ 12

= 16.746666...

Each slice is 16.75 sq inches.

The guys ate 4 pieces each.

16.75 × 4

= 67

Each guy ate 67 sq inches of pizza.

Answer:

5 cases

10 additional units

Step-by-step explanation:

Given that:

Total number of units needed = 60 units

Total number of units per case = 14

Hence, the total number of cases required will

be: Number of units needed / number of units per

case

Number of cases required = 60/14 = 4.285 (this be up to 60 units)

means that 5 cases are required as 4 cases won't

With 5 cases, we have exceeded the required units needed:

Additional units will be: (145)-60

Additional units = 70 - 60 = 10 units

Step-by-step explanation:

if it helped u please mark a brainliest :))

Answer:

In Mathematics, a pattern is a repeated arrangement of numbers, shapes, colours and so on. The Pattern can be related to any type of event or object. If the set of numbers are related to each other in a specific rule, then the rule or manner is called a pattern. Sometimes, patterns are also known as a sequence.

The activity rate for Cost Pool A is $7.97 per unit of Product A, and the activity rate for Cost Pool B is $6.06 per unit of Product B.

The activity rate is a cost accounting term that refers to the cost that a company incurs for each unit of a particular activity or process. It is calculated by dividing the total cost of an activity or process by the total number of units produced or processed.

The purpose of calculating activity rates is to allocate the cost of a particular activity or process to the products or services that use that activity or process. This helps to determine the true cost of producing a product or service and to make informed decisions about pricing, profitability, and resource allocation.

In order to calculate the activity rate for each cost pool, we need to know the total cost for each cost pool.

Let's assume that there are two cost pools: Cost Pool A and Cost Pool B.

If we know the total cost for each cost pool, we can calculate the activity rate for each cost pool by dividing the total cost by the total number of units produced.

For example, if the total cost for Cost Pool A is $100,000 and 12,539 units of Product A were produced, then the activity rate for Cost Pool A would be:

Activity Rate for Cost Pool A = Total Cost for Cost Pool A / Total Units of Product A

Activity Rate for Cost Pool A = $100,000 / 12,539 units

Activity Rate for Cost Pool A = $7.97 per unit of Product A

Similarly, if the total cost for Cost Pool B is $50,000 and 8,254 units of Product B were produced, then the activity rate for Cost Pool B would be:

Activity Rate for Cost Pool B = Total Cost for Cost Pool B / Total Units of Product B

Activity Rate for Cost Pool B = $50,000 / 8,254 units

Activity Rate for Cost Pool B = $6.06 per unit of Product B

To know more about the activity rate visit:

brainly.com/question/14975732

#SPJ1

Answer:

Step-by-step explanation:

To solve the problem, we need to add the two distances Tom jogged:

4 1/6 + 5 4/5

To add the two mixed numbers, we need to convert them into improper fractions:

4 1/6 = (6 x 4 + 1) / 6 = 25 / 6

5 4/5 = (5 x 5 + 4) / 5 = 29 / 5

Now we can add the two fractions:

25/6 + 29/5

To add the fractions, we need to find a common denominator:

LCM of 6 and 5 = 30

25/6 x 5/5 = 125/30

29/5 x 6/6 = 174/30

Now we can add the fractions:

125/30 + 174/30 = 299/30

The sum of the distances in improper fraction form is 299/30 miles. To write the answer as a mixed number in simplest form, we need to divide the numerator by the denominator:

299 / 30 = 9 29/30

Therefore, Tom has jogged 9 29/30 miles in all.

Answer:

14. D) x+25=50; when x=157, x+25=182, which is equal to 50.

15. a) 3; you can solve for r by isolating the variable on one side of the equation. First, add 21 to both sides to get 10g - 21 + 21 = 7r + 12 + 21. Simplify to get 10g = 7r + 33. Then, subtract 33 from both sides to get 10g - 33 = 7r. Finally, divide both sides by 7 to get r = (10g - 33)/7. Plugging in a value for g, such as 3, gives you r = 3.

16. C) 2; combine like terms on both sides of the equation to get r - 8 = 8r + 10. Then, isolate the variable by subtracting r from both sides to get -9r - 8 = 10. Next, add 8 to both sides to get -9r = 18. Finally, divide both sides by -9 to get r = -2.

17. a) -36; start by isolating the variable on one side of the equation. Add 18 to both sides to get m/3 = m + 24. Then, subtract m from both sides to get -2m/3 = 24. Next, multiply both sides by -3/2 to get m = -36.

Step-by-step explanation:

Mark Brainliest!!

If the graph of f(x) is changed to [tex]f(x) = 4(\frac{5}{7} )^{x}-2[/tex], the graph of f(x) would be translated down by 2 units.

An equation of the new horizontal asymptote is y = -2.

In Mathematics and Geometry, the vertical translation a geometric figure or graph downward simply means adding a digit to the value on the y-coordinate of the pre-image or function.

In Mathematics and Geometry, a horizontal translation to the right is modeled by this mathematical equation g(x) = f(x - N) while a vertical translation to the positive y-direction (downward) is modeled by this mathematical equation g(x) = f(x) - N.

Where:

In this scenario, we can logically deduce that the graph of the parent function f(x) was translated or shifted downward (vertically) by 2 units.

Read more on translation here: brainly.com/question/4521517

#SPJ1

Answer:

12 minutes

Step-by-step explanation:

200/17

= 11.7

round up

12 minutes

The value of the variable x for the arc angle CD and DE is -1and the arc angle FCE = 230°. Also x = 5 for the arc angles RS, ST, TU, and UR, and the arc angle RS = 70°.

The angle subtended by an arc of a circle at it's center is twice the angle it substends anywhere on the circles circumference. Also the arc measure and the angle it subtends at the center of the circle are directly proportional.

Thus:

17). 2[(x + 131) + (x + 51)]° = 360°

2x + 182° = 180°

2x = 180° - 182°

2x = -2

x = -1

arc angle CD = -1 + 51 = 50°

arc angle DE = -1 + 131 = 130°

arc angle FCE = 2CD + DE

arc angle FCE = 2(50) + 130 = 230°

18). 92 + 27x + (11x + 8) + 15x - 5 = 360°

53x + 95° = 360°

53x = 360° - 95°

53x = 265

x = 5

arc angle RS = 15(5) - 5 = 70°

Therefore, the value of the variable x for the arc angle CD and DE is -1and the arc angle FCE = 230°. Also x = 5 for the arc angles RS, ST, TU, and UR, and the arc angle RS = 70°.

Read more about angle here:https://brainly.com/question/24423151

#SPJ1

People who made more money generally completed more years of college than those who made less money . So correct option is D.

A graph is a visual representation of data or information that uses a set of points or nodes, connected by lines or curves, to convey relationships or patterns. Graphs can be used to illustrate data in a way that is easy to understand and analyze.

There are several types of graphs, each with its own strengths and weaknesses depending on the type of data being presented. Some common types of graphs include:

Line graph: A line graph displays data as a series of points connected by a line, and is commonly used to show trends or changes over time.

Bar graph: A bar graph displays data using rectangular bars, with the length or height of each bar representing the quantity of data being measured. Bar graphs are useful for comparing different values or categories.

Pie chart: A pie chart shows data as a circular graph, with each slice representing a portion of the whole. Pie charts are commonly used to show proportions or percentages.

Scatter plot: A scatter plot displays data as a set of points on a two-dimensional plane, with each point representing the values of two variables. Scatter plots are useful for identifying patterns or trends in the relationship between two variables.

Histogram: A histogram displays data as a set of bars, with the height of each bar representing the frequency or number of occurrences of data within a certain range or interval.

Graphs can be an effective way to communicate complex information in a simple and easy-to-understand way. They are commonly used in fields such as science, economics, and social sciences, as well as in everyday life to display data and make comparisons.

People who made more money generally completed more years of college than those who made less money .

To know more about years visit:

https://brainly.com/question/28678935

#SPJ1

Answer:

  A.  The system has a single solution. The solution set is (x, y) = (-3, 2).

Step-by-step explanation:

You want the solution to the system of equations ...

These standard form equations are different, so they will have one solution.

That solution can be found by adding the equations, eliminating the y-variable.

  (x +y) +(x -y) = (-1) +(-5)

  2x = -6

  x = -3

  y = x +5 = -3 +5 = 2 . . . . . . from the second equation

The solution is (x, y) = (-3, 2).

Answer: 12 hours (noon)

Step-by-step explanation:

**For simplicity's sake, we'll use military time (Zulu time).**

- It is 00:00 in North America.

- If one full rotation means a day has passed, or more specifically, that 24 hours have passed, then that means the Earth has rotated 360°.

- So if 360° = 24 hrs, then 180°, being 360/2, or half a rotation, will be 24/2 hrs, or 12 hours.

- So the time is now 12:00, or noon.

Okay, let's list the 4 rational numbers from smallest to largest:

5/3

7/15

6/10

25/5

So:

5/3 is A

7/15 is B

6/10 is C

25/5 is D

The surface area of a rectangular prism is the sum of the areas of all its faces. The answer is B) two hundred two and fourteen twenty-fifths cm²

Surface area refers to the total area occupied by the surface of an object. It is found by adding up the areas of all the faces or surfaces of the object. For example, the surface area of a cube is found by multiplying the length of one edge by itself, and then multiplying the result by six, since a cube has six faces of equal area.

A rectangular prism is a three-dimensional solid shape that has six faces, where each face is a rectangle. It is also known as a rectangular parallelepiped.

According to given information :

To find the surface area of the rectangular prism, we need to find the area of each face and then add them together. Using the given dimensions, we can see that the six faces have areas of:

Front and back faces: 7 cm x 2 and 2/5 cm = 29 and 3/5 square cm each

Top and bottom faces: 3 and 3/5 cm x 2 and 2/5 cm = 9 and 9/25 square cm each

Side faces: 7 cm x 3 and 3/5 cm = 25 and 1/5 square cm each

Adding these areas together, we get a total surface area of:

2(29 and 3/5) + 2(9 and 9/25) + 2(25 and 1/5)

= 59 and 1/5 + 18 and 18/25 + 50 and 2/5

= 127 and 11/25 square cm

Therefore, the closest answer to the surface area of the prism is B) two hundred two and fourteen twenty-fifths cm²

To know mor about Surface Area and rectangular prism visit :

https://brainly.com/question/14987814

#SPJ1

Applying the Pythagorean theorem, the exact values of x are:

1. x = 13      2. x = 4      3. x = 6     4. x = 8   5. x = 15    6. x = √7

If a and b are smaller sides (legs) of a right triangle, and c is the longest side (hypotenuse), the Pythagorean theorem states that:

c = √(a² + b²).

Apply the Pythagorean theorem to find the exact value of x:

1. x = √(12² + 5²)

x = 13

2. x = √(5² - 3²)

x = 4

3. x = √(10² - 8²)

x = 6

4. x = √(17² - 15²)

x = 8

5. x = √(12² + 9²)

x = 15

6. x = √(4² - 3²)

x = √7

Learn more about Pythagorean Theorem on:

https://brainly.com/question/23715284

#SPJ1

The amount that was loaned are $15,500 at 4% annual interest and $4000 at 14% annual interest.

Given that,

A bank loaned out $19,500.

Amount loaned at 4% annual interest = x

Amount loaned at 14% annual interest = 19,500 - x

Total interest earned for both loans = $1,180

0.04x + 0.14 (19,500 - x) = 1180

0.04x + 2730 - 0.14x = 1180

-0.1x = -1550

x = 15,500

Amount loaned at 4% annual interest = x = $15,500

Amount loaned at 14% annual interest = 19,500 - x = $4000

Hence the loaned amount are $15,500 and $4000.

Learn more about Annual Interest here :

https://brainly.com/question/29480777

#SPJ1

- tan = opposite/ adjacent

- tan 64 = x(the height of the ladder)/ 9ft

- 2.050= x/9ft

-x= 9ft * 2.050

- x= 18.45ft  = 18.5 ft= 19 ft

so x or the unkown height is 19 ft

Answer:

C. -3x + 2y = 20

Step-by-step explanation:

Since the slope of line P is -2/3, and line Q is perpendicular to line P, the slopes of lines P and Q will be negative reciprocals. So the slope of line Q is 3/2. Since (-6, 1) is on line Q, we have:

1 = (3/2)(-6) + b

1 = -9 + b

b = 10

y = (3/2)x + 10

2y = 3x + 20

-3x + 2y = 20, so the correct answer is C.

The probability that  a random sample of 400 registered voters from this town will have a Maureen Webster under the age of 49 is about 0.0951, or about 9.51%.

Probability is simply how likely something is to happen. When we are uncertain about the outcome of an event, we can talk about the probability of certain outcomes—how likely they are.

We can use the binomial normal approximation to solve this problem because we have a large sample (400) and the probability (p) of preferring Maureen Webster is not too close to 0 or 1.  First, we need to find the mean and standard deviation of the sample proportion, which is given by:

mean = p = 0.53

standard deviation = square (p*(1-p)/n) = square (0.53*0.47/400) = 0.0305

Next, we need to find the z-score corresponding to the sample proportion of 0.49 (which is the "less than 49 percent" threshold). It is given by:

z = (x - mean) / standard deviation = (0.49 - 0.53) / 0.0305 = -1.31

We can now use a standard normal distribution table or calculator to determine the probability that the standard normal variable is less than -1.31. This probability is approximately 0.0951.

Therefore,  we can use the binomial normal approximation to solve this problem because we have a large sample (400) and the probability (p) of preferring Maureen Webster is not too close to 0 or 1.

First, we need to find the mean and standard deviation of the sample proportion, which is given by:

mean = p = 0.53

standard deviation = square (p*(1-p)/n) = square (0.53*0.47/400) = 0.0305

Next, we need to find the z-score corresponding to the sample proportion of 0.49 (which is the "less than 49 percent" threshold). It is given by:

z = (x - mean) / standard deviation = (0.49 - 0.53) / 0.0305 = -1.31

We can now use a standard normal distribution table or calculator to determine the probability that the standard normal variable is less than -1.31. This probability is approximately 0.0951.

Therefore, the probability that  a random sample of 400 registered voters from this town is under the age of 49 Maureen Webster is about 0.0951, or about 9.51%.

Learn more about Probability here

https://brainly.com/question/30034780

#SPJ1