Part A
If you spin the spinner 11 times, what is the prediction for the number of times it will land on red?
​
​
​Each section is equal in size.(it's talking about the spiner)
​
Answer:

​
Part B
What is the probability of green?​
A: 3/11
B:4/11
C:1/11
D:7/11

Answer:

(a) 5040°

(b) 168°

(c) 12°

Step-by-step explanation:

(a) The sum of angles in a polygon of N sides is given as:

S = (N - 2) * 180

For a 30-gon, N = 30.

Therefore, the sum of the angles in the 30-gon will be:

S = (30 - 2) * 180

S = 28 * 180

S = 5040°

(b) To find each interior angle, we simply divide S by 30:

Interior Angle = 5040/30

Interior Angle = 168°

(c) Each exterior angle of a polygon is gotten by subtracting the interior angle from 180°.

Hence, each exterior angle is:

180 - 168 = 12°

Answer:

Step-by-step explanation:

[tex]u.v=|u||v| cos \theta\\(8)(9)+(7)(7)=\sqrt{8^2+7^2 } \sqrt{9^2+7^2} cos \theta\\72+49=\sqrt{64+49} \sqrt{81+49}~ cos ~\theta\\121=\sqrt{113} \sqrt{130} ~cos~\theta\\cos~\theta=\frac{121}{\sqrt{113} \sqrt{130} } \\\theta=cos^{-1} (\frac{121}{\sqrt{113}\sqrt{130} } )\approx 3.3^\circ[/tex]

Answer:

Step-by-step explanation:

Using "s" and "o" to represent the prices of packs of sugar and oatmeal cookies, respectively, we can write the revenue equations as ...

  10s +2o = 56

  9s +3o = 60

In standard form (with common factors removed), these equations are ...

  5s + o = 28

  3s + o = 20

Subtracting the second equation from the first, we find ...

  (5s +o) -(3s +o) = (28) -(20)

  2s = 8 . . . . simplify

  s = 4

Substituting into the first equation, we have ...

  5·4 +o = 28

  o = 8 . . . . . . subtract 20

The price of a pack of sugar cookies is $4; of oatmeal cookies, $8.

The price of a pack of sugar cookies is $4 and the price of a pack of oatmeal cookies is $8.

Let's denote the price of a pack of sugar cookies as s and the price of a pack of oatmeal cookies as o

From Amy's sales, we have the equation:

 10s + 2o = 56 (Equation 1)

 From Adam's sales, we have the equation:

9s + 3o = 60 (Equation 2)

Let's use the elimination method.

3(10s + 2o) = 3(56)

30s + 6o = 168 (Equation 3)

 2(9s + 3o) = 2(60)

18s + 6o = 120 (Equation 4)

 Now we subtract Equation 4 from Equation 3 to eliminate o

(30s + 6o) - (18s + 6o) = 168 - 120

12s = 48

s = 4

 Now that we have the price of a pack of sugar cookies s=4  we can substitute this value back into either Equation 1 or Equation 2 to find the price of a pack of oatmeal cookies.

Let's use Equation 1:

10(4) + 2o = 56

o = 8

Answer:

The equation that represents this relation is y = 3x - 5

The relation is a function

If the domain of the relation is x > 2, the range of the relation is y > 1

Answer:

The equation that represents this relation is   y = 3x - 5 .

The relation is  a function.

If the domain of the relation is x > 2, the range of the relation is y >  1  .

Step-by-step explanation:

The output, y, of a relation, is the difference of three times the input, or 3x, and 5. So, y = 3x − 5.

Substituting any x-value from the domain into the equation will result in exactly one value of y, so the relation is a function.

To find the range of the relation, given the domain, substitute the boundary point of the domain into the function equation:

When x = 2, y = 3(2) − 5 = 6 − 5 = 1.

Because substituting values of x that are greater than 2 will result in values of y that are greater than 1, the range of the relation is y > 1.

Answer:

a) $ [tex]3.46[/tex]

b) Cost of one gallon of gas is Toronto, Canada is higher by $ [tex]1.17[/tex]

Step-by-step explanation:

Complete Question

One gallon of gasoline in Buffalo, New York costs $2.29. In Toronto, Canada, one liter of gasoline costs  $0.91. There are 3.8 liters in one gallon.

a. How much does one gallon of gas cost in  Toronto? Round your answer to the nearest  cent.

b. Is the cost of gas greater in Buffalo or in  Toronto? How much greater?

Solution

Given

Cost of one gallon of gasoline in Buffalo, New York [tex]= 2.29[/tex] dollars

Cost of one liter of gasoline in Toronto, Canada [tex]= 0.91[/tex] dollars

One gallon [tex]= 3.8[/tex] liters

Thus, [tex]1[/tex] liter [tex]= \frac{1}{3.8}[/tex] gallons

a) Cost of [tex]\frac{1}{3.8}[/tex] gallons of gasoline in Toronto, Canada [tex]= 0.91[/tex] dollars

Cost of [tex]1[/tex]gallons of gasoline in Toronto, Canada

[tex]=3.8 * 0.91\\= 3.458\\= 3.46[/tex]

b) Difference in price for a gallon of gas for the two locations

[tex]3.46 - 2.29 \\= 1.17[/tex]

Cost of one gallon of gas is Toronto, Canada is higher by $ [tex]1.17[/tex]

One gallon of gasoline costs $3.46 in Toronto after converting from liters using the 3.8 conversion factor. Comparing this to the cost in Buffalo, which is $2.29, shows that gasoline is more expensive in Toronto by $1.17 per gallon.

The question involves a mathematical calculation to compare the cost of gasoline in two different units of measure and currencies, one being in gallons in the United States and the other in liters in Canada.

To find the cost of one gallon of gasoline in Toronto, we use the given price per liter and the conversion factor between liters and gallons. Since there are 3.8 liters in a gallon, we multiply the cost per liter by 3.8. Therefore, the cost of one gallon of gasoline in Toronto is 0.91 dollars per liter times 3.8 liters per gallon, which equals $3.458. After rounding to the nearest cent, the cost is $3.46 per gallon.

To find the difference in price between Buffalo and Toronto, we subtract the cost in Buffalo from the converted cost in Toronto. Thus, $3.46 (Toronto) - $2.29 (Buffalo) equals $1.17, which means gasoline is more expensive in Toronto by $1.17 per gallon.

Answer:

6 jobs

Step-by-step explanation:

$2,400 - $1,600 = $800

$125 per job

$800 / $125 = 6.4 jobs

Estimated it is 6 jobs

There will be 6 jobs must he work in order to make a profit of at least $2,400.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷. The application of subtraction can be used broadly in different applications to find or solve the problems such as finding differences between two quantities and many more.

It is given that, Noe installs and configures software on home computers. He charges $125 per job. His monthly expenses are $1,600.

The amount that remains after subtracting profit from the monthly expenses is,

$2,400 - $1,600 = $800

If, he charges $125 per job. The number of jobs must he work in order to make a profit of at least $2,400

=$800 / $125

= 6.4 jobs

Thus, there will be 6 jobs must he work in order to make a profit of at least $2,400.

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Answer:

[tex]A=60^0, B=30^0, C=90^0\\a=3.46, b=2, c=4[/tex]

Step-by-step explanation:

In the diagram below:

First, we determine the value of [tex]\beta[/tex]

[tex]\alpha+\beta=90^0 $ (Other Angles of a Right Triangle)$\\60+\beta=90^0\\\beta=90^0-60^0=30^0[/tex]

To determine the value of side a, we apply the Sine rule

[tex]\dfrac{c}{Sin C} =\dfrac{a}{Sin \alpha} \\\dfrac{4}{Sin 90}=\dfrac{a}{Sin 60}\\ a=\dfrac{4*sin60}{sin 90}\\a=3.46[/tex]

Similarly, to determine the value of side b, we apply the Sine rule

[tex]\dfrac{c}{Sin C} =\dfrac{b}{Sin \beta} \\\dfrac{4}{Sin 90}=\dfrac{b}{Sin 30}\\ b=\dfrac{4*sin30}{sin 90}\\b=2[/tex]

Therefore:

[tex]A=60^0, B=30^0, C=90^0\\a=3.46, b=2, c=4[/tex]

This problem involving a right triangle with given values can be solved using the Pythagorean theorem and trigonometric identities. The final values for a, b and β are A=2√3, B=2 and Co = 30°.

In the given question, we are dealing with a right triangle where α=60°, β is the other acute angle and c=4. We can use trigonometric ratios and identities to solve for the unknowns.

Since sin(α)=a/c, we can find side 'a' by substituting α as 60° and c as 4. This gives us a=4sin(60°)=2√3.

Using the Pythagorean theorem a² + b² = c², we can substitute the values we know to solve for 'b'. This gives us b=√[c² - a²]=√[16 - (2√3)²] = √4 = 2.

For the angle β, since it is an acute angle in the right triangle and the sum of angles in a triangle is 180°, we have β= 180° - 90° - α = 180° - 90° - 60° = 30°.

Therefore, the values corresponding to a, b and β would be A=√3 (since a= 2√3), B=2 (since b=2) and Co = 30° (since β = 30°).

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Answer:

12

Step-by-step explanation: Because 12 old dolls - 6 dolls = 6 dolls. Then you add 6 old dolls and 6 new dolls and you get 12 old and new dolls. Sorry  if this is confusing. I tried to make it less confusing.

Answer:

On the 12th day after Lou starts they will be reading the same page

Step-by-step explanation:

Sabrina:

Write the equation for sabrina starting today

36+12d

Lou

Write the equation for lou

15d

Set them equal

36+12d = 15d

Subtract 12d from each side

36+12d-12d = 15d-12d

36 = 3d

Divide by 3

36/3 = 3d/3

12 =d

On the 12th day after Lou starts they will be reading the same page

Answer:

Yes,

12 days after Lou starts reading, they'll be on the same page

Step-by-step explanation:

36 is already read, 12 per day

36 + 12d

15 per day

15d

36 + 12d = 15d

3d = 36

d = 12

The expression '-7/8 - (-5/6)' simplifies to '-1/24' by eliminating the double negative and adding the fractions with a common denominator.

By concept of addition of fraction

To reduce the expression -7/8 - (-5/6) to its simplest form, we need to eliminate the double negative and add the two fractions. First, -(-5/6) becomes +5/6. Now you need to add -7/8 and 5/6, but they have different denominators. To add fractions, they must have the same denominator. The least common denominator (LCD) of 8 and 6 is 24. So, -7/8 becomes -21/24 and 5/6 becomes 20/24. Then, we add -21/24 and 20/24, which gives us -1/24. So, the simplest form of -7/8 - (-5/6) is -1/24.

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To simplify the expression -7/8 - (-5/6), we first convert it to -7/8 + 5/6 by removing the double negative. Then, we find a common denominator (24) and add the fractions to get -1/24, which is the simplest form of the expression.

To reduce the expression -7/8 - (-5/6) to its simplest form, we need to add the two fractions. Since we have a double negative in the second term, it becomes addition:

-7/8 + 5/6

To add fractions, we need a common denominator. The least common multiple of 8 and 6 is 24, so we convert each fraction:

(-7 times 3)/(8 times 3) + (5 times 4)/(6 times 4)

-21/24 + 20/24

Now we can add the numerators while keeping the denominator the same:

(-21 + 20)/24 = -1/24

Therefore, the expression simplifies to -1/24.

Answer:

A=Bh

the area of a parallelogram is base times height

Answer:

2300

Step-by-step explanation:

We are given that

Out of 200 , four ducks are tagged.

We have to find the number of ducks in the preserve if 46 ducks are tagged.

Let x be the number of ducks in the preserve.

If number of tagged ducks increases then number of preserved ducks also increases.It is in direct proportion.

According to question

[tex]\frac{x}{46}=\frac{200}{4}[/tex]

[tex]x=\frac{200\times 46}{4}[/tex]

[tex]x=50\times 46[/tex]

x=2300

Answer:

About 7,500 registered voters are expected to vote for the new dog park.

Step-by-step explanation:

- A town has 15,000 registered voters.

- A random sample of 200 voters shows that 100 voters are in favour of a new dog park.

How many registered voters are likely to vote for the dog park?

The laws of probability allows us to extrapolate and use the proportion of randomly sampled registered voters that vote for a new dog park to calculate the actual number of registered voters that will vote for a new dog park.

Proportion of randomly sampled registered voters that voted for a new dog park

= (100/200) = 0.50

Proportion of overall registered voters that will vote for a new dog park will also be 0.50.

Number of likely registers voters that'll vote for a new dog park = 0.50 × 15,000 = 7,500

Hope this Helps!!!

Approximately 7,500 registered voters are likely to vote for the new dog park

To determine how many of the 15,000 registered voters in a town are likely to vote for a new dog park based on a random sample, follow these steps:

Therefore, approximately 7,500 registered voters are likely to vote for the new dog park.

Answer:

251

Step-by-step explanation:

Answer:

251

Step-by-step explanation:

Hope tis helped brainliest is appreciated. :) stay safe

Answer:

1.80m + 3 ≤ 25

Step-by-step explanation:

We have a flat rate of $3, which means that's the base value. Now, we see that Jennifer has to pay $1.80 per mile, which means that when she has ridden m miles, she has to pay 1.80m. However, remember to add 3 to this:

1.80m + 3

Jennifer only has $25 to spend, so she can't spend any more than 25. This means that the money she can spend must be less than or equal to $25:

1.80m + 3 ≤ 25

Hope this helps!

Answer:

3 + 1.80m《25

m《12 2/9

Step-by-step explanation:

Fixed cost: $3

Per mile: $1.80

Cost for m miles:

3 + 1.80m

She can afford at max $25

3 + 1.80m《25

1.80m《22

m《12 2/9

Answer:

60%

Step-by-step explanation:

3

---

5

x 100% = 60%

The calculated percentage of 5 that is 3 is 60%

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

Percent of 5 is 3

This means that

x% * 5 = 3

So, we have

x% = 3/5

Evaluate the quotient of 3 and 5

x% = 0.6

Multiply through by 100

x = 60

Hence, the percentage of 5 that is 3 is 60%

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Answer:

13

Step-by-step explanation:

square root y^2 = square root 169

so

y = 13

Answer:

y=13

Step-by-step explanation:

y=square root of 169

y=13

Answer:

1. False 2. False 3. True 4. False 5. True

Step-by-step explanation:

Given:

Fred bought 4 liters of liquid laundry detergent,

3,260 millilitres of fabric softener, and

2.3 liters of bleach.

Select true or false for each statement.

1. Fred bought 96 millilitres more fabric softener than bleach.

Solution:

Fred bought fabric softener = 3,260 millilitres

Fred bought bleach = 2.3 liters = 2300 millilitres

1 liter = 1000 millilitres

2.3 liter = 1000 [tex]\times[/tex] 2.3 = 2300 millilitres

Fred bought more fabric softer than bleach = 3,260 - 2300 = 960

Hence, it is false and actually Fred bought 960 millilitres more fabric softer than bleach.

2. Fred bought 1.95 liters more laundry detergent than bleach.

Solution:

Fred bought laundry detergent = 4 liters

Fred bought bleach = 2.3 liters

Fred bought more laundry detergent than bleach = 4 - 2.3 = 1.7 liters

Hence, it is false and actually Fred bought 1.7 liters more laundry detergent than bleach.

3. Fred bought 960 millilitres more fabric softener than bleach.

It is true, as solved above:

4. Fred bought 170 millilitres more laundry detergent than bleach.

Solution:

Solved above:

Fred bought 1.7 liters more laundry detergent than bleach.

1.7 liters = 1.7 [tex]\times[/tex] 1000 = 1700 millilitres

1.7 liters = 1700 millilitres not 170 millilitres

Hence, it is false.

5. Fred bought 0.96 liters more fabric softener than bleach.

Solution:

Solved above:

Fred bought 960 millilitres more fabric softer than bleach.

1000 millilitres = 1 liters

1 millilitre = [tex]\frac{1}{1000}[/tex]

960 millilitre =  [tex]\frac{1}{1000}\times960=\frac{960}{1000} =0.96\ liter[/tex]

960 millilitres = 0.96 liter

Hence, it is true.

Upon converting all quantities to millilitres, Fred bought 960 millilitres more fabric softener than bleach, which is also 0.96 litres more. The other statements comparing millilitres and litres of purchased items are false.

Let's address each statement one by one and convert all measurements to the same unit (millilitres) for consistency:

Fred bought 4 litres of liquid laundry detergent: 1 litre = 1000 millilitres, so 4 litres = 4000 millilitres.

Fred bought 3,260 millilitres of fabric softener.

Fred bought 2.3 litres of bleach: 2.3 litres = 2300 millilitres.

Now, we can compare Fred's purchases:

Fred bought 96 millilitres more fabric softener than bleach: 3,260 millilitres (fabric softener) - 2,300 millilitres (bleach) = 960 millilitres more, not 96. False.

Fred bought 1.95 litres more laundry detergent than bleach: 4 litres (detergent) - 2.3 litres (bleach) = 1.7 litres more, not 1.95. False.

Fred bought 960 millilitres more fabric softener than bleach: As calculated earlier, this is True.

Fred bought 170 milliliters more laundry detergent than bleach is incorrect because the difference is actually 4 liters - 2.3 liters which is significantly more than 170 milliliters. False.

Fred bought 0.96 litres more fabric softener than bleach: Since we have established that he bought 960 millilitres (or 0.96 litres) more of fabric softener, this is True.

Answer:

Step-by-step explanation:

105.80 + 64.20 = 170 +57 = 227

= $46

Answer:

0.99 probability that at least one trip will last less than an hour

Step-by-step explanation:

For each time that the machine is used, there are only two possible outcomes. Either it lasts more than an hour, or it does not. The probability of a trip lasting more than an hour is independent of other trips. So the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

0.8 probability of lasting more than one hour.

So [tex]p = 0.8[/tex]

20 trips

So [tex]n = 20[/tex]

Assuming that each trip is equally likely to last for more than an hour, what is the probability that at least one trip will last less than an hour?

Either all the trips last for more than an hour, or at least one does not. The sum of the probabilities of these outcomes is decimal 1. So

[tex]P(X = 20) + P(X < 20) = 1[/tex]

We want P(X < 20). So

[tex]P(X < 20) = 1 - P(X = 20)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 20) = C_{20,20}.(0.8)^{20}.(0.2)^{0} = 0.0115[/tex]

[tex]P(X < 20) = 1 - P(X = 20) = 1 - 0.0115 = 0.9885[/tex]

0.9885 probability that at least one trip will last less than an hour

Rouding to the nearest hundreth.

0.99 probability that at least one trip will last less than an hour

Answer:

step1

3520268-3433145

step 2

answer after subracting divide that answer by the total area of the texas

Answer:

18:24 or simplest form is 3:4

Step-by-step explanation: If you don't need to simplify then it is 18:24, but if you simplify it by dividing 18 and 24 by 6, then the answer is 3:4 :)

Answer:

18:24 18 to 24 so 3:4

Step-by-step explanation:

Answer:

height= 9 cm

Step-by-step explanation:

Final answer:

The height of the cylinder is 9 cm.

Explanation:

The volume of a cylinder can be calculated using the formula V = Ah, where A is the base area and h is the height. In this case, the volume V is given as 198 cm3 and the base area A is given as 22 cm^2. To find the height, we can rearrange the formula as h = V/A:

h = 198 cm^3 / 22 cm^2 = 9 cm

Therefore, the height of the cylinder is 9 cm.

They're trying to trick you with √2.  Remember in the 30/60/90 triangle the sides are in ratio 1:√3:2, with the "1" opposite the 30 degrees.

Here we have

1:√3:2  = 6√2:x:hypotenuse

or

x/(6√2) = √3/ 1

x = 6√2×√3 = 6√6

Answer: AC=6√6

Answer:

x=2   if i can have brainliest that would be great

Step-by-step explanation:

4x+6+3=17

(4x)+(6+3)=17(Combine Like Terms)

4x+9=17

4x+9=17

Step 2: Subtract 9 from both sides.

4x+9−9=17−9

4x=8

Step 3: Divide both sides by 4.

4x/4=8/4

x=2

y = mx + b

When a function is reflected over the y-axis, the b (2) stays the same but the slope (m) changes to its opposite sign.

since the slope is negative in this equation, it will become positive.

so the new fuction will be

y = 5x + 2

The function y = -5x + 2 when reflected over the y-axis changes to y = 5x + 2 because we change the sign of 'x' in the original equation.

To reflect a function over the y-axis, we replace x with -x in the original function. The function y = -5x + 2 reflects to y = 5x + 2 when reflected over the y-axis.

The original function y = -5x + 2 is transformed by reflecting it over the y-axis, which means we change the sign of 'x' in the original equation. In a reflection over the y-axis, any 'x' in the equation becomes '-x'. The original function is y = -5x + 2, so we replace 'x' with '-x'. Consequently, the equation of the new function after reflecting over the y-axis would be y = -5(-x) + 2, which simplifies to y = 5x + 2.

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Answer:

50 questions x 10 points = 500 points

500 points x 2 years = 1000 points

365 days / 2 = 182 1/2 days

182 1/2 days x 2 years = 365 days

Answer:

2 years

Step-by-step explanation:

The given question is incomplete. The complete question is:

The test scores of 40 students are summarized in the frequency distribution below a summarized in the given frequency distribution. score Find the mean Score Students 50-59 (5) 60-69(15) 70-79(6) 80-89(5) 90-99(9)

A) 70.3 B) 74.0 ) 74.5 D) 66.6

The correct option is B.

Step-by-step explanation:

Given,

Data              Frequency      

50-59                   5                    

60-69                   15                    

70-79                   6                      

80-89                   5                    

90-99                   9                      

To find the mean of given data.

Formula

Mean = Sum of ( Freq× Mid point)÷ total frequency

Data              Frequency       Mid internal         Freq× Mid point

50-59                   5                      54.5                      272.5

60-69                   15                     64.5                      967.5

70-79                   6                       74.5                      447

80-89                   5                      84.5                       422.5

90-99                   9                      94.5                      850.5

Now,

Sum of ( Freq× Mid point) = 2960

Number of students = 40

So,

Mean = 2960÷40 = 74

The correct option is B.

To find the mean of the test scores, add up all the scores and divide by the total number of scores.

To find the mean of the test scores, we need to add up all the scores and divide by the total number of scores. In this case, we have 40 students, so we add up all the scores: 15.5 + 70.3 + 14.1 + 13.3 + ... (continue adding up all the scores). Once we have the sum of all the scores, we divide by 40 to find the mean.

Let's assume that the sum of all the scores is 1000 (this is just an example). We would then divide 1000 by 40 to get the mean: 1000 ÷ 40 = 25. Therefore, the mean of the test scores is 25.

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Answer:

4320 ways.

Step-by-step explanation:

Question asked:

Find the number of ways all 10 letters of the word COPENHAGEN can be arranged so that (i) the vowels (A, E, O) are together and the consonants (C, G, H, N, P) are together,

Solution:

By using Permutation formula:

[tex]^{n} P_{r} \ =\frac{n!}{(n-r)!}[/tex]

[tex]''n'' \ is\ the\ number\ of\ letters\ taking\''r'' at\ a\ time.[/tex]

CGHNP AEO EN

Total number of letters  = 10

Let consonant (CGHNP) = C

And vowel (AEO) = V

Now we have only four letters CVEN

We can arrange this 4 letters in = [tex]^{4} P_{4} \ ways\\ \\[/tex]

                                                     [tex]=\frac{4!}{(4-4!)} \\ \\ =\frac{4!}{(0!)}\\ \\ =4\times3\times2\times1=24\ ways[/tex]

Consonants having 5 letters arrange themselves in = [tex]^{5} P_{5} \ ways\\ \\[/tex]

                                                                                      [tex]=\frac{5!}{(5-5)!} \\ \\ =\frac{5\times4\times3\times2\times1}{0!} \\ \\ =120\ ways[/tex]

Vowels having 3 letters arrange themselves in  = [tex]^{3} P_{3} \ ways\\ \\[/tex]

                                                                               = [tex]=\frac{3!}{(3-3)!} \\ \\ 3\times2\times1=6 \ ways[/tex]  

Repeated letter :-

E = 2 times in [tex]^{2} P_{2} \ ways=2\ ways[/tex]

N = 2 times in 2  ways

Total arrangements of repeated letters = 2 [tex]\times[/tex] 2 = 4 ways

Total number of ways = [tex]\frac{24\times120\times6}{Repated\ letters\ arrangements}[/tex]

                                    = [tex]\frac{17280}{4} =4320\ ways[/tex]

Therefore, the number of ways all 10 letters of the word can be arranged in 4320 ways.

Final answer:

To answer the question, there are 1440 different ways to arrange the letters of the word COPENHAGEN with the vowels and consonants grouped together, by factoring in permutations of each subset and the complete grouping.

Explanation:

The student has asked us to find the number of ways to arrange the letters of the word COPENHAGEN so that the vowels and consonants are grouped together. To solve this, we can use combinatorial mathematics to calculate permutations.

Step 1: Grouping the vowels together

We have three vowels: A, E, and O. We will consider them as a single entity for now. Therefore, the group of vowels can be arranged in 3! (three-factorial) ways, which means 3 times 2 times 1 = 6 ways.

Step 2: Grouping the consonants together

We have five consonants: C, G, H, N, and P. They can be arranged in 5! (five-factorial) ways, which equals 5 times 4 times 3 times 2 times 1 = 120 ways.

Step 3: Arranging the two groups

Now, our word is represented as a combination of two groups: the vowel group and the consonant group. These two groups can be arranged in 2! ways, which is 2 times 1 = 2 ways.

Step 4: Calculating the total arrangements

To find the total number of arrangements, we multiply the permutations from each step together:
6 (vowels) times 120 (consonants) times 2 (groups) = 1440.

Therefore, there are 1440 different ways to arrange the letters of the word COPENHAGEN with the vowels and consonants grouped together.

Answer:

4 units

Step-by-step explanation:

Answer:

C. [tex]\sqrt{98}[/tex]

Step-by-step explanation:

This is the answer