How many permutations are there of the letters APPLE, if the arrangement must begin with a
vowel and end with a consonant?

Answers

Answer 1

Answer:

[tex]18[/tex].

Step-by-step explanation:

Start by considering the two "[tex]\verb!P![/tex]"'s as being different from one another. That way, all five letters in this word would be distinct. With this assumption, the number of arrangements would be [tex]\left(\genfrac{}{}{0}{}{2}{1}\right) = 2[/tex] times that of the actual value.

Start by fixing the first and the last letter since they come with special requirements.

There are [tex]2[/tex] choices for the first letter (the vowel: [tex]\verb!A![/tex] and [tex]\verb!E![/tex].)

Under the assumption that the two "[tex]\verb!P![/tex]"'s are distinct, there would be [tex]3[/tex] choices for the last letter ([tex]\verb!L![/tex] and the two

After choosing the first and the last letters, there would be [tex](5 - 1 - 1) = 3[/tex] choices for the second letter, [tex](3 - 1) = 2[/tex] choices for the third, and [tex](2 - 1) = 1[/tex] for the fourth.

Thus, under the assumption that the two "[tex]\verb!P![/tex]"'s are distinct, there would be [tex](2 \times 3) \times (3 \times 2 \times 1) = 36[/tex] ways to choose the new word. Since this assumption doubles the number of arrangements, dividing the [tex]36[/tex] by [tex]\left(\genfrac{}{}{0}{}{2}{1}\right) = 2[/tex] would give the actual number of arrangements:

[tex]\begin{aligned}\frac{36}{\genfrac{(}{)}{0}{}{2}{1}} = \frac{36}{2} = 18\end{aligned}[/tex].

[tex]\begin{aligned}& 1 && \verb!APPEL!\\& 2 && \verb!APLEP!\\& 3 && \verb!APEPL!\\& 4 && \verb!APELP!\\& 5 && \verb!ALPEP!\\& 6 && \verb!ALEPP!\\& 7 && \verb!AEPPL!\\& 8 && \verb!AEPLP!\\& 9 && \verb!AELPP!\\& 10 && \verb!EAPPL!\\& 11 && \verb!EAPLP!\\& 12 && \verb!EALPP!\\& 13 && \verb!EPAPL!\\& 14 && \verb!EPALP!\\& 15 && \verb!EPPAL!\\& 16 && \verb!EPLAP!\\& 17 && \verb!ELAPP!\\& 18 && \verb!ELPAP!\end{aligned}[/tex].


Related Questions

GIVING BRAINLIEST

In the figure below, if AB=11√7 , what is CD?

Answers

 CD is 11 square root of 14.  

The measure of the side length CD in the given right angled triangle as per the measurements is equal to option C. 11√14 .

In right triangle ABE,

Measure of angle ABE = 90 degrees

Measure of angle AEB = 60 degrees

AB = 11√7

Using trigonometric ratio we have,

tan 60° = AB / BE

⇒ √3 = 11√7 / BE

⇒ BE = 11√7 / √3

⇒BE = 11√21 / 3

In right triangle BED,

Measure of angle BED = 90 degrees

Measure of angle EBD= 45°

⇒Measure of angle EDB= 45°

BE ≅ ED

BE = 11√21 / 3

⇒ED = 11√21 / 3

Using Pythagoras theorem,

BD² = BE² + ED²

⇒BD = √ 2 (11√21 / 3 )²

⇒BD = 11√21 / 3 × √2

⇒ BD = 11√42 / 3

In right triangle CDB,

Measure of ∠CDB = 90°

Measure of ∠DCB = 30°

tan 30° = BD / CD

⇒ ( 1/ √3) = 11√42 / 3 / CD

⇒ CD =  [11√42 / 3 ] × √3

⇒ CD = 11√14

Therefore, the length of the side CD in the triangle is equal to option C. 11√14 .

learn more about length here

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y + 2x = 2 and y + 4x = 0?

Answers

Answer:

y=4

Step-by-step explanation:

   y+2x=2

2(y+2x)=2(2)

 2y+4x=4

(2y+4x)-(y+4x)=4-0

                    y=4

Michael can swim 5 lengths of a swimming pool in 130 seconds.
Use this information to show that he could swim 100 lengths in under 45 minutes

Answers

Answer:

Yes, he can swim 100 lengths in under 45 minutes.

Step-by-step explanation:

First we divide 100 by 5

100 ÷ 5 = 20

Now we can multiply this by 130 seconds

Now we have 2600 seconds

Since 1 minute is 60 seconds we divide 2600 by 60 seconds

2600 ÷ 60, this gets us 43.33... minutes, which is less than 45 minutes.

This is all assuming his rate is constant.

Micheal takes 43.333 minutes to swim 100 lengths.

What is length?

Length is a measurement or extent of something from one end to another end.

The SI unit of length is meter.

Given that,

To cover 5 lengths, time taken by Micheal =  130 seconds,

Therefore,

Time taken by Micheal to cover 1 length = 130/5 = 26 seconds

Time to cover 100 length = 26×100=2600 seconds

1 minute = 60 seconds

100 length is covered = 2600×1/60 minute

                                    = 43.333 minute

So, To swim 100 lengths Micheal takes 43.333 minutes, which is under 45 minutes.

To know more about Length on :

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Today, Petland sold 8 times as many dogs as cats. If a total of 72 dogs and cats were sold, how many cats were sold?

Answers

72 divided by 8 is 9.

9 cats were sold

If represents the number of entry tickets sold and the hours of space rental, which inequality represents the constraints in the situation

Answers

2000000000017827272626728182

Answer:

no question or any number or question available

1. Two angles added together to produce 90 degrees a) Supplementary b) Complementary c) Right od) Vertical​

Answers

Answer: B: complementary

Step-by-step explanation: :)

Evaluate a + b + cd if a = 7/8 b = -7/16 and c= .8 d = 1/4 Write your answer as a fraction in simplest form.

Answers

Refer to the attachment

Si se duplica el radio(2) del círculo anterior, el número de veces que aumenta el area del círculo es?

Answers

Answer:

4

Step-by-step explanation:

The price of the trail mix at the health food store is $7.50 per pound at this rate what is total cost of 8 ounces bags of trail mix

Answers

Answer:

Below

Step-by-step explanation:

1 pound = 16 ounces

Therefore if you're looking for 8 ounces, divide $7.50 in half.

You get $3.75

Answer:

At this rate, the total cost of 8 ounce bag of trail mix would be $3.75.

Step-by-step explanation:

So first I found that for 1 LB (pound), there is 16 ounces so 8 oz is half of 16. If we know that, we have to divide 7.5 by 2 to get 3.75.

BRAINLIEST
please help me finish these

Answers

Answer:

15) 44.6 inches

16) 77.8 degrees

Step-by-step explanation:

15) we are given the angle and length of 16, drawing this out, 16 inches (the height) would be opposite of the angle and the length of the ramp would be hypotenuse.

we know that sine is opposite over hypotenuse, so we can use that to help find the length.

Rearrange:

sin21degrees = opposite/hypotenuse

hypotenuse*sin21degrees = opposite

hypotenuse = opposite/sin21degrees

Sub in values:

hypotenuse = 16/sin21degrees

hypotenuse = 44.6468 inches

16) we are given two side lengths and expected to find an angle, we now need to use the inverse of one of the trigonometric ratios.

Drawing this out, we are given the hypotenuse and adjacent lengths, so we can use the inverse cosine to find the angle

angle = cos^-1 adjacent/hypotenuse

angle = cos^-1 (7/26)

angle = 74.381 degrees

please, help!!!! Bussines Calc. I give 20 points. I need a full explanation.

Answers

I believe you are trying to find the most Cheapest cost?

Since the area had to be 1200m^2 the most biggest numbers we could divide with is 30 x 40, which equals to 1200.

30 x 20 (expensive one the lower) = 600 (wall 3) + 20 x 20 = 1000 (wall 3 + wall 1)

40 x 13 (cheapter one the higher) = 520 (wall 4) + 32 x 13 = 936 (wall 4 + wall 2)

Add all together, $1936 to build the whole fence.

(I don't know for sure if I am right. If I am right, can I have a brainliest?)

10+5-7=3y

-10x+5x+5=-15

3x+2x-4x+10

pre algebra 8th grade math

Answers

Answer:

1) y=8/3=2 2/3   2) x=4    3) x+10

Step-by-step explanation:

1) 10+5-7=3y

Calculate the sum or difference.

8=3y

Swap the sides of the equation.

3y=8

Divide both sides by 3.

y=8/3=2 2/3

2) -10x+5x+5=-15

Collect like terms.

-5x+5=-15

Move the constant to the right-hand side and change the sign.

-5x=-15-5

Calculate the difference.

-5x=-20

Divide both sides by -5.

x=4

3) 3x+2x-4x+10

Collect like terms.

(3+2-4)x+10

Calculate the sum or difference.

1x+10

When the term has a coefficient of 1, it doesn't have to be written.

x+10

Hope this helps :)

A recipe calls for

23

cup of sugar for every 4 teaspoons of vanilla. How much vanilla should be used for every 1 cup of sugar?

Answers

Answer:

.....

Step-by-step explanation:

Use the pattern in the sequence to determine the next two terms.

-16, 8, -4, 2. . .

Answers

Answer:

-1 , 1/2

Step-by-step explanation:

Each term is obtained by dividing by (-2)

-16/-2 = 8

So, the next two terms are:

2/-2 = -1

-1/-2 = 1/2

solve pls brainliest

Answers

Answer:

48.95

Step-by-step explanation:

A city council acquired 3,437.5 acres of land to add to their park system. The city plans to divide the acreage evenly into 22 separate parks.
There will be ___ acres in each park.

please help

Answers

there will b 156.2 acres in each park. hope this helps!!

Please help me with this, im kinda struggling

Answers

Answer:

X=4

Step-by-step explanation:

Let's make an equation,

7/4 ÷ 14 = x ÷ 3

We can cross multiply

7/4 * 32 = x * 14

Now we have 56 = 14x

Divide both sides by 14

56 ÷ 14 = 4, 14x ÷ 14 = x

4 = x

x = 4

Use the quadratic formula to solve x2 – 3x - 2 = 0

Answers

Answer:

C

Step-by-step explanation:

C

Answer:

c

Step-by-step explanation:

c is the answer to this problem

Use elimination to solve the system of equations.
x+y=−3
2x−3y=29

Answers

Answer:

(4,-7)

Step-by-step explanation:

Answer:

(4,-7)

Step-by-step explanation:

2x-3y=29

2x+2y=-6

subtracting gives us -5y=35 so y is -7 and x-7=-3 so x is 4. therefore the ordered pair is (4,-7)

Blake was listening to his favorite radio station. He noticed that during one hour, 15 songs were played and 3 of them were by a group from Michigan.

A. What is the ratio of songs by the group from Michigan to the number of songs played?


B. Write the ratio in simplest form.


C. Suppose the station continues to play the ratio of songs. How many songs from the Michigan group will Blake hear in the next three hours?

Answers

Answer:

Step-by-step explanation:

A. What is the ratio of songs by the group from Michigan to the number of songs played?  3/15

B. In lowest terms, 3/15 is 1/5.

C. Suppose the station continues to play the ratio of songs. How many songs from the Michigan group will Blake hear in the next three hours?  To answer this, multiply the 1-hour unit rate by 3:  3*3 = 9 Michigan group songs over the next 3 hours.

it takes 3 brick layers 2 hours to build a wall how long would it take 4 brick layers
please show steps in ratio​

Answers

Answer:

Ratios are basically proportions so in this scenario

We can make it…

brick layers : hours

We’re given the first one which is

3:2

Whilst the one we need to find is only given for brick

For the unknown hours we can make it “x”

4: x

Now we have 2 ratios

3:2

4:x

Now these are fractions and we can make them equal to each other by

3/2 = 4/x

Now cross multiply to solve for x

3x=8

2 2/3 = x

So 2 2/3 hours

ABC is a triangle
AB = AC and BA is parallel to CD
Work out the size of the angle marked x

Answers

Step-by-step explanation:

so as ∆BCE is a right angled triangle

angle BEC = 90°

angle CBE = 22° (given)

apply angle sum property of triangle

so according to that

BCE + CBE + ECB = 180

22° + 90° + ECB = 180

102° + ECB = 180

ECB = 180 - 102

ECB = 78°

and also we know, that exterior angle of a triangle is equal to 2 interior angle of triangle,

so ,

x = 78°

hope this answer helps you dear! take care

Find the slope of the line that passes through point A (-2,0)and point B (0,10) using m=rise/run

Answers

Answer:

m = 5

Step-by-step explanation:

The x-coordinate of A is -2 and that of B is 0.  The increase in this coordinate from A to B is 2.  Similarly, the y-coordinate increases by 10.  The slope is therefore m = rise / run = 10/2, or m = 5

Write the expression 83⋅83⋅83⋅83⋅83⋅83 as a power.Enter your answer by filling in the boxes.$$

Answers

Answer:

It's (8/3) 6  I took the test and that was the answer. Your Welcome!!!!!!!!!!!!!

Answer:

Its 83 the power of 6. Also Please choose my anwer as brainliest

During a closeout sale, some television models are discounted 40%. If a television is on sale for $1,485, what is the original price of the television to the nearest dollar?

Answers

Answer: it should be 70

Step-by-step explanation:

because the re adding of the dollars

$2079


1485 x 1.4 = 2079


Can anyone help me with this?

Answers

Answer:

A & C are correct.

Step-by-step explanation:

Yes, I can help!

Absolute value makes any number positive.

12 < 50 (yes)

12 < 50 (yes)

12 > 50 (no)

12 > 50 (no)

You are welcome!

Kayden Kohl

8th Grade Student

Nadine plans to ride her bike between 12 mi and 15 mi. Write and solve an inequality to model how many hours she will be riding if she will be riding at a rate of 10 mph

Answers

Answer:

inequality is:12 ≤ x ≤ 15

Step-by-step explanation:

Three bowls of frozen yogurt cost 8.25. At the same rate how much do 9 bowls of frozen yogurt cost.

Answers

Answer:

$24.75

Step-by-step explanation:

$8.25 is for 3. So triple that cost gets you $24.75

PLS HELP ASAP ILL GIVE BRAINLKEST

Answers

Answer:

number 5

Step-by-step explanation:

an equal sign means "is not equal to"

A student solved a system of equations by elimination. The answer is not correct. Describe the error in the solution.

Original Problem:

3x−2y=8

x+y=2

Student Work:

3x−2y=8

2x+2y=2

5x=10

x=2

Answers

The student went from x+y = 2 to 2x+2y = 2, which is not correct. They multiplied the left side by 2, but forgot about the right hand side.

They should have gone from x+y = 2 to 2x+2y = 4 after multiplying both sides by 2.

So they should have this new equivalent system

[tex]\begin{cases}3x-2y = 8\\2x+2y = 4\end{cases}[/tex]

Add straight down and we end up with the new equation 5x = 12 which solves to x = 12/5 = 2.4

Use that x value to solve for y. You should get y = -2/5 = -0.4

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