amara needs to create a special tasting menu at her restaurant. She needs to select 4 dishes from 7 available dishes and put them in a tasty sequence. How many unique ways are there to arrange 4 of the 7 dishes?

Answers

Answer 1

By taking in mind the number of combinations of 4 out of the 7 dishes, and the possible orders of these 4 dishes, we will find that there are 840 unique ways to arrange 4 of the 7 dishes.

We know that if we have a set of N elements, the total number of different combinations of K elements (K ≤ N) out of the N elements is given by:

[tex]C(N, K) = \frac{N!}{(N - K)!*K!}[/tex]

In this particular case, we have:

N = number of available dishes = 7K = number that we need to select = 4

Then the number of different combinations is given by:

[tex]C(7, 4) = \frac{7!}{(7 - 4)!*4!} = \frac{7*6*5}{3*2} = 35[/tex]

Now we have 4 dishes selected, but we also need to order them.

For the first dish, there are 4 options.For the second, there are 3 options (as one was already selected).For the third, there are 2 options.For the last one there is only one option.

The number of different arrangements of the dishes is given by the product between the numbers of options above, this gives:

4*3*2*1 = 24

Then the total number of unique ways of arranging 4 of the 7 dishes is:

C = 24*35 = 840

Where we take in mind the possible number of combinations of 4 out of the 7 dishes, and the possible orders of these 4 dishes.

If you want to learn more, you can read:

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Related Questions

Calcular la masa que tiene un cuerpo que se le aplica una fuerza que empuja al lado derecho de 230 N y otra fuerza que empuja al lado izquierdo de - 150N. Considerar que la aceleración que adquiere es de 2 m/s2.​

Answers

Answer:

Calculate the mass of a body that is applied with a force that pushes the right side of 230 N and another force that pushes the left side of - 150N. Consider that the acceleration it acquires is 2 m / s2.

Step-by-step explanation:

230 e dos

If the terminal side of angle θ passes through a point on the unit circle in the first quadrant where y=2√2, what is the exact measure of θ? Give your answer in radians.

Answers

Answer:

Please double check the question

y = 2√2 is not on the unit circle

The exact measure of the angle is 45°. If the terminal side of angle θ passes through a point on the unit circle in the first quadrant where y=2√2,

How to get the angle?

A Unit circle is defined as a circle having a radius of 1 unit and having its center at the origin.

We know that the terminal side passes through a point of the form (√2/2, y).

Notice that the point is on the unit circle, so its module must be equal to 1, so we can write:

[tex]1=\sqrt{(\dfrac{\sqrt{2}}{2})^2+y^2}[/tex]

[tex]1^2=\dfrac{2}{4}+y^2[/tex]

[tex]1-\dfrac{1}{2}=y^2[/tex]

[tex]Y=\dfrac{1}{\sqrt{2}}[/tex]

We know that y is positive because the point is on the first quadrant.

Now, we know that our point is:

(√2/2, 1/√2)

And we can rewrite:

√2/2 = 1/√2

So the point is:

( 1/√2,  1/√2)

Finally, remember that a point (x, y), the angle that represents it is given by:

θ = Atan(y/x).

Then in this case, we have:

θ = Atan(1/√2/1/√2) = Atan(1) = 45°

If you want to learn more about angles, you can read:

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60. Write the equation of a line through the point (-2,6) with a slope -5.

Answers

Answer:

y = - 5x - 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - 5 , then

y = - 5x + c ← is the partial equation

To find c substitute (- 2, 6 ) into the partial equation

6 = 10 + c ⇒ c = 6 - 10 = - 4

y = - 5x - 4 ← equation of line

William sold half of his comic book collection then purchased 10 more. He now has 24 comic books . How many books did William begin with?

Answers

Answer:

28

Step-by-step explanation:

24-10=14

14x2=28

Answer:

willaim had 28 comic books to begin with

Step-by-step explanation:

So we can take 24-10=  to see how many comics he had before his total of 24  which :

24-10=14

Then we want to find how many he had in the beging so to reverse division we would use multiplication so we would do 14x2=  because a half x a half will equal a whole :

14x2=28

So therefor William started of with 28 comic books

What is the slope of the line ?

Answers

The slope at the line would be the 360 point turn.

The slope of the line would be 2/3, I think… I can’t really tell because the image is bad quality.

If you can put up a better image or tell me two ordered pairs from the line, I can give you the slope. :)

SOMEONE HELP ME WITH THIS PLS

Answers

Answer:

D

Step-by-step explanation:

You add the "columns."  The equations are arranged so that like terms are stacked vertically.  3x and 7x are like terms; when you add them, you get 10x.

-y and y are like terms; when you add them, you get 0 (that doesn't appear in the sum).

-5 and 15 are like terms; add them to get 10.

The sum of the two equations is the equation 10x = 10.

Given h(t) = -2(t+ 5)^2 +4, find h(-8).

Answers

Answer:

Substitute -8 as x into the equation.

h(-8)=-2(-8+5)^2+4

h(-8)=-2(-3)^2+4

h(-8)=-2(9)+4

h(-8)=-18+4

h(-8)=-14

:)

BRAINLIEST TO WHOEVER ANSWERS RIGHT

Answers

Answer:

the answer is -1  have a great day!

Step-by-step explanation:

Answer:

its D

D = I

Step-by-step explanation:

The powers of i repeat in cycle of 4. For example, here are the first 4:

1: i

2: -1

3: -i

4: 1

If a number is divisible by 4, i to the power of that number would be 1. So, i^20 is 1, but we are multiplying it by i again, so the answer would be 1 * i = i

Got the answer from aklee18oo from brainly give him some credit

8x + 1/3 = 2/3 what is the answer?

Answers

Answer:

1/24

Step-by-step explanation:

8x + 1/3 = 2/3

    - 1/3   - 1/3

8x = 1/3

8x/8 = (1/3)/8

x = 1/24

solve pls brainliest

Answers

Answer:

for the first one it 2

3

12

Please answer number 8

Answers

Answer:

d q knows

Step-by-step explanation:

sory need points

If Isabella runs 23 mile each day, how many miles will Isabella run in 6 days?

Answers

Answer:

[tex]138[/tex] miles in 6 days

Step-by-step explanation:

Our [tex]Rate[/tex] is [tex]23[/tex] miles per day.

Definition

Rate in Math - The speed of something happening in a certain amount of time, it is usually consistent.

Rate in Physics - Rate means rate of change. Basically, how much a certain quantity changes with respect to another quantity that is also changing. You may also sometimes hear the term gradient which describes the same thing.

To find how many miles she will run in 6 days we will multiply our [tex]Rate[/tex] by our Time, to find our distance, [tex](Miles, Physics)[/tex]

Our equation

[tex]23\cdot6[/tex]

Solve

[tex]138[/tex] miles in 6 days

Brainliest please :)

plz answer this question fast

Answers

Nsnsjdksbvdjdosjsbhs

ayo is 37 years old and Abdul salami is 6 years old. how many years ago was the product of their ages 96​

Answers

It wouldn’t be possible as when you do 36x5, 35x4, 34x3, 33x2, 32x1 or 31x0, none of these actual make 96 so it would be impossible.

Does anyone know this?

Answers

Answer:

I think 7.6 i remember i had something like this  

Step-by-step explanation:

A garden supply store spends $750 on an order. They spend $250 on potting supplies
and buy plants that cost $25 each. How many plants do they buy?

Answers

Answer:

They bought 20 plants

Step-by-step explanation:

If you minus the total 750- 250 of potting supplies it leaves you with 500.

Divide 500/ 25 = 20

Answer:

20 plants

Step-by-step explanation:

500 divided by 25 = 20

have a nice day

The weight of an object on the moon is
1 of its weight on Earth. If a moon rock
weighs 20 lb on Earth, how much did
the moon rock weigh on the moon?

Answers

Answer:

10 lb on planet earth which turns very slowly

Answer:

10 pounds on planet earth which turns very slowly

Step-by-step explanation:

So There Are 3 Dogs In 25 Parks How Many Dogs In Parks Are There So This Is 3×25=? I mean It's Ez ​

Answers

Answer: You are right! Just multiply for your answer!

Step-by-step explanation:

The answer is 25•3 is 75

19+0.12x=0.16x

This whole entire unit is pretty simple, but apparently my brain won't think.

Could you please help? ​

Answers

Answer:

0.04x = 19

x = 475

Step-by-step explanation:

19 + 0.12x = 0.16x

Take away 0.12x from both sides

19 = 0.04x

Divide 19 by 0.04 to find x

x = 475

Answer:

475

Step-by-step explanation:

First, you have to simplify the equation by moving all the like terms to one side of the equal sign.

This entails the taking of 0.12x to the right side of the equal sign.

Remember, when we take anything over the equal sign if it was a positive sign like in this case, it becomes a negative one and the opposite is true if the sign was negative.

So we have

19=0.16x - 0.12x

We then simplify further and get the equation

19=0.04x

To obtain the true value of x, we divide both sides of the equation by 0.04x as follows:

19/0.04=0.04x/0.04

We then find that

x= 475

The expression 13x + 5 represents the number of marbles you have after purchasing 13 bags of marbles.

What does the term 13x represent?
What does 5 represent?
What does x represent

Answers

13x represents the number of marbles in all the bags purchased combined. 5 is the amount of marbles you already own. X represents the amount of marbles in the bag.

The weight of an object on the moon is
1 of its weight on Earth. If a moon rock
weighs 203 lb on Earth, how much did
the moon rock weigh on the moon?

Answers

Answer:

The answer would be 124.4

Step-by-step explanation:

The simple answer is 124.4 lb on the moon it would way the explation behind this is that the moons gravity is 1.62m/s so dividing that by 1.62 it would be 12.4.4 lb but because of the moons twist on it's axes would make it 90 Ib

Hope this helps :)

what is the meaning of decimal explain

Answers

Answer:

ddecimal is a fraction

Step-by-step explanation:

Oh a decimal is a fraction written in a special form

Lamis purchased n notebooks. They were 5 dollars each. Write an equation to represent the total cost c that Lamis paid.

Answers

N x 5 = c hope this helps!
n5=c

n=number of notebooks
c=total cost

A check for two hundred fifty dollars as a withdrawal:

Answers

A check for $250 serves as an instruction to the bank to withdraw that amount from the account holder's balance and provide it to the recipient upon deposit or cashing.

When a check is written for two hundred fifty dollars ($250) as a withdrawal, it means that the individual is requesting a withdrawal of $250 from their account using a check.

The check serves as a formal written order instructing the bank to pay the specified amount, which in this case is $250, to the person or entity named on the check. The account holder will typically write the check and provide it to the recipient as a means of transferring funds.

The recipient can then deposit or cash the check at their bank, and the bank will process the transaction by deducting $250 from the account holder's bank balance and providing the recipient with the requested funds.

for such more question on transaction

https://brainly.com/question/1016861

#SPJ8

1. Mark each of the following graphs as (a) a function, but not one-to-one, (b) one-to-one function, or (c) not a function. In each case, explain how you know. (1 point each)​

Answers

Answer:

  (a) a function, but not one-to-one

Step-by-step explanation:

The graph is of a function if it passes the vertical line test: a vertical line intersects the graph in at most 1 point.

The function is one-to-one if it passes the horizontal line test: a horizontal line intersects the graph in at most 1 point.

__

Here, the graph consists of a series of non-overlapping horizontal lines. It passes the vertical line test (is a function), but a horizontal line can intersect the graph in an infinite number of points (is not one-to-one).

The graph is a function, but not one-to-one.

I really need help with my question!

Answers

Answer:

4

Step-by-step explanation:

because the others are shown wrong in 2 there are 5 tally marks and in 10 there are 6 telly marks

Answer: i just did this and its 4

Step-by-step explanation:

im dum as fudge

The triangles shown below must be congruent. True or False?

Answers

Answer:

they are technically congruent due to same angles n same or equal sides

Answer:

A. True

Step-by-step explanation:

Two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.

so your amswer is A. True

In a bag of 50 marbles, 20 marbles are blue or pink.


What percentage of marbles are blue or pink?


Enter the missing values in the boxes to complete the ratio table.

Thanks.

Answers

Answer:

40%

Step-by-step explanation:

The ratio is 20:50, we can expand to 40:100, so 40%

Factorise
x2 + 11x + 28

Answers

Answer:

[tex]\huge\boxed{(x+7)(x+4)}[/tex]

Step-by-step explanation:

To factor a polynomial expression with a degree of 2, simply look at the second and last term (11x and 28).  Discard the x and you are left with 11 and 28.  

To factor the equation, simply find two numbers that add to 11, and multiply to 28, 4 and 7.  Then, simply use those two numbers to make the terms.

Hope it helps :) and let me know if you want me to elaborate.

PLS HELP WILL MARK BRAINLIEST

Answers

No, the answer would be no because that’s the correct option
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