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3 years ago

A catering service offers

Mathematics

1 answer:

Fiesta28 [93]3 years ago

5 0

Answer:

There are 52920 ways to do the banquet

Step-by-step explanation:

* Lets revise the combination to solve this problem

- A combination is a collection of the objects where the order

doesn't matter

- The order is not important in this problem, so we can use the

combination nCr to find how many ways can this done

* Lets solve the problem

- A catering service offers 6 appetizers, 7 main courses, 10 desserts.

- A customer is to select 5 appetizers, 4 main courses, 5 desserts

for a banquet

∵ We want to select 5 appetizers from 6

∴ There are 6C5 ways to chose the appetizers

∵ 6C5 = 6

∴ There are 6 ways to chose the appetizers

∵ We want to select 4 main courses from 7

∴ There are 7C4 ways to chose the main courses

∵ 7C4 = 35

∴ There are 35 ways to chose the main courses

∵ We want to select 5 desserts from 10

∴ There are 10C5 ways to chose the desserts

∵ 10C5 = 252

∴ There are 252 ways to chose the desserts

- To find the number of ways to do the banquet multiply all the

answers above

∵ The total ways = 6C5 × 7C4 × 10C5

∴ The total ways = 6 × 35 × 252 = 52920

* There are 52920 ways to do the banquet

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The sum of two numbers is 48. Their difference is 38. Find the numbers.

Setler79 [48]

Answer:

43 and 5

Step-by-step explanation:

Let's let the two unknown numbers be a and b.

Their sum is 48, therefore:

$a+b=48$

And their difference is 38. In other words:

$a-b=38$

We now have a system of equations. To solve, we can use substitution. First, add b to both sides in the second equation:

$a=38+b$

Substitute this into the first equation:

$(38+b)+b=48$

Combine like terms:

$2b+38=48$

Subtract 38 from both sides:

$2b=10$

Divide both sides by 2:

$b=5$

So, one of the numbers is 5.

The sum of them is 48. Therefore, the other number is 48-5 or 43.

So, our two numbers are 43 and 5.

And we're done!

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2 years ago

The weights of adobe bricks used for construction are normally distributed with a mean of 3 pounds and a standard deviation of 0

dedylja [7]

Answer: a) 0.8413, b) 0.9987.

Step-by-step explanation:

Since we have given that

Mean = 3 pounds

Standard deviation = 0.25 pounds

n = 28 bricks

So, (a) What is the probability that all the bricks in the sample exceed 2.75 pounds?

$P(X>2.75)\\\\=P(z>\dfrac{2.75-3}{0.25}\\\\=P(z>\dfrac{-0.25}{0.25})\\\\=P(z>-1)\\\\=0.8413$

b) What is the probability that the heaviest brick in the sample exceeds 3.75 pounds?

$P(X>3.75)\\\\=P(z>\dfrac{3.75-3}{0.25})\\\\=P(z>\dfrac{0.75}{0.25})\\\\=P(z>3)\\\\=0.9987$

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3 years ago

Assume that there is a 150 year old law in the statutes of your state which makes kissing in a public graveyard a crime punishab

pickupchik [31]

Answer: Natural law.

Step-by-step explanation:

Natural law this is a theory which is based on ethics and philosophy which states that human beings possess intrinsic values which guide our reasoning and behaviors. Natural law stands to maintain that these rules of right and wrong are inborn in people and are not created by the society or court judges. An example of Natural law is that it is bad to kill someone, and it’s is right to punish whoever kills someone.

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2 years ago

find the value of solid figure not including hole cutout. Round to two decimal places. Cube figure is 12 feet long with 4 ft cut

Artemon [7]

Answer:

1577.20 ft³

Step-by-step explanation:

Cube of length = 12 ft = a

Hole diameter which is cutout = 4 ft = d

Hole radius which is cutout = 4/2 =2 ft = r

Volume of the cube = a³

⇒Volume of the cube = a×a×a

⇒Volume of the cube = 12×12×12

⇒Volume of the cube = 1728 ft³

The hole cut out will be in the shape of a cylinder

Volume of cylinder = πr²h

⇒Volume of cylinder = π×2²×12

⇒Volume of cylinder = 150.79 ft³

Now volume of the solid figure with hole cut out is

Volume of the cube - Volume of cylinder

=1728 - 150.79

=1577.20 ft³

∴ Volume of solid figure not including hole cutout is 1577.20 ft³

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