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Arturiano [62]
3 years ago
11

How many different menus showing 10 main courses can a restaurant make if it has 15 main courses from which to choose?

Mathematics
1 answer:
oksian1 [2.3K]3 years ago
6 0
The number of ways or different menus containing 10 main courses that the restaurant can make out of the 15 main courses is calculated through the combination. 

                     15C10

This is read as "combination of 15 taken 10" which can be calculated through the equation,

                     nCr = n! / ((r!) x(n - r)!) 

In this item, n is equal to 15 and r is equal to 10. 

Substituting the known values to the equation above, 


                    15C10 = 15! / (10!)x(10 - 5)! = 3003

Thus, there are 3003 different menus that the restaurant can choose from. 
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3 years ago
Triangle XYZ is shown, where n ≥ 5. Triangle X Y Z is shown. The length of side X Y is n + 4, the length of side Y Z is 2 n, and
motikmotik

Answer:

The longest side of the triangle is YZ, the shortest side is ZX, the largest angle is ∠X and the smallest angle is ∠Y.

Step-by-step explanation:

The lengths of the sides of the triangle XYZ are as follows:

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According to the triangle inequality theorem, the sum of two sides of a triangle is always greater than the third side.

Then,

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ZX < XY + YZ ⇒ n - 2 < n + 4 + 2n ⇒ n - 2 < 3n + 4 ⇒ 2n > -6 ⇒ n > -3

It is provided that <em>n</em> ≥ 5.

Then the sides of the triangle are:

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The largest angle of a triangle is opposite to the longest side.

The angle opposite to YZ would be X. So, the largest angle is ∠X.

The smallest angle of a triangle is opposite to the shortest side.

The angle opposite to ZX would be Y. So, the smallest angle is ∠Y.

Thus, the longest side of the triangle is YZ, the shortest side is ZX, the largest angle is ∠X and the smallest angle is ∠Y.

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