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Llana [10]
4 years ago
10

Please help with this

Mathematics
2 answers:
LiRa [457]4 years ago
5 0
False, I believe. Not so sure if you can make a triangle out of three sides that are not the same size

zaharov [31]4 years ago
3 0
<h2>Answer:</h2>

The answer to the statement is:

                     TRUE

<h2>Step-by-step explanation:</h2>

In order for a segment to form a triangle.

The sum of the lengths of any two sides of a triangle must be greater than the length of the remaining third side of the given triangle.

Here we have three segments of length:

7 units, 9  units and 12 units.

Also, for any two pair:

7 and 9 we have:

7+9=16> 12

for 9 and 12 we have:

9+12=21>7

and for 7 and 12 we have:

7+12=19>9

Hence, the segments could form a triangle.

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Is 16.45 greater than, less than or equal to 16.454
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Twenty different books are to be put on five book shelves, each of which holds at least twenty books.
olya-2409 [2.1K]

Answer:

(a) 10,626 different arrangements

(b) 95,367,431,640,625 different arrangements

(c) 2.5852017 × 10²² different arrangements

Step-by-step explanation:

(a) How many different arrangements are there if you only care about the number of books on the shelves (and not which book is where)?

We use the combination formula for this

C(n , r) = n + r - 1C r - 1

n = 20

r = 5

= 20 + 5 - 1 C 5-1

= 24C4

= 24!/4 ! × (24 - 4)

= 24!/4! × 20!

= 10,626 arrangements

(b) How many different arrangements are there if you care about which books are where, but the order of the books on the shelves doesn't matter?

Since the order of the books on the shelves does not matter,

The calculation is given as

5²⁰ = 95,367,431,640,625 arrangements

(c) How many different arrangements are there if the order on the shelves does matter?

Since order matters now

Step 1

We use the combination formula for this

C(n , r) = n + r - 1C r - 1

n = 20

r = 5

= 20 + 5 - 1 C 5-1

= 24C4

= 24!/4 ! × (24 - 4)

= 24!/4! × 20!

= 10,626

Step 2

We find the factorial of the number books

= 20!

= 2,432,902,008,176,640,000

Step 3

The different arrangements there are if the order on the shelves does matter is calculated

= 10,626 × 2,432,902,008,176,640,000

= 2.5852017 × 10²² different arrangements

8 0
3 years ago
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