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zloy xaker [14]
3 years ago
15

Does anybody know the answer

Mathematics
2 answers:
Wittaler [7]3 years ago
7 0
1.
Part 14/25
Total .56
Percent 56
2.
Part 16/20
Total .8
Percent 80
3. 11/20 55%
4. 40
5. 300%
6. 140
nordsb [41]3 years ago
4 0

1. Part 14/25
Total .56
Percent56%
2. 16/20
Total. .8
Percent 80%
3. 11/20 55%
4. 40
5. 300%
6. 140
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Let C(n, k) = the number of k-membered subsets of an n-membered set. Find (a) C(6, k) for k = 0,1,2,...,6 (b) C(7, k) for k = 0,
vladimir1956 [14]

Answer:

(a) C(6,0) = 1, C(6,1) = 6, C(6,2) = 15, C(6,3) = 20, C(6,4) = 15, C(6,5) = 6, C(6,6) = 1.

(b) C(7,0) = 1, C(7,1) = 7, C(7,2) = 21, C(7,3) = 35, C(7,4) = 35, C(7,5) = 21, C(7,6) = 7, C(7,7)=1.

Step-by-step explanation:

In this exercise we only need to recall the formula for C(n,k):

C(n,k) = \frac{n!}{k!(n-k)!}

where the symbol n! is the factorial and means

n! = 1\cdot 2\cdot 3\cdot 4\cdtos (n-1)\cdot n.

By convention 0!=1. The most important property of the factorial is n!=(n-1)!\cdot n, for example 3!=1*2*3=6.

(a) The explanations to the solutions is just the calculations.

  • C(6,0) = \frac{6!}{0!(6-0)!} = \frac{6!}{6!} = 1
  • C(6,1) = \frac{6!}{1!(6-1)!} = \frac{6!}{5!} = \frac{5!\cdot 6}{5!} = 6
  • C(6,2) = \frac{6!}{2!(6-2)!} = \frac{6!}{2\cdot 4!} = \frac{5!\cdot 6}{2\cdot 4!} = \frac{4!\cdot 5\cdot 6}{2\cdot 4!} = \frac{5\cdot 6}{2} = 15
  • C(6,3) = \frac{6!}{3!(6-3)!} = \frac{6!}{3!\cdot 3!} = \frac{5!\cdot 6}{6\cdot 6} = \frac{5!}{6} = \frac{120}{6} = 20
  • C(6,4) = \frac{6!}{4!(6-4)!} = \frac{6!}{4!\cdot 2!} = frac{5!\cdot 6}{2\cdot 4!} = \frac{4!\cdot 5\cdot 6}{2\cdot 4!} = \frac{5\cdot 6}{2} = 15
  • C(6,5) = \frac{6!}{5!(6-5)!} = \frac{6!}{5!} = \frac{5!\cdot 6}{5!} = 6
  • C(6,6) = \frac{6!}{6!(6-6)!} = \frac{6!}{6!} = 1.

(b) The explanations to the solutions is just the calculations.

  • C(7,0) = \frac{7!}{0!(7-0)!} = \frac{7!}{7!} = 1
  • C(7,1) = \frac{7!}{1!(7-1)!} = \frac{7!}{6!} = \frac{6!\cdot 7}{6!} = 7
  • C(7,2) = \frac{7!}{2!(7-2)!} = \frac{7!}{2\cdot 5!} = \frac{6!\cdot 7}{2\cdot 5!} = \frac{5!\cdot 6\cdot 7}{2\cdot 5!} = \frac{6\cdot 7}{2} = 21
  • C(7,3) = \frac{7!}{3!(7-3)!} = \frac{7!}{3!\cdot 4!} = \frac{6!\cdot 7}{6\cdot 4!} = \frac{5!\cdot 6\cdot 7}{6\cdot 4!} = \frac{120\cdot 7}{24} = 35
  • C(7,4) = \frac{7!}{4!(7-4)!} = \frac{6!\cdot 7}{4!\cdot 3!} = frac{5!\cdot 6\cdot 7}{4!\cdot 6} = \frac{120\cdot 7}{24} = 35
  • C(7,5) = \frac{7!}{5!(7-2)!} = \frac{7!}{5!\cdot 2!} = 21
  • C(7,6) = \frac{7!}{6!(7-6)!} = \frac{7!}{6!} = \frac{6!\cdot 7}{6!} = 7
  • C(7,7) = \frac{7!}{7!(7-7)!} = \frac{7!}{7!} = 1

For all the calculations just recall that 4! =24 and 5!=120.

6 0
2 years ago
If two solids are similar and the ratio between the lengths of their edges is 2;7 what is the ratio of their volumes?
Art [367]

Answer:

8 : 343

Step-by-step explanation:

Given 2 similar figures

ratio of sides = a : b, then

ratio of volumes = a³ : b³

Here the ratio of edges = 2 : 7, hence

ratio of volumes = 2³ : 7³ = 8 : 343

3 0
3 years ago
Hannah buys ice cream and onions at the store
Snezhnost [94]

Answer:

x=5.12

Step-by-step explanation:

35.16= 4.44+6x

30.72=6x

5.12=x

x=5.12

Hope this helps :)

3 0
3 years ago
Compare this: |a| and 0
slavikrds [6]

Answer:

when they are pronounce /a/ does not need any force while /o/ w need more force

3 0
3 years ago
PJ will begin her cake deliveries at 12:20 . She asked to remind her 30 minutes before she has to leave. What time should I remi
mojhsa [17]

Answer:

At 11:50  

Step-by-step explanation:

1. Subtract the hours and the minutes separately

12:  20

<u>- 0</u>: <u> 30</u>

12: -10

2. If the minutes are negative, subtract 1 from the hours and add 60 to the minutes.

12:    -10

<u> - 1</u>: <u>+ 60 </u>

11:   50

You should remind PJ about her deliveries at 11:50.

4 0
3 years ago
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