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lianna [129]
3 years ago
8

An urn contains 5 white ball and 8 black balls. 4 balls are randomly selected.

Mathematics
1 answer:
larisa86 [58]3 years ago
5 0

|\Omega|=13^4=28561\\ |A|=8^3\cdot5=2560\\\\ P(A)=\dfrac{2560}{28561}\approx9\%

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Solve. Use the strategy "work backward."
cestrela7 [59]

Let that be x

ATQ

\\ \rm\Rrightarrow 3x-6/5=9

Arrange accordingly to work backwards(Every thing is reversed)

\\ \rm\Rrightarrow 9(5)+6/3=x

\\ \rm\Rrightarrow 45+6/3=x

\\ \rm\Rrightarrow 51/3=x

\\ \rm\Rrightarrow x=17

.

8 0
2 years ago
Prove the following by induction. In each case, n is apositive integer.<br> 2^n ≤ 2^n+1 - 2^n-1 -1.
frutty [35]
<h2>Answer with explanation:</h2>

We are asked to prove by the method of mathematical induction that:

2^n\leq 2^{n+1}-2^{n-1}-1

where n is a positive integer.

  • Let us take n=1

then we have:

2^1\leq 2^{1+1}-2^{1-1}-1\\\\i.e.\\\\2\leq 2^2-2^{0}-1\\\\i.e.\\2\leq 4-1-1\\\\i.e.\\\\2\leq 4-2\\\\i.e.\\\\2\leq 2

Hence, the result is true for n=1.

  • Let us assume that the result is true for n=k

i.e.

2^k\leq 2^{k+1}-2^{k-1}-1

  • Now, we have to prove the result for n=k+1

i.e.

<u>To prove:</u>  2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-1

Let us take n=k+1

Hence, we have:

2^{k+1}=2^k\cdot 2\\\\i.e.\\\\2^{k+1}\leq 2\cdot (2^{k+1}-2^{k-1}-1)

( Since, the result was true for n=k )

Hence, we have:

2^{k+1}\leq 2^{k+1}\cdot 2-2^{k-1}\cdot 2-2\cdot 1\\\\i.e.\\\\2^{k+1}\leq 2^{(k+1)+1}-2^{k-1+1}-2\\\\i.e.\\\\2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-2

Also, we know that:

-2

(

Since, for n=k+1 being a positive integer we have:

2^{(k+1)+1}-2^{(k+1)-1}>0  )

Hence, we have finally,

2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-1

Hence, the result holds true for n=k+1

Hence, we may infer that the result is true for all n belonging to positive integer.

i.e.

2^n\leq 2^{n+1}-2^{n-1}-1  where n is a positive integer.

6 0
3 years ago
“twice the sum of a number and 6 is more than 84”
stealth61 [152]

Answer:

81

Step-by-step explanation:

2x+6=84

2x=78

81

find your own way

3 0
2 years ago
Find the greatest common factor of 26 and 14​
Nookie1986 [14]
The greatest common factor of 26 and 14 is 2.
6 0
3 years ago
Read 2 more answers
The population of kansas city, missouri was 435,000 in 1990 and 482,300 in 2005. if the population is changing linearly, write a
Jlenok [28]
Find the slope of the line connecting (1990,435000) and (2005,482300):

        482300-435000        47300
m = ----------------------- = ---------------- = 3153/yr (approx)
          2005 - 1990                15 yr

Use the point-slope formula to find the equation of this str. line:

y-435000 = (3153/yr)(x-1990)

The year 2020 is 30 years after 1990.  Thus, the expected pop in 2020 is

given by     y-435000 = 3153(30) = 94590, so that y = 529590.
4 0
3 years ago
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