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Simora [160]
3 years ago
6

The probability a person is infected by a certain cold virus is 0.2. If a random sample of 12 people is taken, what is the proba

bility that at least one person will be infected by the cold virus?
Mathematics
1 answer:
inna [77]3 years ago
3 0

Answer:

If 0.2 = 20%, The probability that 1 person will be infected is 100%, according to theory.

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Which of these is least likely to be the average salary of another of the groups?
Finger [1]

Answer:

$104,000

The probability that the average salary between two groups is the same, is actually low. It could be close, but it's quite difficult to get the same exact amount.

3 0
3 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
What is the equivalent expression of 8x+7y+5x+4y+2y
Natalija [7]

Answer:

13x+13y

Step-by-step explanation:

(combine like terms)

8x+5x=13x

7y+4y+2y=13y

hope this helped you!

4 0
3 years ago
Lo siento, solo voy a despotricar en español. Estoy tan cansado y realmente no quiero hacer nada, y todavía tengo Zooms para hac
Crazy boy [7]

Answer:

hola yo estoy aqui contigo

6 0
2 years ago
Given f(x) = 2x² + 4 and g(x) = 3x – 1 ……<br> What is (fg)(x)? <br><br> Show your work.
Lelu [443]

Answer:

(fg)(x) = 6x³ - 2x² + 12x - 4

Step-by-step explanation:

( f g ) ( x ) = f ( x ) * g ( x )

f(x) = 2x² + 4

g(x) = 3x – 1

( f g ) ( x ) = (2x² + 4) (3x – 1)

               = 6x³ - 2x² + 12x - 4

6 0
3 years ago
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