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Juli2301 [7.4K]
2 years ago
11

for every natural number n, n^5 + 4n is a multiple of 5 could begin with... what is the appropriate next step

Mathematics
1 answer:
Vilka [71]2 years ago
6 0

Answer:  The proof is done below.

Step-by-step explanation:  We are given to prove that the following statement is true :

"For every natural number n, n^5+4n is a multiple of 5."

We will prove the above statement by MATHEMATICAL INDUCTION.

Let n = 1. Then, we get

n^5+4n=1^5+4\times5=5, a multiple of 5.

Let n = 2. Then, we get

n^5+4n=2^5+4\times2=40, a multiple of 5.

Let the statement be true for n = m, where m is a natural number.

So,

m^5+4m=5k, for any natural number k.

Then,

(m+1)^5+4(m+1)\\\\=m^5+5m^4+10m^3+10m^2+5m+1+4m+4\\\\=(m^5+4m)+5m^4+10m^3+10m^2+5m+5\\\\=5k+5(m^4+2m^3+2m^2+m+1)\\\\=5(k+m^4+2m^3+2m^2+m+1), which is a multiple of 5.

Therefore, if the statement is true for n = m, then it is true for n = m+1.

That is, the statement is true for all natural numbers n.

Hence proved.

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Of the 80 boys polled at lunch, 55% say they play video games daily. According to the poll, how many boys play video games daily
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55% = \frac{55}{100} = \frac{11}{20}

Multiply \frac{11}{20} by 80 and you will get how many boys play video games daily.

\frac{11}{20}*80=\frac{11}{1}*4=11*4=44

44 is the number of boys who play video games daily.

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A total of 480 were sold for the school play. They were either adult tickets or students tickets. The number of student tickets
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Ok so basically, the number of student tickets is 3x, where x=the number of adult tickets sold. And we know that s(for student tickets)+x=480 total tickets sold. So if we replace s with 3x we have 3x+x=480, or 4x=480. We divide by 4 and get x=120, which is the amount of adult tickets sold.

5 0
3 years ago
If A and B are independent events, P(A) = 0.25, and P(B) = 0.3, what is P(AB)?
Marrrta [24]

Answer:

P(A) = 0.25, P(B= 0.3

And if we want to find P(A \cap B) we can use this formula from the definition of independent events :

P(A \cap B) =P(A) *P(B) = 0.25*0.3= 0.075

And the best option would be:

P(A \cap B) =0.075

Step-by-step explanation:

For this case we have the following events A and B and we also have the probabilities for each one given:

P(A) = 0.25, P(B= 0.3

And if we want to find P(A \cap B) we can use this formula from the definition of independent events :

P(A \cap B) =P(A) *P(B) = 0.25*0.3= 0.075

And the best option would be:

P(A \cap B) =0.075

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Somebody help me with this question
vampirchik [111]
I think u do 3•5 then divide by 110
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