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Sidana [21]
3 years ago
12

The prime factorization of 441 is

Mathematics
2 answers:
OLga [1]3 years ago
8 0

441 is odd, so we can't divide it by 2.

Since the sum of its digits is 4+4+1=9, which is divisible by 3, we can divide 441 by 3, and we have

441\div 3=147

Which is still divisible by 3, because 1+4+7=12. We have

147\div 3=49

49 is not divisible by 3 anymore, nor by 5 (it doesn't end with 0 or 5).

It is divisible by 7 though, we have

49\div 7=7

and finally,

7\div 7=1

So, the factorization of 441 is

441=3^2\times 7^2

amm18123 years ago
7 0

Answer:3x3x7x7

Step-by-step explanation:

441 divide by3=147 remaining 0

147 divide by3=49 remaining 0

49 divide by 7=7 remaining 0

7 divide by 7=1 remaining 0

Therefore the prime factorization of 441 is 3x3x7x7

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2 years ago
A certain company sends 40% of its overnight mail parcels by means of express mail service A1. Of these parcels, 4% arrive after
Harrizon [31]

Answer:

(a) The probability that a randomly selected parcel arrived late is 0.026.

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(c) The probability that a parcel was late was being shipped through the overnight mail service A₂ is 0.192.

(d) The probability that a parcel was late was being shipped through the overnight mail service A₃ is 0.192.

Step-by-step explanation:

Consider the tree diagram below.

(a)

The law of total probability sates that: P(A)=P(A|B)P(B)+P(A|B')P(B')

Use the law of total probability to determine the probability of a parcel being late.

P(L)=P(L|A_{1})P(A_{1})+P(L|A_{2})P(A_{2})+P(L|A_{3})P(A_{3})\\=(0.04\times0.40)+(0.01\times0.50)+(0.05\times0.10)\\=0.026

Thus, the probability that a randomly selected parcel arrived late is 0.026.

(b)

The conditional probability of an event A provided that another event B has already occurred is:

P(A|B)=\frac{P(B|A)P(A)}{P(B)}

Compute the probability that a parcel was late was being shipped through the overnight mail service A₁ as follows:

P(A_{1}|L)=\frac{P(L|A_{1})P(A_{1})}{P(L)} \\=\frac{0.04\times 0.40}{0.026} \\=0.615

Thus, the probability that a parcel was late was being shipped through the overnight mail service A₁ is 0.615.

(c)

Compute the probability that a parcel was late was being shipped through the overnight mail service A₂ as follows:

P(A_{2}|L)=\frac{P(L|A_{2})P(A_{2})}{P(L)} \\=\frac{0.01\times 0.50}{0.026} \\=0.192

Thus, the probability that a parcel was late was being shipped through the overnight mail service A₂ is 0.192.

(d)

Compute the probability that a parcel was late was being shipped through the overnight mail service A₂ as follows:

P(A_{3}|L)=\frac{P(L|A_{3})P(A_{3})}{P(L)} \\=\frac{0.05\times 0.10}{0.026} \\=0.192

Thus, the probability that a parcel was late was being shipped through the overnight mail service A₃ is 0.192.

4 0
3 years ago
<img src="https://tex.z-dn.net/?f=%20-%20x%20-%202%20%5Cdiv%20x%28x%20%7B%7D%5E%7B2%7D%20%20-%204%29" id="TexFormula1" title=" -
saw5 [17]

Answer:

Step-by-step explanation:

Hello,

First of all we will take any real number x different from 0, -2, +2 as dividing by 0 is not allowed and then we can write

\dfrac{( - x - 2)}{x(x^2 - 4)}=-\dfrac{x+2}{x(x-2)(x+2)}=\large \boxed{ -\dfrac{1}{x(x-2)}}

because we know that

x^2-4=x^2-2^2=(x-2)(x+2)

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

8 0
3 years ago
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