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Thepotemich [5.8K]
3 years ago
14

Write 56 as a product of primes. Use index notation when giving your answer.

Mathematics
1 answer:
mixas84 [53]3 years ago
3 0

Answer:

56 as a product of primes using index notation is: \mathbf{2^3 \times 7}

Step-by-step explanation:

We need to write 56 as a product of primes.

Prime Numbers:

<em>Numbers that are divisible by 1 or itself.</em>

Now, writing 56 as product of primes

56 = 2 x 2 x 2 x 7

Now, Use index notation when giving your answer.

Index Notation:

<em>Express elements in power form i.e. if we have 2 x 2 we can write it as 2^2</em>

So, answer will be:

56 = 2 \times 2 \times 2 \times 7

=2^3 \times 7

So, 56 as a product of primes using index notation is: \mathbf{2^3 \times 7}

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A new security system needs to be evaluated in the airport. The probability of a person being a security hazard is 4%. At the ch
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Then,

P(H^{c})=1-P(H)=1-0.04=0.96\\P(P|H^{c})=1-P(P|H)=1-0.02=0.98\\

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Compute the probability that a person passes the security system using the total probability rule as follows:

The total probability rule states that: P(A)=P(A|B)P(B)+P(A|B^{c})P(B^{c})

The value of P (P) is:

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Thus, the probability that a person passes the security system is 0.9412.

(b)

Compute the probability that a person who passes through the system is without any security problems as follows:

P(H^{c}|P)=\frac{P(P|H^{c})P(H^{c})}{P(P)} \\=\frac{0.98\times0.96}{0.9412} \\=0.9996\\\approx1

Thus, the probability that a person who passes through the system is without any security problems is approximately 1.

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