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2 years ago

Between what two consecutive integers must log2(17) lie

Mathematics

1 answer:

miss Akunina [59]2 years ago

3 0

Answer:

4 and 5

Step-by-step explanation:

For answering questions like this, it can be useful to remember a few of the powers of small integers:

2^4 = 16

2^5 = 32

<h3>Exponents and logarithms</h3>

A logarithm can be considered to be an exponent of the base.

$\log_b(x) = a \ \Longleftrightarrow\ b^a=x$

The ordering of powers of 2 relative to the number of interest (17) is ...

16 < 17 < 32

2⁴ < 17 < 2⁵ . . . . . . . . . . . . . . . . . . . expressed as powers of 2

log₂(2⁴) < log₂(17) < log₂(2⁵) . . . . . log₂ of the above inequality

4 < log₂(17) < 5 . . . . . . . . . . . . . . . . showing the values of the logs

Log₂(17) lies between 4 and 5.

Additional comment

Using the "change of base" formula, you can use a calculator to find the value of log₂(17). It shows you the value is between 4 and 5.

log₂(17) = log(17)/log(2) . . . . . . using logs to the same base

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The probability a household in a community uses gas for cooking is 0.18. If a shopper from the community is from a household tha

Lyrx [107]

Answer:

The probability of a person from the community not shopping at Prime Foods given that he uses gas for cooking at his household is 0.092

Step-by-step explanation:

Hello!

Given the information:

A: "The household uses gas for cooking" ⇒ P(A)= 0.18

B: "The person from the comunity shops at Prime Foods"

The person shops at Prime Foods given that he uses gas for cooking:

P(B/A)= 0.7

The person shops at Prime Foods given that he doesn't use gas for cooking:

P(B/Ac)= 0.35

If the person doesn't shop at Prime Foods, what is the probability that he uses gas for cooking?

Symbolically:

P(A/Bc) = P(A∩Bc)

P(Bc)

The event Bc is the complement of event B, so it's probability is P(Bc)= 1 - P(B)

You can calculate the probability of B as:

P(B)= P(A∩B)+ P(Ac∩B)

Using the information of P(B/A)= 0.7 and P(B/Ac)= 0.35 you can reach the values of both intersections.

P(B/A)= P(A∩B)

P(A)

P(B/A)*P(A)= P(A∩B)

P(A∩B)= 0.7*0.18= 0.126

and

P(B/Ac)= P(Ac∩B)

P(Ac)

If A and Ac are complementary events, then P(Ac)= 1 - P(A)= 1 - 0.18= 0.82

Then:

P(B/Ac)*P(Ac)= P(Ac∩B)

P(Ac∩B)= 0.35*0.82= 0.287

The probability of B is:

P(B)= P(A∩B)+ P(Ac∩B)= 0.126+0.287= 0.413

P(Bc)= 1 - P(B)= 1 - 0.413= 0.587

And

P(A)= P(A∩B)+P(A∩Bc)

P(A∩Bc)=P(A)=-(A∩B)= 0.18-0.126= 0.054

Finally:

P(A/Bc) = P(A∩Bc) =0.054 = 0.0919≅ 0.092

P(Bc) 0.587

I hope it helps!

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Answer:

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olga_2 [115]

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