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bazaltina [42]
3 years ago
15

Given the exponential equation 4x = 64, what is the logarithmic form of the equation in base 10?

Mathematics
2 answers:
krok68 [10]3 years ago
8 0
4^{x} = 64

By taking <span>logarithmic of base 10

∴ </span><span>log 4^{x} = log 64

∴ x log 4 = log 64

∴ x =  \frac{log \ 64}{log \ 4}

∴ The correct choice is
</span><span>x = log base 10 of 64, all over log base 10 of 4</span>
Karolina [17]3 years ago
6 0
The correct answer is <span><u>x = log base 10 of 64, all over log base 10 of 4.</u></span>
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The third term in an arithmetic sequence is 10 and the fifth term is 26.If the first term is a1,which is an equation for the nth
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Just plug in 3 for n and then 5 for n to see if an turns out to be 10 and 26.

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<em />

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Samples of emissions from three suppliers are classified for conformance to air-quality specifications. The results from 100 sam
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Answer

P(A) = 0.30

P(B) = 0.77

P(A\ n\ B) = 0.22

P(A\ u\ B) = 0.85

Explanation:

Given

See attachment for proper data presentation

n = 100 --- Sample

A = Supplier 1

B = Conforms to specification

Solving (a): P(A)

Here, we only consider data in sample 1 row.

Here:

Yes = 22 and No = 8

n(A) = Yes + No

n(A) = 22 + 8

n(A) = 30

P(A) is then calculated as:

P(A) = \frac{n(A)}{Sample}

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Solving (b): P(B)

We only consider data in the Yes column.

Here:

(1) = 22    (2) = 25 and (3) = 30

n(B) = (1) + (2) + (3)

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P(B) is then calculated as:

P(B) = \frac{n(B)}{Sample}

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P(B) = 0.77

Solving (c): P(A n B)

Here, we only consider the similar cell in the yes column and sample 1 row.

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This is represented as: n(A n B)

n(A\ n\ B) = 22

The probability is then calculated as:

P(A\ n\ B) = \frac{n(A\ n\ B)}{Sample}

P(A\ n\ B) = \frac{22}{100}

P(A\ n\ B) = 0.22

Solving (d): P(A u B)

This is calculated as:

P(A\ u\ B) = P(A) + P(B) - P(A\ n\ B)

This gives:

P(A\ u\ B) = \frac{30}{100} + \frac{77}{100} - \frac{22}{100}

Take LCM

P(A\ u\ B) = \frac{30+77-22}{100}

P(A\ u\ B) = \frac{85}{100}

P(A\ u\ B) = 0.85

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