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3 years ago

What’s the answer to 7^3x=54

Mathematics

1 answer:

HACTEHA [7]3 years ago

5 0

Answer:

x = 54/343

Step-by-step explanation:

$7^3x=54\\\rightarrow 7^3 = 343\rightarrow \text {Solve Exponents} \\343x=54\\\frac{343x}{343} =\frac{54}{343}\\x =\frac{54}{343}$

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Chocolate chip cookies have a distribution that is approximately normal with a mean of 24.1 chocolate chips per cookie and a sta

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Probabilities are used to determine the chances of an event

The probability that a person is sick is: 0.008
The probability that a test is positive, given that the person is sick is 0.9833
The probability that a test is negative, given that the person is not sick is: 0.9899
The probability that a person is sick, given that the test is positive is: 0.4403
The probability that a person is not sick, given that the test is negative is: 0.9998
A 99% accurate test is a correct test

(a) Probability that a person is sick

From the table, we have:

$\mathbf{Sick = 59+1 = 60}$

So, the probability that a person is sick is:

$\mathbf{Pr = \frac{Sick}{Total}}$

This gives

$\mathbf{Pr = \frac{60}{7500}}$

$\mathbf{Pr = 0.008}$

The probability that a person is sick is: 0.008

(b) Probability that a test is positive, given that the person is sick

From the table, we have:

$\mathbf{Positive\ and\ Sick=59}$

So, the probability that a test is positive, given that the person is sick is:

$\mathbf{Pr = \frac{Positive\ and\ Sick}{Sick}}$

This gives

$\mathbf{Pr = \frac{59}{60}}$

$\mathbf{Pr = 0.9833}$

The probability that a test is positive, given that the person is sick is 0.9833

(c) Probability that a test is negative, given that the person is not sick

From the table, we have:

$\mathbf{Negative\ and\ Not\ Sick=7365}$

$\mathbf{Not\ Sick = 75 + 7365 = 7440}$

So, the probability that a test is negative, given that the person is not sick is:

$\mathbf{Pr = \frac{Negative\ and\ Not\ Sick}{Not\ Sick}}$

This gives

$\mathbf{Pr = \frac{7365}{7440}}$

$\mathbf{Pr = 0.9899}$

The probability that a test is negative, given that the person is not sick is: 0.9899

(d) Probability that a person is sick, given that the test is positive

From the table, we have:

$\mathbf{Positive\ and\ Sick=59}$

$\mathbf{Positive=59 + 75 = 134}$

So, the probability that a person is sick, given that the test is positive is:

$\mathbf{Pr = \frac{Positive\ and\ Sick}{Positive}}$

This gives

$\mathbf{Pr = \frac{59}{134}}$

$\mathbf{Pr = 0.4403}$

The probability that a person is sick, given that the test is positive is: 0.4403

(e) Probability that a person is not sick, given that the test is negative

From the table, we have:

$\mathbf{Negative\ and\ Not\ Sick=7365}$

$\mathbf{Negative = 1+ 7365 = 7366}$

So, the probability that a person is not sick, given that the test is negative is:

$\mathbf{Pr = \frac{Negative\ and\ Not\ Sick}{Negative}}$

This gives

$\mathbf{Pr = \frac{7365}{7366}}$

$\mathbf{Pr = 0.9998}$

The probability that a person is not sick, given that the test is negative is: 0.9998

(f) When a test is 99% accurate

The accuracy of test is the measure of its sensitivity, prevalence and specificity.

So, when a test is said to be 99% accurate, it means that the test is correct, and the result is usable; irrespective of whether the result is positive or negative.