Select the correct answer. which exponential equation is equivalent to this logarithmic equation?
1 answer:
<u>logarithmic equation</u><u> log x = 4 is given by-</u><u> </u><u> = x</u>
What is logarithmic equation?
- A logarithmic equation is an equation that involves the logarithm of an expression containing a variable.
- To solve exponential equations, first see whether you can write both sides of the equation as powers of the same number.
The given logarithmic equation is;
Since, log with base 10 is written as simply, therefore, we have:
= 4
Using the definition of logarithm, we get;
Equivalently,
Thus, the exponential equation out of the specified options that is equivalent to this logarithmic equation log x = 4 is given by- = x
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<u>The complete question is -</u>
Which exponential equation is equivalent to this logarithmic equation?
log x = 4
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Answer:
Probability that the sample will have a mean that is greater than $52,000 is 0.0057.
Step-by-step explanation:
We are given that the population mean for income is $50,000, while the population standard deviation is 25,000.
We select a random sample of 1,000 people.
<em>Let </em><em> = sample mean</em>
The z-score probability distribution for sample mean is given by;
Z = ~ N(0,1)
where, = population mean = $50,000
= population standard deviation = $25,000
n = sample of people = 1,000
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
So, probability that the sample will have a mean that is greater than $52,000 is given by = P( > $52,000)
P( > $52,000) = P(
>
) = P(Z > 2.53) = 1 - P(Z
2.53)
= 1 - 0.9943 = 0.0057
<em>Now, in the z table the P(Z </em><em> x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 2.53 in the z table which has an area of 0.9943.</em>
Therefore, probability that the sample will have a mean that is greater than $52,000 is 0.0057.