What is the inverse of f(x) =1/3 x + 2?
1 answer:
Answer:
Step-by-step explanation:
To begin, we will replace f(x) with y, since they mean the same thing, except y does not represent function notation. We will put it back when we're done.
The rules for finding an inverse function algebraically is to switch the x and the y, then solve for the new y. Our function then becomes, with the variables switched:
Begin to isolate the new y by subtracting 2 from both sides:
Now multiply both sides by 3:
3(x - 2) = y and
3x - 6 = y
That's the inverse, so now we will put it back into function notation:
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Answer:
1963.2 pounds (lbs.)
Step-by-step explanation:
Things to understand before solving:
- - <u>Normal Probability Distribution</u>
- The z-score formula can be used to solve normal distribution problems. In a set with mean ц and standard deviation б, the z-score of a measure X is given by:
The Z-score reflects how far the measure deviates from the mean. After determining the Z-score, we examine the z-score table to determine the p-value associated with this z-score. This p-value represents the likelihood that the measure's value is less than X, or the percentile of X. Subtracting 1 from the p-value yields the likelihood that the measure's value is larger than X.
- - <u>Central Limit Theorem</u>
- The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean ц and standard deviation б , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean ц and standard deviation
As long as n is more than 30, the Central Limit Theorem may be applied to a skewed variable. A specific kind of steel cable has an average breaking strength of 2000 pounds, with a standard variation of 100 pounds.
This means, ц = 2000 and б = 100.
A random sample of 20 cables is chosen and tested.
This means that n = 20,
Determine the sample mean that will exclude the top 95 percent of all size 20 samples drawn from the population.
This is the 100-95th percentile, or X when Z has a p-value of 0.05, or X when Z = -1.645. So
- By the Central Limit Theorem
The sample mean that will cut off the top 95% of all size 20 samples obtained from the population is 1963.2 pounds.
9514 1404 393
Answer:
2
Step-by-step explanation:
I find it convenient to remember that a logarithm is an exponent.
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log₂(8) +log₃(1/3) = log₂(2³) +log₃(3⁻¹)
= 3 -1 = 2
The value of the expression is 2.
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Some calculators can compute this for you directly.
