Which of the following pairs of functions are inverses of each other?
2 answers:
Answer:
Proved!
Step-by-step explanation:
For two functions f(x) and g(x) to be inverses of each other then;
f(g(x)) = x and g(f(x)) = x condition must be satisfied.
<u>Checking: A. f(x) = 7x³ + 10 and g(x) = ∛</u><u />
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So f(g(x)) = 7()³ + 10
We get; 7() + 10 = x - 10 + 10 = x (*<em>This is correct!)</em>
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So g(f(x)) =
Ten cancels out and we are left with;
=
= x (* <em>This is also correct!)</em>
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Answer:
For a mean oil change time of 20.51 minutes there would be a 10% chance of being at or below
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem, we have that:
Treating this as a random sample, at what mean oil-change time would there be a 10% chance of being at or below?
This is the 10th percentile, which is X when Z has a pvalue of 0.1. So it is X when Z = -1.28.
By the Central Limit Theorem
For a mean oil change time of 20.51 minutes there would be a 10% chance of being at or below
Answer:
The answer; – 15
I hope I helped you^_^