Identify the remainder when x3 - 3x2 - 9x is divided by x - 6.
1 answer:
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<h3>Answer: 33%</h3>
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Explanation:
1/3 converts to the decimal form 0.333333... where the 3's go on forever
5/3 is a similar story but 5/3 = 1.666666.... where the '6's go on forever
The notation indicates that the 6's go on forever.
So,
The horizontal bar tells us which digits repeat. As another example,
The three dots just mean "keep this pattern going forever".
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Everything mentioned so far has the decimal portions go on forever repeating some pattern over and over.
The only one that doesn't do this is 33% which converts to the decimal form 0.33
The value 0.33 is considered a terminating decimal since "terminate" means "stop". So this is the value that doesn't fit in with the other three items mentioned.
Answer:
The interval containing the middle-most 48% of sample means is between 218.59 to 221.41.
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 distributied random variable X, with mean and standard deviation
, the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
Find the interval containing the middle-most 48% of sample means:
50 - 48/2 = 26th percentile to 50 + 48/2 = 74th percentile. So
74th percentile
value of X when Z has a pvalue of 0.74. So X when Z = 0.643.
By the Central Limit Theorem
26th percentile
Value of X when Z has a pvalue of 0.26. So X when Z = -0.643
The interval containing the middle-most 48% of sample means is between 218.59 to 221.41.