Which expression is equivalent to Negative 28 x y 35 y? 7 y (Negative 4 x y 5 y) 7 x (negative 4 x 5 y) 7 x (negative 4 y 5 y) 7
1 answer:
You can use the distributive property of multiplication over addition to find the equivalent expression to the given expression.
The expression which is equivalent to the given expression is given by
Option D:
Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.
<h3>What is distributive property of multiplication over addition?</h3>Suppose a, b and c are three numbers. Then we have:
(a(b+c) means a multiplied to (b+c). The sign of multiplication is usually hidden when using symbols and both quantities which are in multiplication are written together without space)
<h3>Using the above property and the fact that 28 and 35 are multiples of 7 to get the equivalent expression</h3>The given expression is
Since 28 = 7 times 4 and 35 = 7 times 5
Thus,
Thus,
The expression which is equivalent to the given expression is given by
Option D:
Learn more about equivalent expressions here:
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Answer:
There is a 92.32% probability that the sample mean would differ from the population mean by less than 633 miles in a sample of 49 tires if the manager is correct.
Step-by-step explanation:
Problems of normally distributed samples can be 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 random variable X, with mean and standard deviation
, a large sample size can be approximated to a normal distribution with mean \mu and standard deviation
In this problem, we have that:
The operation manager at a tire manufacturing company believes that the mean mileage of a tire is 33,208 miles, with a standard deviation of 2503 miles.
This means that .
What is the probability that the sample mean would differ from the population mean by less than 633 miles in a sample of 49 tires if the manager is correct?
This is the pvalue of Z when subtracted by the pvalue of Z when
By the Central Limit Theorem, we have t find the standard deviation of the sample, that is:
So
X = 33841
has a pvalue of 0.9616
X = 32575
has a pvalue of 0.0384.
This means that there is a 0.9616 - 0.0384 = 0.9232 = 92.32% probability that the sample mean would differ from the population mean by less than 633 miles in a sample of 49 tires if the manager is correct.