1. (10m - 14) + 9 = 12 1. Given
2. 5m - 7 + 9 = 12 2. Distributive Property
3. 5m + 2 = 12 3. Simplify (added like terms)
4. 5m = 10 4. Subtraction Property of Equality
5. m = 2 5. Division Property of Equality
Graph the inequality plz help me solve this and explain how plzzzzzz x-y <4
2 answers:
Answer:
Step-by-step explanation:
first you have to get the inequality to a point where you can actually graph it
to do this you have to get the x to the same side of the less than symbol
you do this like any other equation, subtract x from the left and right sides because whatever you do to one side, you do to the other
this leaves you with -y < -x + 4
you have to multiply the entire thing by -1 because y cannot be negative
this gives you y < x - 4, now you can graph it
because x is isolated you just have to graph y < -4 like so
im not the best at explanations, i apologize
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Answer:
58.32% probability that a randomly selected application will report a GMAT score of less than 600
93.51% probability that a sample of 50 randomly selected applications will report an average GMAT score of less than 600
98.38% probability that a sample of 100 randomly selected applications will report an average GMAT score of less than 600
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:
What is the probability that a randomly selected application will report a GMAT score of less than 600?
This is the pvalue of Z when X = 600. So
has a pvalue of 0.5832
58.32% probability that a randomly selected application will report a GMAT score of less than 600
What is the probability that a sample of 50 randomly selected applications will report an average GMAT score of less than 600?
Now we have
This is the pvalue of Z when X = 600. So
has a pvalue of 0.9351
93.51% probability that a sample of 50 randomly selected applications will report an average GMAT score of less than 600
What is the probability that a sample of 100 randomly selected applications will report an average GMAT score of less than 600?
Now we have
has a pvalue of 0.9838
98.38% probability that a sample of 100 randomly selected applications will report an average GMAT score of less than 600