The hypotenuse of a right triangle is 4 times the smallest side. The third side is 4√15 cm. Find the length of the smallest side
2 answers:
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Answer:
Add one to all the x and subtract 4 to all the y values
Step-by-step explanation:
(1,4)= (2,0)
(-4,2)=(-3,-2)
(4,-3)=(5,-7)
Answer:
10.93% probability of observing 51 or fewer vapers in a random sample of 300
Step-by-step explanation:
I am going to use the normal approximation to the binomial to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
The standard deviation of the binomial distribution is:
Normal probability distribution
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.
When we are approximating a binomial distribution to a normal one, we have that ,
.
In this problem, we have that:
So
What is the approximate probability of observing 51 or fewer vapers in a random sample of 300?
Using continuity corrections, this is , which is the pvalue of Z when X = 51.5 So
has a pvalue of 0.1093.
10.93% probability of observing 51 or fewer vapers in a random sample of 300