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2 answers:
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We assume that we need to simplify the expression in two different ways.
Answer:
One way: Raise both, the numerator and denominator, to the third power, and then simplify the expression.
Second way: Simplify the terms inside parentheses, and then raise the result to the third power.
The result of both ways is the same:
Step-by-step explanation:
<em>One way</em>
Raise both, the numerator and denominator, to the third power, and then simplify the expression:
This is the first simplification.
<em>Second way</em>
Simplify the terms inside parentheses, and then raise the result to the third power.
or .
Answer:
0.9909 = 99.09% probability that the proportion of flops in a sample of 404 released films would be greater than 4%
Step-by-step explanation:
I am going to use the binomial approximation to the normal 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
If the manager is correct, what is the probability that the proportion of flops in a sample of 404 released films would be greater than 4%?
This is the pvlaue of Z when X = 0.04*404 = 16.16. So
has a pvalue of 0.0091
1 - 0.0091 = 0.9909
0.9909 = 99.09% probability that the proportion of flops in a sample of 404 released films would be greater than 4%
Answer:
12
Step-by-step explanation:
Given: Diagonal of square=
To find the perimeter of square, we need to find the length of sides of square.
∴ Using the formula of diagonal to find side of square.
Formula;
Where, s is side of square.
⇒
Dividing both side by √2
⇒
∴
Hence, Length of side of square is 3.
Now, finding the perimeter of square.
Formula;
⇒
∴
Hence, Perimeter of square is 12.