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scoray [572]
4 years ago
12

Worth 20 points, please help!

Mathematics
1 answer:
serg [7]4 years ago
5 0

Answer: 3


Step-by-step explanation:

To solve this problem you must apply the proccedure shown below:

1. Find the prime factorization of 27:

27=3*3*3 or 27=3^{3}

2.  The index of the radical is 3, therefore, you have rewrite it as following:

\sqrt[3]{27}=\sqrt[3]{3^{3}}=3^{\frac{3}{3}}=3^{1}=3

3. Therefore, as you can see, the answer is 3.


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A true-false quiz with 10 questions was given to a statistics class. Following is the probability distribution for the score of
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Answer:

E(X)=\sum_{i=1}^n X_i P(X_i)  

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E(X)=5*0.05 +6*0.15 +7*0.33 +8*0.28+ 9*0.12 +10*0.07=7.48  

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Step-by-step explanation:

For this case we assume the following probability distribution:

X         5       6         7       8        9        10

P(X)   0.05   0.15  0.33  0.28   0.12   0.07

First we need to find the expected value (first moment) and the second moment in order to find the variance and then the standard deviation.

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E(X)=\sum_{i=1}^n X_i P(X_i)  

And if we use the values obtained we got:  

E(X)=5*0.05 +6*0.15 +7*0.33 +8*0.28+ 9*0.12 +10*0.07=7.48  

For this case this value means that the expected score is about 7.48

In order to find the standard deviation we need to find first the second moment, given by :  

E(X^2)=\sum_{i=1}^n X^2_i P(X_i)  

And using the formula we got:  

E(X^2)=(5^2 *0.05)+(6^2 *0.15)+(7^2 *0.33)+(8^2 *0.28)+ (9^2 *0.12 +(10^2 *0.07))=57.46  

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Var(X)=E(X^2)-[E(X)]^2 =57.46-(7.48)^2 =1.5096  

And then the standard deviation would be given by:  

Sd(X)=\sqrt{Var(X)}=\sqrt{1.5096}=1.229  

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