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Elan Coil [88]
2 years ago
13

What happens when a triangle is dilated using one of the vertices as the center of dilation?

Mathematics
1 answer:
iren2701 [21]2 years ago
5 0

Answer:

When a Triangle is Dilated taking one of the vertices as the center of dilation

There are two Possibility, either Dilation factor will be (0<Dilation factor<1), or greater than 1.

1. When,0< Dilation Factor < 1

Size Of Preimage < Size of Image

2. When Dilation Factor > 1

Size Of Preimage > Size of Image

Step-by-step explanation:

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Answer:

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  

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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.

In order to calculate the expected value we can use the following formula:  

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  

Then we can find the variance with the following formula:  

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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