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djverab [1.8K]
3 years ago
6

-------100 POINTS------ Complete the proof of the Pythagorean theorem.

Mathematics
2 answers:
KIM [24]3 years ago
7 0

Step-by-step explanation:

Complete the proof of the Pythagorean theorem is given below.

         Statement                                              Reason

1. ΔABC is a right triangle, with a     1. Given

right angle at ∠C

2. Draw an altitude from point C     2. From a point not on a line, exactly                    

to AB               one perpendicular can be drawn through the point to the line

3. ∠CDB and ∠CDA are right          3. Definition of altitude

angles

4. ∠BCA  ≅ ∠BDC                            4. All right angles are congruent

5. ∠B  ≅ ∠B                                      5. Reflexive\:Property

6. ΔCBA ~ ΔDBC                             6. AA Similarity Postulate                                                                                                                                                                                                                                      

7. \frac{a}{x}\:=\:\frac{c}{a}                                           7. Polygon\:Similarity\:Postulate\:\:\:

8. a^{2}  = cx                                          8. Cross\:Multiply\:and\:Simplify

9. ∠CDA  ≅ ∠BCA                           9. All\:Right\:Angles\:are\:Congruent

10. ∠A  ≅ ∠A                                    10. Reflexive\:Property

11. ΔCBA ~ ΔDBA                             11. AA Similarity Postulate

12. \frac{b}{y}\:=\:\frac{c}{b}=                                      12. Polygon\:Similarity\:Postulate

13. b^2\:=\:cy                                       13. Cross\:Multiply\:and\:Simplify

14. a^2\:+\:b^2\:=\:cx\:+cy                    14. Addition\:Property\:of\:Equality

15. \left(CB\right)^2+\left(CA\right)^2=\left(AB\right)\left(DB+BA\right)  15. Distributive Property

16. x + y = c                                    16. Segment\:Addition\:Postulate

17. a^2\:+\:b^2\:=\:c^2                             18. Substitution\:Property

Marina CMI [18]3 years ago
6 0

Answer:

b

Step-by-step explanation:

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Answer:

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b) P(X>30000|X>15000)=P(X>15000)=1-( 1- e^{-\frac{15000}{30000}})=e^{-0.5}=0.607

Step-by-step explanation:

Previous concepts

The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution". The probability density function is given by:

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And 0 for other case. Let X the random variable that represent "life lengths of automobile tires of a certain brand" and we know that the distribution is given by:

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The cumulative distribution function is given by:

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Part a

We want to find this probability:

P(X>30000) and for this case we can use the cumulative distribution function to find it like this:

P(X>30000)=1-( 1- e^{-\frac{30000}{30000}})=e^{-1}=0.368

Part b

For this case w want to find this probability

P(X>30000|X>15000)

We have an important property on the exponential distribution called "Memoryless" property and says this:

P(X>a+t| X>t)=P(X>a)  

On this case if we use this property we have this:P(X>30000|X>15000)=P(X>15000+15000|X>15000)=P(X>15000)

We can use the definition of the density function and find this probability:

P(X>15000)=1-( 1- e^{-\frac{15000}{30000}})=e^{-0.5}=0.607

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