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siniylev [52]
2 years ago
9

Given the equation of the circle find the center and the radius: (x - 3)2 + (y + 1)2 = 49

Mathematics
1 answer:
marta [7]2 years ago
3 0

Answer:

(3, -1), 7

Step-by-step explanation:

To find the center of this circle:  compare the given equation

(x - 3)^2 + (y + 1)^2 = 7^2   to the standard equation of a circle with center at (h, k):

(x - h)^2 + (y -k)^2 = r^2

From this comparison we see that the center is at

h = 3 and k = -1, and also that r must be 7:    (3, -1), 7

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Solve for x<br> (-4x + 4).-3= 24
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Two more than 11 times a number is equal to 24. What is the number?
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Of the 9-letter passwords formed by rearranging the letters AAAABBCCC (4 A's, 2 B's, and 3 C's), I select one at random. Determi
Tanya [424]

Answer:

a) 3

b) (8!/9!)-(7!/9!)

c) (1-(8!/9!))*(7!/9!)

Step-by-step explanation:

a)With 4 As ;  2Bs and 3Cs it is possible to get a palindrome if you fixed the  letters C according to: (2) in the extremes of the word and the other one at the center therefore you only have palindrome in the following cases

<u>C</u> (       ) <u>C</u> (       ) <u>C</u>

To fill in the gaps we have  4 letters  A and 2 letters B, wich we have two divide in two palindrome gaps,  

AAB         and    BAA the palindrome is  C  AAB C BAA C

BAA         and    AAB    "           "           is  C  BAA C AAB C  

ABA         and    ABA    "           "           is  C  ABA C ABA C

b) 4 A  ;   2B  ; 3C

We have the total number of elements  9, so the total number of possible outcomes is : 9!

Total events: 9!

if we fixed 3 C we have (the group of 3 Cs becoming one element) so the total amount of events with 3 adjacent Cs is: 7!

Therefore the probability of having 3 adjacent Cs is: 7!/9!

If we fixed only 2 Cs we have:

4 A  ; 2 B  ; 2C  : 1C

Total number of words (events) in this case is 8! (2C becomes 1 element)

so the total numbers of events is 8! the probability in this case is 8!/9!(this value includes cases of adjacent 3 Cs previous calculated ) so this value minus the case of 3 adjacent Cs ) give us 2 adjacent C and the other no next to them

Probability (of words with 2 adjacent Cs and the other no next to them is); 8!/9! - 7!/9!

c) Probability of B apart from each other is the whole set of events minus those where 2 B are adjacent or (become 1 element)

4 A ; 2B ; 3C

Total of events 9! and events with adjacent B is 8!/9!

Therefore the probability of words with 3 adjacent Cs and 2 B separeted is

the probability of 3 adjacent Cs (7!/9!) times probability of words with no adjacent Bs wich is (1-(8!/9!))*(7!/9!)

5 0
3 years ago
PLEASE HELP!!!!!! This season, the probability that the Yankees will win a game is 0.46 and the probability that the Yankees wil
tatuchka [14]

Answer:

Given:

Probability that the Yankees wins a game is

P(A) = 0.46

Probability that the Yankees loses a game is

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Probability that the Yankees scores 5 or more runs in a game is

P(B) = 0.59

Probability that the Yankees scores fewer than 5 runs in a game is

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Probability that the Yankees wins and scores 5 or more runs is

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Applying the De Morgan's law, the probability that the Yankees scores fewer than 5 runs and they loses the game would satisfy:

1 - P(A'⋂B') = P(A) ⋃ P(B) = P(A) + P(B) - P(A⋂B)

or

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or

1 - P(A'⋂B') = 0.66

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Applying the Bayes theorem, the probability that the Yankees would score fewer than 5 runs, given they lose the game:

P(B'|A')  = P(A'⋂B')/P(A')

or

P(B'|A') = 0.34/0.54 = 0.630

Hope this helps!

:)

7 0
3 years ago
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