The probability is p = 2/5, the correct option is the third one.
<h3>
How to find the probability?</h3>
There is a total of 6 socks, such that 4 are black and 2 are blue.
Then the probability of first getting a black sock is the quotient between the number of black socks and the number of blue socks, which gives:
P = 4/6
Now there are 5 socks in total, such that 3 are black and 2 blue.
Then the probability of getting another black one is:
Q = 3/5
The joint probability (getting the two black socks) is given by the product of the individual probabilities:
p = (4/6)*(3/5) = 2/5
The correct option is the third one.
If you want to learn more about probability:
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18. P(x then y) = 1/11
19. P(both y) = 5/22
To find the probability of these compound events, we have to multiply the probability of each individual event. Remember, on the second trial, there are only 11 options.
18. 2/12 x 6/11 = 1/11
19. 6/12 x 5/11 = 5/22
Answer:
f(x) = (3x -2)(2x +1)
Step-by-step explanation:
The procedure for factoring expression of the form ...
ax² +bx +c
is to look for factors of a·c that have a sum of b.
The product a·c is 6·(-2) = -12. You are looking for factors that have a sum of b = -1. From your familiarity with multiplication tables, you know ...
-12 = 1(-12) = 2(-6) = 3(-4)
The sums of the factor pairs in this list are -11, -4, -1. So, the last pair of factors, {3, -4} is the one we're looking for.
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At this point, there are several ways to proceed. Perhaps the simplest is to rewrite the linear term as the sum of terms involving these factors:
-x = 3x -4x
f(x) = 6x² +3x -4x -2
Now, the expression can be factored 2 terms at a time:
f(x) = (6x² +3x) -(4x +2) . . . . . pay attention to signs
f(x) = 3x(2x +1) -2(2x +1) . . . . factor each pair
f(x) = (3x -2)(2x +1) . . . . . . . . factor out the common factor of (2x+1)
I. {(0, 0), (0, 1), (0, 2)} II. {(0, 0), (1, 1), (2, 4)} III. {(0, 0), (1, 2), (2, 2)} IV. {(0, 0), (1, 2), (1, 3)} (A) I, II, a
PolarNik [594]
Answer:
(C) II and III only
Step-by-step explanation:
Given
![I. \{(0, 0), (0, 1), (0, 2)\}](https://tex.z-dn.net/?f=I.%20%5C%7B%280%2C%200%29%2C%20%280%2C%201%29%2C%20%280%2C%202%29%5C%7D)
![II. \{(0, 0), (1, 1), (2, 4)\}](https://tex.z-dn.net/?f=II.%20%5C%7B%280%2C%200%29%2C%20%281%2C%201%29%2C%20%282%2C%204%29%5C%7D)
![III. \{(0, 0), (1, 2), (2, 2)\}](https://tex.z-dn.net/?f=III.%20%5C%7B%280%2C%200%29%2C%20%281%2C%202%29%2C%20%282%2C%202%29%5C%7D)
![IV.\ {(0, 0), (1, 2), (1, 3)\}](https://tex.z-dn.net/?f=IV.%5C%20%7B%280%2C%200%29%2C%20%281%2C%202%29%2C%20%281%2C%203%29%5C%7D)
Required
Which is a function?
A relation is of the form ![\{(x_1,y_1),(x_2,y_2),(x_2,y_2),(x_2,y_2).........(x_n,y_n)\}](https://tex.z-dn.net/?f=%5C%7B%28x_1%2Cy_1%29%2C%28x_2%2Cy_2%29%2C%28x_2%2Cy_2%29%2C%28x_2%2Cy_2%29.........%28x_n%2Cy_n%29%5C%7D)
Where
and ![y = range](https://tex.z-dn.net/?f=y%20%3D%20range)
And for a relation to be regarded as a function, all its x values must be unique. i.e. unrepeated.
Analyzing the options
![I. \{(0, 0), (0, 1), (0, 2)\}](https://tex.z-dn.net/?f=I.%20%5C%7B%280%2C%200%29%2C%20%280%2C%201%29%2C%20%280%2C%202%29%5C%7D)
This is not a function because 0 in multiple times for different y values (range)
i.e. (0,0), (0,1) and (0,2)
![II. \{(0, 0), (1, 1), (2, 4)\}](https://tex.z-dn.net/?f=II.%20%5C%7B%280%2C%200%29%2C%20%281%2C%201%29%2C%20%282%2C%204%29%5C%7D)
This is a function because each of the x values (domains) are unique for different y values (range)
![III. \{(0, 0), (1, 2), (2, 2)\}](https://tex.z-dn.net/?f=III.%20%5C%7B%280%2C%200%29%2C%20%281%2C%202%29%2C%20%282%2C%202%29%5C%7D)
This is a function because each of the x values (domains) are unique for different y values (range)
![IV.\ {(0, 0), (1, 2), (1, 3)\}](https://tex.z-dn.net/?f=IV.%5C%20%7B%280%2C%200%29%2C%20%281%2C%202%29%2C%20%281%2C%203%29%5C%7D)
This is not a function because 1 in multiple times for different y values (range)
i.e. (1,2) and (1,3)
Answer:
x = -5 or x= 2
Step-by-step explanation:
|-4x-6| = 14
There are two solutions, one positive and one negative
-4x-6 = 14 -4x-6 = -14
Add 6 to each side
-4x-6+6 = 14+6 -4x-6+6 = -14+6
-4x = 20 -4x = -8
Divide by -4
-4x/-4 = 20/-4 -4x/-4 = -8/-4
x = -5 x = 2