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cricket20 [7]
3 years ago
6

Jack rolls a number cube twice. What is the probability that the sum of the 2 rolls is less than 8 given that the first roll is

a 4?
one over two

one over six

one over three

five over six
Mathematics
2 answers:
disa [49]3 years ago
8 0
If the first roll is a 4, the possibilities to add less than 8 are that the second cube roll is 1, 2 or 3.

These are 3 different events out of 6 possilbe ones, which is 3 / 6 = 1 / 2; i.e. half of times.

Then the answer is the first option: 1 / 2
nevsk [136]3 years ago
3 0

Answer:  The correct option is (a) one over two.

Step-by-step explanation:  Given that Jack rolls a number cube twice. We are to find the probability that the sum of the 2 rolls is less than 8 given that he first roll is a 4.

A cube rolls 1, 2, 3, 4, 5 and 6. So, the sample space will be

S = {1, 2, 3, 4, 5, 6}.

That is, n(S) = 6.

Since the first roll is a 4, so the options for the second roll are 1, 2 and 3 so that the sum is less than 8.

Therefore, if 'A' is the event that the sum is less than 4, then

A = {1, 2, 3}.

That is, n(A) = 3.

So, the probability of happening of event A is given by

P(A)=\dfrac{n(A)}{n(S)}=\dfrac{3}{6}=\dfrac{1}{2}.

Thus, the required probability is one over half.

Option (a) is correct.

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Which of the following equations is not equivalent to the others?
nadya68 [22]
Y=-4+3x is different because all others have a negative 4 AND a -3x
8 0
3 years ago
Read 2 more answers
(x + y + 3)(x + y - 4)
ohaa [14]

Answer:

(X+Y+3)(X+Y-4)

= X^2+XY-4X+XY+Y^2_4Y+3X+3Y-12

=X^2+Y^2+2XY-X-Y-12

Step-by-step explanation:

5 0
3 years ago
Find the length of AB
aniked [119]
FIRST QUESTION
Given points are:
A(2, -4)  and B(6, 2)
Now,  Use the distance formula.
distance formula = \sqrt{  (x_{2}- x_{1})^{2} + ( y_{2} - y_{1} )^{2}  }
 
Now, plug the values into the formula, So,
distance  = \sqrt{  (6- 2)^{2} + ( 2 - (-4))^{2}  }
               
                = \sqrt{  (6- 2)^{2} + ( 2 +4))^{2}  }
    
                = \sqrt{  (4)^{2} + ( 6))^{2}  }
 
                = \sqrt{ 16+36}
 
                = \sqrt{52}
  
               = 2 \sqrt{13}

So, the length of AB is 2 \sqrt{13}.




<span>THIRD QUESTION
</span>Two points given are:
A(3, -2) and B(1, 1)
Also given that B is the midpoint of AC.

Let, the co-ordinates of C be C(a, b).
Now, using midpoint formula,
Midpoint = (\frac{  x_{1}+ x_{2}   }{2} , \frac{ y_{1}+ y_{2}  }{2} )
        
(1, 1)=(\frac{ 3+ a }{2} , \frac{ -2+b }{2} )


Now, equaling the ordered pair, we have,

1=\frac{ 3+ a }{2}  .............equation (1)   

1=\frac{ -2+b }{2}  ................equation (2) 

Now, taking equation (1)
1=\frac{ 3+ a }{2}

1*2=3+a

2-3=a

a=-1

Now, taking equation (2)
1=\frac{ -2+b }{2}

1*2=-2+b

2+2=b

b=4

<span>So, the co ordinates of C are (a, b) which is <u>(-1 , 4)



</u></span>
<span>SECOND QUESTION:
</span>Given equations are:
2x + 3y = 14.....................equation (1)
-4x + 2y = 4 .....................equation (2)
Taking equation (2)
-4x + 2y = 4
2y = 4 + 4x
y = (4 + 4x) / 2
y = 2 + 2x .......................equation (3)
Now, Taking equation (1)
2x + 3y = 14
Substituting the value of y from equation (3), we get,
2x + 3(2 + 2x) = 14
2x + 6 + 6x = 14
8x = 14 - 6
x = (14 - 6) / 8
x = 1

Taking equation (3)
y = 2 + 2x
Now, substituting the value of x in equation (3), we get,
y= 2 + 2 (1)
y = 2 + 2
y = 4

So, x=1 and y=4

6 0
3 years ago
I am between 24 and 34 . you say my name when you count by twos from zero. you say my name when you count by fives from zero. wh
jonny [76]
The answer is 30

2 * 15 = 30
5 * 6 = 30
30 is between 24 and 34
4 0
3 years ago
Which graph represents the solution to the given system? y = –2x + 5 and y = 3x – 2
DaniilM [7]
Y = -2x + 5        y =3x - 2
Since both equations are equal to 'y' you can set them equal to each other to solve.
-2x + 5 = 3x - 2             Subtract 3x from both sides
-5x + 5 = -2                  Subtract 5 from both sides
-5x = -7                        Divide -5 on both sides
x = 7/5
Plug 7/5 back in for x and solve for y.
y = -2(7/5) + 5
y = (-14/5) + (25/5)
y = 11/5
(7/5, 11/5) OR (1.4, 2.2)


4 0
3 years ago
Read 2 more answers
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