6x6 to find the probability for every single roll which is 36.
Ways to make 5 ; 1+4, 4+1, 2+3, 3+2. 4 ways, therefore it’s 4/36 which simplifies to 1/9

6 0

4 years ago

1/3(x-1/3)-1/2(2/3x-1/2)

kenny6666 [7]

For this case we must simplify the following expression:

$\frac {1} {3} (x- \frac {1} {3}) - \frac {1} {2} (\frac {2} {3} x- \frac {1} {2})$

So, if we apply distributive property to the terms within parentheses we have:

$\frac {1} {3} x- \frac {1} {9} - \frac {2} {6} x + \frac {1} {4} =\\\frac {1} {3} x- \frac {1} {9} - \frac {1} {3} x + \frac {1} {4} =$

We simplify taking into account that:

Equal signs are added and the same sign is placed.

Different signs are subtracted and the major sign is placed.

$- \frac {1} {9} + \frac {1} {4} =\\- \frac {4} {36} + \frac {9} {36} =\\\frac {-4 + 9} {36} =\\\frac {5} {36}$

Answer:

$\frac {5} {36}$

4 0

3 years ago

A coffee mixture has beans that sell for $0.20 a pound and beans that sell for $0.68. If 120 pounds of beans create a mixture wo

atroni [7]

Let x be the number of pounds of the $1.35 beans. The cost of those beans is $1.35 * x, or 1.35x.
Let y be the number of pounds of the $1.05 beans. The cost of those beans is $1.05 * y, or 1.05y. 
We know that 120 pounds of the mix sells for $1.15/pound, for a total of 120 * 1.15 = $138. 

x + y = 120 
1.35(x) + (1.05)y = 138 

We can rewrite the first as 
x = -y + 120 

Now we can substitute (-y + 120) in for (x) in the second equation, because we just proved they're equal. 

1.35(x) + 1.05(y) = 138 
1.35(-y + 120) + 1.05y = 138 
-1.35y + 162 + 1.05y = 138 
-0.3y + 162 = 138 
-0.3y = -24 
y = 80 

And since x + y = 120, that means x = 40. 

Check: 
40 pounds of x at $1.35 costs 40 * 1.35, or $54. 
80 pounds of y at $1.05 costs 80 * 1.05, or $84. 
Do those add up to our target total, according to the question, of 120 * 1.15 = $138?

3 0

3 years ago