Answer:
Step-by-step explanation:
The sample space of a single dice is:
Required:
The probability of rolling 3 sixes
In a sample space of a roll of die, we have:
In a roll of dice, the probability of rolling a 6 is:
In 3 rolls, the probability is:
![Pr = [\frac{1}{6}]^3](https://tex.z-dn.net/?f=Pr%20%3D%20%5B%5Cfrac%7B1%7D%7B6%7D%5D%5E3)
2. x + y = 82
x - y = 24
---------------add
2x = 106
x = 53
x + y = 82
53 + y = 82
y = 82 - 53
y = 29
solution is : (53,29)
=======================
3. y = 2x
y = 4x + 6
2x = 4x + 6
2x - 4x = 6
-2x = 6
x = -3
y = 2x
y = 2(-3)
y = -6
solution is (-3,-6)
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4. 5x + 8y = -29
7x - 2y = -67...multiply by 4
----------------
5x + 8y = -29
28x - 8y = - 268 ..result of multiplying by 4
-----------------add
33x = - 297
x = - 9
5x + 8y = -29
5(-9) + 8y = -29
-45 + 8y = -29
8y = -29 + 45
8y = 16
y = 2
solution is : (-9,2)
=======================
5. y = -4x + 6
y = -5x - 4
-4x + 6 = -5x - 4
-4x + 5x = -4 - 6
x = -10
y = -4x + 6
y = -4(-10) + 6
y = 40 + 6
y = 46
solution is (-10,46)
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6. H(m) = 2m + 12
H(m) = 3m + 10
=========================
7. -8x + 4y > -52
4y > 8x - 52
y > 2x - 13 <==
=========================
8. 3x - y = 28
3x + y = 14
---------------add
6x = 42
x = 7
3x - y = 28
3(7) - y = 28
21 - y = 28
-y = 28 - 21
-y = 7
y = -7
solution is (7,-7)
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10. 5x - 5y > 70
-5y > -5x + 70
y < x - 14 <==
=====================
11. sorry...dont know
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12. y = 4x + 4
y = -3x - 3
4x + 4 = -3x - 3
4x + 3x = -3 - 4
7x = -7
x = -1
y = 4x + 4
y = 4(-1) + 4
y = 0
solution is (-1,0)
=======================
13. -12x - 2y > - 42
-2y > 12x - 42
y < -6x + 21 <==
=======================
14. -5x + 2y = 9
3x + 5y = 7
solution is (-1,2)
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15. 3x + 6y = -2
15x + 30y = -10....divide by 5 to reduce = 3x + 6y = -2
is the same line....infinite solutions
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1. (the graph).....y < = 3x - 4....3rd one
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9. (2nd graph)....y < = -3x + 4....last one
Answer:
9 inches
Step-by-step explanation:
