Answer:
b³
Step-by-step explanation:
The lowest common multiple of the expression is b². This because, taking out a factor of b, b ( b² + 6b ), taking out a factor of b², b² ( b + 6 ),
taking out a factor of ( b + 6 ), ( b + 6 ) b². As a result b² is only the option which is not a factor.
Since the dice are fair and the rolling are independent, each single outcome has probability 1/15. Every time we choose

We have
and
, because the dice are fair.
Now we use the assumption of independence to claim that

Now, we simply have to count in how many ways we can obtain every possible outcome for the sum. Consider the attached table: we can see that we can obtain:
- 2 in a unique way (1+1)
- 3 in two possible ways (1+2, 2+1)
- 4 in three possible ways
- 5 in three possible ways
- 6 in three possible ways
- 7 in two possible ways
- 8 in a unique way
This implies that the probabilities of the outcomes of
are the number of possible ways divided by 15: we can obtain 2 and 8 with probability 1/15, 3 and 7 with probability 2/15, and 4, 5 and 6 with probabilities 3/15=1/5
Answer:
1.25 liters of oil
Step-by-step explanation:
Volume in Beaker A = 1 L
Volume of Oil in Beaker A = 1*0.3 = 0.3 L
Volume of Vinegar in Beaker A = 1*0.7 = 0.7 L
Volume in Beaker B = 2 L
Volume of Oil in Beaker B = 2*0.4 = 0.8 L
Volume of Vinegar in Beaker B = 1*0.6 = 1.2 L
If half of the contents of B are poured into A and assuming a homogeneous mixture, the new volumes of oil (Voa) and vinegar (Vva) in beaker A are:

The amount of oil needed to be added to beaker A in order to produce a mixture which is 60 percent oil (Vomix) is given by:

1.25 liters of oil are needed.
Answer:

Step-by-step explanation:
Given
See attachment for box
Required
The volume of the box
The number of boxes in each direction represents the length of that dimension.
So, from the attachment



The volume is:



Answer:
1. x^8
2. x^8
3. 1024
4. -21a^4
5. z^10
6. -9x^7
7. 42r^7
8. b^7
9. 8a^11
10. 12p^12
Step-by-step explanation: