A sealed rectangular container 10 inches by 12 inches by 6 inches is sitting on its largest face. If it is filled with water up
1 answer:
Answer:
8 inches
Step-by-step explanation:
Given: Dimension of rectangular container=
Water is filled up to a level 2 inches from the top.
As given that container is sitting on its largest face, then it is standing on
Which means the height of container is 6 inches and it ie filled with water up to 2 inches from the top.
∴ Height of water inside the container=
Now, finding the volume of water inside.
we know, Volume=
Volume=
Next, if container is placed in its smallest face then it is standing on and lets assume height to be "x"
Forming an equation now to express the volume conservation law.
⇒
⇒
dividing both side by 60
⇒
∴ x= 8 inches
Hence, 8 inches from the bottom will the water level reach if the container is placed on its smallest face
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Answer:
The probability is 0.0052
Step-by-step explanation:
Let's call A the event that the four cards are aces, B the event that at least three are aces. So, the probability P(A/B) that all four are aces given that at least three are aces is calculated as:
P(A/B) = P(A∩B)/P(B)
The probability P(B) that at least three are aces is the sum of the following probabilities:
- The four card are aces: This is one hand from the 270,725 differents sets of four cards, so the probability is 1/270,725
- There are exactly 3 aces: we need to calculated how many hands have exactly 3 aces, so we are going to calculate de number of combinations or ways in which we can select k elements from a group of n elements. This can be calculated as:
So, the number of ways to select exactly 3 aces is:
Because we are going to select 3 aces from the 4 in the poker deck and we are going to select 1 card from the 48 that aren't aces. So the probability in this case is 192/270,725
Then, the probability P(B) that at least three are aces is:
On the other hand the probability P(A∩B) that the four cards are aces and at least three are aces is equal to the probability that the four card are aces, so:
P(A∩B) = 1/270,725
Finally, the probability P(A/B) that all four are aces given that at least three are aces is:
9514 1404 393
Answer:
sum = ∑[n=1,5] 4^(n-4)
Step-by-step explanation:
First of all, you need to be able to describe the n-th term.
Here, we have ...
term #: 1, 2, 3, 4, 5
value: 4^-3, 4^-2, 4^-1, 4^0, 4^1
That is, the exponent of 4 is 4 less than the term number. So, the n-th term is 4^(n-4). The sum of the 5 terms shown is then ...