Answer:
D(1, –5), (7, 1), (–11, 7)
Step-by-step explanation:
The given inequalities are:
y + x ≥ –4
y ≥ x – 6
3y + x ≤ 10
We graph the inequalities as shown in the attachment.
The coordinates of the vertices of the figure formed by the given system of inequalities are:
(1, –5), (7, 1), (–11, 7)
The correct choice is D.
Answer:
17.80% probability that all of them are wearing their seat belts.
Step-by-step explanation:
For each driver stopped, there are only two possible outcomes. Either they are wearing their seatbelts, or they are not. The drivers are chosen at random, which mean that the probability of a driver wearing their seatbelts is independent from other drivers. So we use the normal probability distribution to solve this problem.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
Police estimate that 25% of drivers drive without their seat belts.
This means that 75% wear their seatbelts, so
If they stop 6 drivers at random, find the probability that all of them are wearing their seat belts.
This is .
17.80% probability that all of them are wearing their seat belts.
Delete the commas if necessary.
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Explanation:
There are 6 freshmen total and we want to pick 2 of them, where order doesn't matter. The reason it doesn't matter is because each seat on the committee is the same. No member outranks any other. If the positions were labeled "president", "vice president", "secretary", etc, then the order would matter.
Plug n = 6 and r = 2 into the nCr combination formula below
This tells us there are 15 ways to pick the 2 freshmen from a pool of 6 total.
Repeat those steps for the other grade levels.
n = 13 sophomores, r = 5 selections leads to nCr = 13C5 = 1287. This is the number of ways to pick the sophomores.
You would follow the same type of steps shown above to get 1287. Let me know if you need to see these steps.
Similarly, 8C4 = 70 is the number of ways to pick the juniors.
Lastly, 14C3 = 364 is the number of ways to pick the seniors.
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To recap, we have...
Multiply out those values to get to the final answer.
15*1287*70*364 = 491,891,400
This massive number is a little under 492 million.