Let the no. of stars one can expect to see at Bryce Canyon be x.
Given that : No. of stars visible in the night sky = 2000
Also, given that, it is 4/15 of x.
Now, we have
∴ You can expect to see 7,500 stars at Bryce Canyon.
What multiplies to 42 and adds to 10
1 answer:
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Answer:
(-1, 6)
Step-by-step explanation:
A graphing calculator shows the vertex to be (x, y) = (-1, 6).
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You can also find it by putting the equation into vertex form.
y = -2(x^2 +2x) +4
y = -2(x^2 +2x +1) +4 +2(1) . . . . . add 1 inside parens; the opposite outside
y = -2(x +1)^2 +6
Compare to ...
y = a(x -h)^2 +k
and you see a=-2, h=-1, k=6
The vertex is (h, k) = (-1, 6).
The rocks are chosen without replacement, which means that the hypergeometric distribution is used to solve this question. First we get the parameters, and then we answer the questions. From this, we get that:
- P(X < 6) = 0.9545
- P(all specimens of one of the two types of rock are selected for analysis) = 0.2046.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
is the number of different combinations of x objects from a set of n elements, given by the following formula.
The mean and the variance are:
We have that:
5 + 7 = 12 rocks, which means that
9 are chosen, which means that
7 are granite, which means that
Question a:
Thus:
Question b:
Since there are only 5 specimens of basaltic rock, at least 9 - 5 = 4 specimens of granite are needed, which means that:
In which
Thus
So P(X < 6) = 0.9545.
Question c:
5 of basaltic and 4 of granite: 0.1591 probability.
7 of granite is P(X = 7), in which
0.1591 + 0.0455 = 0.2046, thus:
P(all specimens of one of the two types of rock are selected for analysis) = 0.2046.
A similar question is found at brainly.com/question/24008577