What is the probability that a junior non-Nutrition major and then a sophomore Nutrition major are chosen at random? Express you
r answer as a fraction or a decimal number rounded to four decimal places.
1 answer:
Answer:
0.0032
The complete question as seen in other website:
There are 111 students in a nutrition class. The instructor must choose two students at random Students in a Nutrition Class Nutrition majors Academic Year Freshmen non-Nutrition majors 17 18 Sophomores Juniors 13 Seniors 18 Copy Data. What is the probability that a senior Nutrition major and then a junior Nutrition major are chosen at random? Express your answer as a fraction or a decimal number rounded to four decimal places.
Step-by-step explanation:
Total number of in a nutrition class = 111 students
To determine the probability that the two students chosen at random is a junior non-Nutrition major and then a sophomore Nutrition major, we would find the probability of each of them.
Let the probability of choosing a junior non-Nutrition major = Pr (j non-N)
Pr (j non-N) = (number of junior non-Nutrition major)/(total number students in nutrition class)
There are 13 number of junior non-Nutrition major
Pr (j non-N) = 13/111
Let the probability of choosing a sophomore Nutrition major = Pr (S N-major)
Pr (S N-major)= (number of sophomore Nutrition major)/(total number students in nutrition class)
There are 3 number of sophomore Nutrition major
Pr (S N-major) = 3/111
The probability that the two students chosen at random is a junior non-Nutrition major and then a sophomore Nutrition major = 13/111 × 3/111
= 39/12321
= 0.0032
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Step-by-step explanation:
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Positive integers between (inclusive) and
(inclusive) that are multiples of
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terms. The sum of these integers would thus be:
Positive integers between (inclusive) and
(inclusive) that are multiples of
(integers that are both multiples of
and multiples of
) include:
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The common difference of this arithmetic series is . There would be
terms. The sum of these integers would thus be:
.
The requested sum will be equal to:
- the sum of all integers from
to
,
- minus the sum of all integer multiples of
between
and
, and the sum integer multiples of
between
- plus the sum of all integer multiples of
between
That is:
.
Answer with Step-by-step explanation:
We are given that
and
are linearly independent.
By definition of linear independent there exits three scalar and
such that
Where
We have to prove that and
are linearly independent.
Let and
such that
...(1)
..(2)
..(3)
Because and
are linearly independent.
From equation (1) and (3)
...(4)
Adding equation (2) and (4)
From equation (1) and (2)
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area linearly independent.