A production facility employs 20 workers on the day shift, 15 workers on the swing shift, and 10 workers on the graveyard shift.
1 answer:
Answer:
1. 77520
2. = 0.0017
3. = 0.0019
4. = 0.9981
5. = 0.2036
Step-by-step explanation:
The number of ways or combinations in which we can select x elements from a group of n can be calculated as:
So, there are 77520 selections that result in all 7 workers coming from the day shift. It is calculated as:
At the same way, the total number of selections of 7 workers from the 45 is 45C7, so the probability that all 7 selected workers will be from the day shift is:
The probability that all 7 selected workers will be from the same shift is calculated as:
Because the consultant can select all workers from the day shift (20C7) or can select all workers from the swing shift (15C7) or can select all workers from the graveyard shift (10C7).
On the other hand, the probability that at least two different shifts will be represented among the selected workers is the complement of the probability that all 7 selected workers will be from the same shift. So it is calculated as:
Finally, the probability that at least one of the shifts will be un-represented in that sample of workers is:
Where 25C7 is the number of ways to select all 7 workers from swing or graveyard shift, 30C7 is the number of ways to select all 7 workers from day or graveyard shift and 35C7 is the number of ways to selects all 7 workers from day shift and swing shift.
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Answer:
Step-by-step explanation:
We have the system of equations:
We can convert this to a matrix. In order to convert a triple system of equations to matrix, we can use the following format:
Importantly, make sure the coefficients of each variable align vertically, and that each equation aligns horizontally.
In order to solve this matrix and the system, we will have to convert this to the reduced row-echelon form, namely:
Where the (x, y, z) is our solution set.
Reducing:
With our system, we will have the following matrix:
What we should begin by doing is too see how we can change each row to the reduced-form.
Notice that R₁ and R₂ are rather similar. In fact, we can cancel out the 1s in R₂. To do so, we can add R₂ to -2(R₁). This gives us:
Now, we can multiply R₂ by -1/5. This yields:
From here, we can eliminate the 3 in R₃ by adding it to -3(R₁). This yields:
We can eliminate the -5 in R₃ by adding 5(R₂). This yields:
We can now reduce R₃ by multiply it by -1/4:
Finally, we just have to reduce R₁. Let's eliminate the 2 first. We can do that by adding -2(R₂). So:
And finally, we can eliminate the second 1 by adding -(R₃):
Therefore, our solution set is
And we're done!
Answer:
Step-by-step explanation:
Given
Required
Find x such that:
This gives:
Collect like terms
Expand
Factorize
Factor out x - 1
Solve: