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4vir4ik [10]
2 years ago
14

PLEASE HELP WILL GIVE BRAINLIEST!!!!!!

Mathematics
1 answer:
Reptile [31]2 years ago
7 0

(2,-6,1)

There are a few way to solve this with linear programming, but I am using a simple substitution method.

The goal is to isolate the variables by subtracting or adding the equations. (note: I will refer to the equations as A,B, and C)

2x+y−z=−3

5x−2y+2z=24

3x−z=5

C already has just two variables, x and z. This means a good place to start is by eliminating at least y from one other equation, if not y and another value. To do this, we need to either add two equations where the y values are opposite or subtract one where the y value is equal. However, the two equations with a y value do not have opposite or the same y values.

To get a new equation, we can multiply A by 2. This will give us +2y, which can be added to B to eliminate the value all together- AND the z value. Remember that the WHOLE A equation needs to be multiplied by 2:

2(2x+y-z)=2(-3)

4x+2y-2z=-6

We can now add 2A to B.

(4x+2y-2z=-6)+(5x−2y+2z=24 )

9x=18

x=2

We now know x=2. We can plug this into C to find the z value.

3x−z=5

3(2)-z=5

6-z=5

-z=-1

z=1

With both x and z, we can find y using A.

2x+y−z=−3

2(2)+y-(1)=-3

4+y-1=-3

3+y=-3

y=-6

x=2, y=-6, z=1

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2. A statistics student plans to use a TI-84 Plus calculator on her final exam. From past experience, she estimates that there i
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  1. P(≥1 working) = 0.9936
  2. She raises her odds of completing the exam without failure by a factor of 13.5, from 11.5 : 1 to 155.25 : 1.

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1. Assuming the failure is in the calculator, not the operator, and the failures are independent, the probability of finishing with at least one working calculator is the complement of the probability that both will fail. That is ...

... P(≥1 working) = 1 - P(both fail) = 1 - P(fail)² = 1 - (1 - 0.92)² = 0.9936

2. The odds in favor of finishing an exam starting with only one calculator are 0.92 : 0.08 = 11.5 : 1.

If two calculators are brought to the exam, the odds in favor of at least one working calculator are 0.9936 : 0.0064 = 155.25 : 1.

This odds ratio is 155.25/11.5 = 13.5 times as good as the odds with only one calculator.

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My assessment is that there is significant gain from bringing a backup. (Personally, I might investigate why the probability of failure is so high. I have not had such bad luck with calculators, which makes me wonder if operator error is involved.)

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