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bazaltina [42]
4 years ago
6

How do set up a substitution equation like 3x-y=5,x-4y=-24

Mathematics
1 answer:
Pavlova-9 [17]4 years ago
4 0
Well to set up a substitution equation, you need to make sure you have something you can sub in that's identical in both equations.

we have 
3x-y=5
x-4y=-24

what's in common? x and y.
take one of the equations and solve for x or y like so (i'm doing y)
3x-5=y
then substitute the whole 3x-5 equation for y in the second equation. it is quite similar to how you would normally substitute a number like if y=5, then you substitute 5 for y in the second equation, but instead the "5" is an equation "3x-5"

x-4y=-24
x-4(3x-5) = -24

Now that you got it set up, you just need to solve for x and once you got x value, plug the x value in the original equations to find y.

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Complete question is:

Seventy million pounds of trout are grown in the U.S. every year. Farm-raised trout contain an average of 32 grams of fat per pound, with a standard deviation of 7 grams of fat per pound. A random sample of 34 farm-raised trout is selected. The mean fat content for the sample is 29.7 grams per pound. Find the probability of observing a sample mean of 29.7 grams of fat per pound or less in a random sample of 34 farm-raised trout. Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.

Answer:

Probability = 0.0277

Step-by-step explanation:

We are given;

Mean: μ = 32

Standard deviation;σ = 7

Random sample number; n = 34

To solve this question, we would use the equation z = (x - μ)/(σ/√n) to find the z value that corresponds to 29.7 grams of fat.

Thus;

z = (29.7 - 32)/(7/√34)

Thus, z = -2.3/1.200490096

z = -1.9159

From the standard z table and confirming with z-calculator, the probability is 0.0277

Thus, the probability to select 34 fish whose average grams of fat per pound is less than 29.7 = 0.0277

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