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shusha [124]
3 years ago
8

Why the systems must have the same solution?system(a)4x-5y=13.....3x+6y=11........system(b) 8x-10y=26.....x-11y=2.........AKA QU

ESTION 3

Mathematics
1 answer:
Y_Kistochka [10]3 years ago
3 0
When you add the equations in (a) you get 7x+y=24.

When you subtract the equations in (b) you also get 7x+y=24.

That means to solve both systems you can work with the same equation. However that is not enough. We must have two equivalent equations. We found only one.

Notice however that in the (b) we can take the first equation and divide every term by 2. When we do this we get 4x-5y=13. That’s the first equation in (a).

So both systems can be solved by working with the same two equations. These are 5x-5y=13 and 7x+y=24. And since we have two equations and two unknowns (the number of equations matches the number of variables) there is only one solution — one x and y that would make both systems true — solve both systems.

Basically we showed the systems are equivalent!
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artcher [175]

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The probability of the carton weight being between 775g and 825g is 0.71

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Hello!

The variable of interest is

X: the weight of an egg of a certain breed of hen. (g)

This variable is normally distributed with mean μ= 65.9g and standard deviation σ=5.5 g

If a carton (a random sample of 12 eggs) is taken, you need to calculate the probability of it weighting 775g and 825g, symbolically: P(775≤X[bar]≤825)

For this, you have to use the distribution of the sample mean X[bar]~N(μ;σ²/n)

If the carton weights 775g, then its eggs will have an average weight of 775/12= 64.48g

If the carton weights 825g, then its eggs will have an average weight of 825/12=68.75g

P(64.48≤X[bar]≤68.75)= P(X[bar]≤68.75) - P(X[bar]≤ 64.48)

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The probability of the carton weight being between 775g and 825g is 0.71

I hope you have a SUPER day!

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3 years ago
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