How can you analyze connections between linear equations and use them to solve problems

Mathematics

1 answer:

Alexeev081 [22]2 years ago

6 0

Answer:

Step-by-step explanation:

One of the more obvious "connections" between linear equations is the presence of the same two variables (e. g., x and y) in these equations.

Assuming that your two equations are distinct (neither is merely a multiple of the other), we can use the "elimination by addition and subtraction" method to eliminate one variable, leaving us with an equation in one variable, solve this 1-variable (e. g., in x) equation, and then use the resulting value in the other equation to find the value of the other variable (e. g., y). By doing this we find a unique solution (a, b) that satisfies both original equations. Not only that, but also this solution (a, b) will also satisfy both of the original linear equations.

I urge you to think about what you mean by "analyze connections."

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algol [13]

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1 year ago

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The mean per capita income is 23,037 dollars per annum with a variance of 149,769. What is the probability that the sample mean

mihalych1998 [28]

Answer:

Probability that the sample mean would be less than 23,013 dollars is 0.2358.

Step-by-step explanation:

We are given that the mean per capita income is 23,037 dollars per annum with a variance of 149,769.

Also, a sample of 134 persons is randomly selected.

Firstly, Let $\bar X$ = sample mean

The z-score probability distribution for sample mean is given by;

Z = $\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = population mean per capita income = 23,037 dollars p.a.

$\sigma$ = standard deviation = $\sqrt{Variance}$ = $\sqrt{149,769}$ = 387 dollars p.a

n = sample of persons = 134

So, probability that the sample mean would be less than 23,013 dollars is given by = P( $\bar X$ < 23,013 dollars)

P( $\bar X$ < 23,013) = P( $\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }$ < $\frac{23,013-23,037}{\frac{387}{\sqrt{134} } }$ ) = P(Z < -0.72) = 1 - P(Z $\leq$ 0.72)