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3 years ago

X+2y + z = 4 1. 4y - 3z = 1 y + 5z = 6

Mathematics

1 answer:

Feliz [49]3 years ago

4 0

Answer:

The values of x = y = z = 1

Step-by-step explanation:

Given three linear equation as ,

x + 2y + z = 4 .......a

4y - 3z = 1 .......b

y + 5z = 6 ........c

Now solve eq a and b first

4y - 3z = 1 × 5

y + 5z = 6 × 3

Or, 20y - 15z = 5

3 y + 15z = 18

so ,(20y - 15) + (3y +15 ) = 5 +18

or, 23 y = 23

∴ y = 1

Now put this y value in eq c

so , 1 + 5z = 6 ,

Or, 5z = 6-1 =5

∴ z = 1

Again put this y and z value in eq a

so, x + 2(1) + (1) = 4

Or, x = 4 -3

∴ x = 1

Hence from the above solutions , the value of x = y =z = 1 Answer

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Here’s a graph of a linear function. Write the equation that describes that function

inessss [21]

Answer:

The equation of the line is y = 1/4x - 4

Step-by-step explanation:

In order to find this, start with two points that are on the line. We'll use (0, -4) and (4, -3). Now we can use the slope formula to find the slope.

m(slope) = (y2 - y1)/(x2 - x1)

m = (-4 - -3)/(0 - 4)

m = -1/-4

m = 1/4

Now that we have this, we can use that slope and a point in point-slope form. Then we solve for y to get the equation.

y - y1 = m(x - x1)

y - -4 = 1/4(x - 0)

y + 4 = 1/4x

y = 1/4x - 4

8 0

3 years ago

Wal-Mart conducted a study to check the accuracy of checkout scanners at its stores. At each of the 60 randomly selected Wal-Mar

Mamont248 [21]

Answer:

The 95% confidence interval is

$0.7811 < p < 0.9529$

Generally the interval above can interpreted as

There is 95% confidence that the true proportion of Wal-Mart stores that have more than 2 items priced inaccurately per 100 items scanned lie within the interval

Generally 99% is outside the interval obtained in a above then the claim of Wal-mart is not believable

$n = 125 \ stores$

Step-by-step explanation:

From the question we are told that

The sample size is n = 60

The number of stores that had more than 2 items price incorrectly is k = 52

Generally the sample proportion is mathematically represented as

$\^ p = \frac{ k }{ n }$

=> $\^ p = \frac{ 52 }{ 60 }$

=> $\^ p = 0.867$

From the question we are told the confidence level is 95% , hence the level of significance is

$\alpha = (100 - 95 ) \%$

=> $\alpha = 0.05$

Generally from the normal distribution table the critical value of $\frac{\alpha }{2}$ is

$Z_{\frac{\alpha }{2} } = 1.96$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p (1- \^ p)}{n} }$

=> $E = 1.96 * \sqrt{\frac{ 0.867 (1- 0.867)}{60} }$

=> $E = 0.0859$

Generally 95% confidence interval is mathematically represented as

$\^ p -E < p < \^ p +E$

=> $0.867 - 0.0859 < p < 0.867 + 0.0859$

=> $0.7811 < p < 0.9529$

Generally the interval above can interpreted as

There is 95% confidence that the true proportion of Wal-Mart stores that have more than 2 items priced inaccurately per 100 items scanned lie within the interval

Considering question b

Generally 99% is outside the interval obtained in a above then the claim of Wal-mart is not believable

Considering question c

From the question we are told that

The margin of error is E = 0.05

From the question we are told the confidence level is 95% , hence the level of significance is

$\alpha = (100 - 95 ) \%$

=> $\alpha = 0.05$

Generally from the normal distribution table the critical value of $\frac{\alpha }{2}$ is

$Z_{\frac{\alpha }{2} } = 1.645$