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2 years ago

Given the equation y=1/2x-2 , determine the value for x when y = 8

Mathematics

1 answer:

marissa [1.9K]2 years ago

3 0

Answer:

$x=20$

Step-by-step explanation:

we have

$y=\frac{1}{2}x-2$

This is a linear equation (equation of a line)

To determine the value of x when the value of y=8, substitute the value of y in the equation and solve for x

For y=8

substitute

$8=\frac{1}{2}x-2$

isolate the variable x

Adds 2 both sides

$8+2=\frac{1}{2}x-2+2$

$10=\frac{1}{2}x$

Multiply by 2 both sides

$10*2=(2)\frac{1}{2}x$

Rewrite

$x=20$

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$\hat p =\frac{955-812}{955}= 0.150$

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And the 90% confidence interval would be given (0.131;0.169).

Step-by-step explanation:

We have the following info given:

$n= 955$ represent the sampel size slected

$x = 812$ number of students who read above the eighth grade level

The estimation for the proportion of tenth graders reading at or below the eighth grade level is given by:

$\hat p =\frac{955-812}{955}= 0.150$

The confidence interval for the proportion would be given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 90% confidence interval the significance is $\alpha=1-0.9=0.1$ and $\alpha/2=0.05$ , with that value we can find the quantile required for the interval in the normal standard distribution and we got.

$z_{\alpha/2}=1.64$

And replacing into the confidence interval formula we got:

$0.150 - 1.64 \sqrt{\frac{0.150(1-0.150)}{955}}=0.131$

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