What numbers have an absolute value of 2 1/2

1 answer:

7 0

The absolute value of a number is that number's distance from zero. It will always be positive, even if the original number was negative.

| x | = x
| -x | = x

So,
|2 1/2| = 2 1/2
and
|-2 1/2| = 2 1/2

Hope this helps! :)

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Which expression should you simplify to find the 90% confidence interval,

bogdanovich [222]

Answer:

$0.45 - 1.96\sqrt{\frac{0.45(1-0.45)}{36}}=0.2870.45 + 1.96\sqrt{\frac{0.45(1-0.45)}{36}}=0.613$

we can conclude at 95% of confidence that the true proportion of interest for this case is between 0.287 and 0.613

Step-by-step explanation:

The estimated proportion of interest is $\hat p=0.45$

We need to find a critical value for the confidence interval using the normla standard distributon. For this case we have 95% of confidence, then the significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ .

And the critical value is: $z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

The confidence interval for the true population proportion is interest is given by this formula:

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

Replacing the values provided we got:

$0.45 - 1.96\sqrt{\frac{0.45(1-0.45)}{36}}=0.287\\\\0.45 + 1.96\sqrt{\frac{0.45(1-0.45)}{36}}=0.613$

And we can conclude at 95% of confidence that the true proportion of interest for this case is between 0.287 and 0.613

5 0

3 years ago

Whats the answer to: 3x + 5y = 2 9x + 11y = 14

valkas [14]

\begin{gathered}\{\begin{array}{ccc}3x+5y=2&|\cdot(-3)\\9x+11y=14\end{array}\\\underline{+\{\begin{array}{ccc}-9x-15y=-6\\9x+11y=14\end{array}}\ \ |\text{add both sides of equations}\\.\ \ \ \ \ -4y=8\ \ \ |:(=4)\\.\ \ \ \ \ y=-2\\\\\text{substitute the value of y to the first equation}\\\\3x+5\cdot(-2)=2\\3x-10=2\ \ \ |+10\\3x=12\ \ \ |:3\\x=4\\\\Answer:\ x=4;\ y=-2\to(4;\ -2)\end{gathered}

{

3x+5y=2

9x+11y=14

∣⋅(−3)

−9x−15y=−6

9x+11y=14

add both sides of equations

. −4y=8 ∣:(=4)

. y=−2

substitute the value of y to the first equation

3x+5⋅(−2)=2

3x−10=2 ∣+10