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3 years ago

Need help ASAP Integrated math ll

Mathematics

1 answer:

Solnce55 [7]3 years ago

7 0

Answer:

∠ EFH = 112°

Step-by-step explanation:

∠ ACD and ∠ EFH are Alternate exterior angles and are congruent, thus

11x - 20 = 9x + 4 ( subtract 9x from both sides )

2x - 20 = 4 ( add 20 to both sides )

2x = 24 ( divide both sides by 2 )

x = 12

Thus

∠ EFH = 11x - 20 = 11(12) - 20 = 132 - 20 = 112°

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Answer:

$\begin{tabular}{c|ccccc}{$x$&10&12&16&17&20&z&-1.397&-0.839&0.2795&0.559&1.397&\end{tabular}$

Step-by-step explanation:

z-score is denoted by:

$z=\dfrac{x-\mu}{\sigma}$

here,

$\mu$ : mean

$\sigma$ : standard deviation (or the square root of the variance)

so first we need to find the means of our sample:

$\mu=\dfrac{10+20+12+17+16}{5}\\\mu = 15\\$

Now to find the standard deviation we first need to find the variance of the sample. The variance is the sum of the squares of the differences of each value from the mean.

$\sigma^2 = \dfrac{(10-15)^2+(20-15)^2+(12-15)^2+(17-15)^2+(16-15)^2}{5}\\\sigma^2 = 12.8$

the standard derviation is simply the square root of the variance!

$\sigma = \sqrt{\sigma^2} \\\sigma = \sqrt{12.8} \\\sigma = 3.5778$

Now that we all the values for our z-score formula. we can plug it in!

$z=\dfrac{x-\mu}{\sigma}$

$z=\dfrac{x-15}{3.5778}$

Finally we'll use each value in place of x from our sample into the formula to find the z-score of each value.

$z=\dfrac{10-15}{3.5778} = -1.397$

$z=\dfrac{20-15}{3.5778} = 1.397$

$z=\dfrac{12-15}{3.5778} = -0.839$

$z=\dfrac{17-15}{3.5778} = 0.559$

$z=\dfrac{16-15}{3.5778} = 0.2795$

We can even display the z-scores in a table: (the x-values are in ascending order)

$\begin{tabular}{c|ccccc}{$x$&10&12&16&17&20&z&-1.397&-0.839&0.2795&0.559&1.397&\end{tabular}$

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Step-by-step explanation:

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