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2 years ago

Help me solve this please

Mathematics

1 answer:

shutvik [7]2 years ago

7 0

Answer:

D'G' = 52.5 units

Step-by-step explanation:

Since the dilatation is centred at the origin then multiply the original coordinates by the scale factor 3.5

D' = (1 × 3.5, 7 × 3.5 ) = (3.5, 24.5 )

G' = (- 8 × 3.5, - 5 × 3.5 ) = (- 28, - 17.5 )

Calculate D'G' using the distance formula

d = $\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }$

with (x₁, y₁ ) = D' (3.5, 24.5) and (x₂, y₂ ) = G' (- 28, - 17.5)

D'G' = $\sqrt{(-28-3.5)^2+(-17.5-24.5)^2}$

= $\sqrt{(-31.5)^2+42^2}$

= $\sqrt{992.25+1764}$

= $\sqrt{2756.25}$

= 52.5 units

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3 years ago

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Answer:

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Step-by-step explanation:

1) Notation and definitions

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The margin of error is the range of values below and above the sample statistic in a confidence interval.

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In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by $\alpha=1-0.90=0.1$ and $\alpha/2 =0.05$ . And the critical value would be given by:

$z_{\alpha/2}=\pm 1.64$

The margin of error for the proportion interval is given by this formula:

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

And on this case we have that $ME =\pm 0.06$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

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2 years ago

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Answer:

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Step-by-step explanation:

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