-6, -12 after a dilation by a scale factor of 1/3

Mathematics

1 answer:

joja [24]3 years ago

3 0

Answer:

(- 2, - 4 )

Step-by-step explanation:

Assuming the dilatation is centred at the origin, then

multiply each of the coordinates by $\frac{1}{3}$ , thus

(- 6, - 12 ) → ( $\frac{1}{3}$ × - 6 , $\frac{1}{3}$ × - 12 ) → (- 2, - 4 )

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Pls help im so bad at math

Kamila [148]

Angle E and D are supplementary and need to equal 170 when added together.

Angle D = 180-35 = 145

Angle D is split into two with part of it being 44

The missing angle is 145-44 = 101 degrees

The answer is 101

5 0

3 years ago

Of 1000 randomly selected cases of lung cancer, 823 resulted in death within 10 years.

Arada [10]

Answer:

a) $0.823 - 1.96\sqrt{\frac{0.823(1-0.823)}{1000}}=0.799$

$0.823 + 1.96\sqrt{\frac{0.823(1-0.823)}{1000}}=0.847$

The 95% confidence interval would be given by (0.799;0.847)

b) $n=\frac{0.823(1-0.823)}{(\frac{0.03}{1.96})^2}=621.79$

And rounded up we have that n=622

c) $n=\frac{0.5(1-0.5)}{(\frac{0.03}{1.96})^2}=1067.11$

And rounded up we have that n=1068

Step-by-step explanation:

Part a

$\hat p=\frac{823}{1000}=0.823$

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 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by: