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Jet001 [13]
3 years ago
9

-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:

z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96

The confidence interval for the mean is given by the following formula:  

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

If we replace the values obtained we got:

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)

Part b

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 0.03 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)  

And replacing into equation (b) the values from part a we got:

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

And rounded up we have that n=622

Part c

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

And rounded up we have that n=1068

5 0
3 years ago
Guys I need help... will mark brannliest IF CORRECT
SVEN [57.7K]

Answer: answer is C

Step-by-step explanation:

7 0
3 years ago
2a−1/2a and 3a−1/3a , where a is a positive number.
Andrew [12]

Answer:

  • 3/2a
  • 8/3a

Step-by-step explanation:

Maybe you want to simplify each of these expressions.

  2a -1/2a = (2 -1/2)a = (3/2)a

__

  3a -1/3a = (3 -1/3)a = (8/3)a

6 0
3 years ago
HELP!!!!!!!!!!!! LOTS OF POINTS!!!!!!!!!!!!!
Veronika [31]
 the volume of the  sphere is  =4/3.pi.r^3
6 0
4 years ago
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