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3 years ago

Please help me, this is frustrating!

Mathematics

2 answers:

vodka [1.7K]3 years ago

8 0

A) mes ∠ DAB) = mes ARC DAB/2

if mes ARC DAB = 40° , then mes DAB = 20

b) ∠ BDA is inscribed in half cercle, so its mesure is 90°

c) ∠DBA =90° - 20° = 70° (COMPLEMENTARY angles in a right triangle)

d) LENGTH OF ARC DB:

The central angle DCB = mes ARC DB = 40°;

Arc LENGTH = (40°) * (2πR)/360°, with R = 12 and π ≈ 3.14

Arc Length = (40°)*2*3.14*12/360 = 8.37 CM

kolbaska11 [484]3 years ago

5 0

Check the picture below

for the DB length, make sure your calculator is in Degree mode, since the angles are in degrees.

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Answer:

$4-2.326\frac{1}{\sqrt{100}}=3.767$

$4+2.326\frac{1}{\sqrt{100}}=4.233$

So on this case the 98% confidence interval would be given by (3.767;4.233)

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Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

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

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

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.98 or 98%, the value of $\alpha=0.02$ and $\alpha/2 =0.01$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.01,0,1)".And we see that $z_{\alpha/2}=2.326$

Now we have everything in order to replace into formula (1):

$4-2.326\frac{1}{\sqrt{100}}=3.767$

$4+2.326\frac{1}{\sqrt{100}}=4.233$

So on this case the 98% confidence interval would be given by (3.767;4.233)

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