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AlekseyPX
3 years ago
6

A circle has a radius of 17 cm find the length s of the arc intercepted by a central angle of 66 degrees

Mathematics
2 answers:
pav-90 [236]3 years ago
5 0
Arc length (s) = radius (r) x θ (in radians)

First, convert 66° into radians using the proportion π = 180°
\frac{ \pi}{180} =  \frac{x}{66}
\frac{66 \pi }{180} = x
\frac{11 \pi }{30} = x

s = r θ
  = 17 (\frac{11 \pi }{30})
  = \frac{187 \pi }{30}

Answer: \frac{187 \pi }{30} ≈ 19.6 cm
SpyIntel [72]3 years ago
4 0
Circumference = 2*17 pi = 34pi cms

length of s = (66/360) * 34 pi  =  6.233 pi  =   19.58 cm to nearest hundredth
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Answer:

A 90% confidence interval to estimate the mean DRP score in Henrico County Schools  is =32±2.7280

i.e. C.I.  [29.3,34.7]

Hence the results are not significant.

Step-by-step explanation:

Given:

Total no of students =44

True mean =32

Standard deviation=11

And all 4 students score also given.

To Find:

90 % confidence interval and conclusion on it.

Solution:

Here for C.I. we required mean, standard deviation and no of students.

So mean =32,S.D.=11 and n=44

Therefore , For 90 % interval Zscore is Z=1.645

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Now Here to commit on calculated interval we should check  value of Z-score

So we need to calculate the sample mean.

Sample mean =Sum of all values /Total no of values.

=[40+ 26 +39+ 14+ 42+ 18 +25+ 43+ 46 +27 +19+ 47+ 19 +26+ 35 +34+ 15+ 44 40+ 38+ 31+ 46 +52 +25+ 35 +35+ 33 +29 +34 +41 +49+ 28+ 42+ 47 +35 +48 +22 33+ 41 +51 +27 +14+ 54 +45]/44

=34.86

Z-score=(sample mean -true mean)/[standard deviation/Sqrt(n)]

=(34.86-32)/[11/Sqrt(44)]

Z=1.72465

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P(Z≥1.72465)=0.08544

For 0.05 significance level  the results are not significant at  p<0.01.

Researcher claimed mean is not correct upto 0.05 significant level

i.e calculated mean and Sample mean are different.

Hence the results are not significant.

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