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Masteriza [31]
3 years ago
15

In circle O, chord AOB is drawn. Point C is located on the exterior of the circle with tangent CB and secant CDA drawn.Itisknown

that CD2 and DA6.
(a) Determine the length of BC .
(b) What is the length of the radius of circle O in simplest radical form.
(c) Determine the measure of C . Hint - consider right triangle trigonometry instead of circle theorems.
REASONING
(d) Find the measure of AD . Show how you arrived at your answer.
Mathematics
1 answer:
ser-zykov [4K]3 years ago
3 0

Answer:

  (a) 4

  (b) 2√3

  (c) 60°

  (d) 120°

Step-by-step explanation:

(a) The relationship between tangents and secants is ...

  CB^2 = CD·CA

Filling in the given values, we find ...

  CB^2 = 2·(2+6) = 16

  CB = √16 = 4

The length of BC is 4 units.

__

(b) Triangle ABC is a right triangle, so the sides of it satisfy the Pythagorean theorem.

  CA^2 = CB^2 +AB^2

  8^2 = 16 +AB^2

  AB = √48 = 4√3

The radius is half the length of AB, so the radius is 2√3.

__

(c) The measure of angle C can be determined from the cosine relation:

  cos(C) = CB/CA = 4/8 = 1/2

  C = arccos(1/2) = 60°

The measure of angle C is 60°.

__

(d) Arc AD is intercepted by angle ABD, which has the same measure as angle C. Hence the measure of arc AD is twice the measure of angle C.

The measure of arc AD is 120°.

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Answer:

The sample size used to compute the 95% confidence interval is 1066.

Step-by-step explanation:

The (1 - <em>α</em>)% confidence interval for population proportion is:

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The 95% confidence interval for proportion of the bank's customers who also have accounts at one or more other banks is (0.45, 0.51).

To compute the sample size used we first need to compute the sample proportion value.

The value of sample proportion is:

\hat p=\frac{Upper\ limit+Lower\ limit}{2}=\frac{0.45+0.51}{2}=0.48

Now compute the value of margin of error as follows:

MOE=\frac{Upper\ limit-Lower\ limit}{2}=\frac{0.51-0.45}{2}=0.03

The critical value of <em>z</em> for 95% confidence level is:

z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96

Compute the value of sample size as follows:

MOE=z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}\\0.03=1.96\times \sqrt{\frac{0.48(1-0.48)}{n}}\\(\frac{0.03}{1.96})^{2}=\frac{0.48(1-0.48)}{n}\\n=1065.404\\n\approx1066

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