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ExtremeBDS [4]
2 years ago
13

SBC is an isosceles triangle with main vertex S.

Mathematics
1 answer:
stira [4]2 years ago
4 0

Answer + Step-by-step explanation:

1) D be the symmetric of B with respect to C then CD = BC

A the symmetric of C with respect to B then AB = BC

We obtain :

CD = BC

AB = BC

Then AB = CD

2) m∠SBA = 180 - SBC = 180 - SCB = m∠SCD

3) we have :

BA = CD

BS = CS

m∠SBA = m∠SCD

Then

the triangles SBA and SCD are congruent

4)

the triangles SBA and SCD are congruent Then SA = SD

Therefore SAD is an isosceles triangle.

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Answer:

Step-by-step explanation:

Given that:

the sample proportion p = 0.39

sample size = 100

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Using normal approximation

The sampling distribution from the sample proportion is approximately normal.

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(b)

Here;

the sample proportion = 0.39

the sample size n = 400

Since np = 400 * 0.39 = 156

Thus, using normal approximation.

From the sample proportion, the sampling distribution is approximate to the mean \mu_{\hat p} =  p = 0.39

the standard deviation \sigma_{\hat p} = \sqrt{\dfrac{p(1-p)}{n} }

\sigma_{\hat p} = \sqrt{\dfrac{0.39 (1-0.39)}{400} }

\sigma_{\hat p} =0.0244

The test statistics can be computed as:

Z = \dfrac{{\hat _{p}} - \mu_{_ {\hat p}} }{\sigma_{\hat p}}

Z = \dfrac{0.3 - 0.39 }{0.0244}

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(c) The effect of the sample size on the sampling distribution is that:

As sample size builds up, the standard deviation of the sampling distribution decreases.

In addition to that, reduction in the standard deviation resulted in increases in the Z score, and the probability of having a sample proportion  that is less than 30% also decreases.

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