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artcher [175]
3 years ago
9

The diameter of a circle is 14cm. Which TWO statements are correct? A

Mathematics
1 answer:
Reika [66]3 years ago
3 0

Answer:

(a) and (e)

Step-by-step explanation:

Given

d = 14cm

Required

Select the true statements

First, is a statement about the area.

The area is calculated as:

Area= \pi*\frac{d^2}{4}

So, we have:

Area= 3.14*\frac{14^2}{4}

Area= 3.14*49

(a) is true

Next, is a statement about the circumference.

This is calculated as:

C = \pi d

So, we have:

C = 3.14 * 14

(e) is true

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Part A

b. 14.6 ± 7.38

Part B

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Part C

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Part D

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Part A

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\left (\bar{x}_{2}- \bar{x}_{1}  \right )\pm t_{\alpha /2}\sqrt{\dfrac{s_{1}^{2}}{n_{1}}+\dfrac{s_{2}^{2}}{n_{2}}}

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C.I. ≈ 14.6 ± 7.37714603353

The 90% C.I. ≈ 14.6 ± 7.38

b. 14.6 ± 7.38

Part B

With the hypotheses are given as follows;

H₀; μ₂ - μ₁ = 0

Hₐ; μ₂ - μ₁ ≠ 0

The two sample t-statistic is given as follows;

t=\dfrac{(\bar{x}_{2}-\bar{x}_{1})}{\sqrt{\dfrac{s_{1}^{2} }{n_{1}}+\dfrac{s _{2}^{2}}{n_{2}}}}

t-statistic=\dfrac{(109.1-94.5)}{\sqrt{\dfrac{10^{2} }{10}+\dfrac{9^{2}}{10}}} \approx 3.43173361147

The two sample t-statistic ≈ 3.43

b. 3.43

Part C

From the t-table, the p-value, we have, the p-value < 0.01

a. P-value < 0.01

Part D

Given that a significance level of 0.05 level is used and the p-value of 0.01 is less than the significance level, there is enough statistical evidence to reject the null hypothesis

b. There is sufficient evidence to reject the null hypothesis.

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