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3 years ago

Find the diameter of a circle with an area of 676π square centimeters.

Mathematics

1 answer:

Alex_Xolod [135]3 years ago

8 0

$A = \pi r^2 \\
676\pi = \pi r^2 \\
r = \sqrt{676} = 26$

Therefore, the diameter is twice of that:
52 centimeters.

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5) Is 3 a zero (or root) of f(x) = x3 - 9x2 + 11x + 21?

frozen [14]

Answer:

Yes

Step-by-step explanation:

f(x) = x³ − 9x² + 11x + 21

f(3) = (3)³ − 9(3)² + 11(3) + 21

f(3) = 27 − 81 + 33 + 21

f(3) = 0

6 0

3 years ago

A school authority claims that the average height of students is 178 cm. A researcher has taken a well-designed survey and his s

Hunter-Best [27]

Answer:

d) The difference exists due to chance since the test statistic is small

Step-by-step explanation:

From the given information:

Population mean = 178 cm

the sample mean = 177.5 cm

the standard deviation = 2

the sample size = 25

The null hypothesis and the alternative hypothesis can be computed as:

Null hypothesis:

$H_o: \mu = 178$

Alternative hypothesis:

$H_1: \mu \neq 178$

The t-test statistics is determined by using the formula:

$t = \dfrac{X - \mu}{\dfrac{\sigma}{\sqrt{n}}}$

$t = \dfrac{177.5 - 178}{\dfrac{2}{\sqrt{25}}}$

$t = \dfrac{-0.5}{\dfrac{2}{5}}}$

$\mathbf{t= -1.25}$

Degree of freedom df = n- 1

Degree of freedom df = 25 - 1

Degree of freedom df = 24

At the level of significance ∝ = 0.05, the critical value = 2.064

Decision rule: To reject the null hypothesis if the test statistics is greater than the critical value at 0.05 level of significance

Conclusion: We fail to reject the null hypothesis since the test statistics is lesser than the critical value and we conclude that the difference exists due to chance since the test statistic is small

5 0

3 years ago

Sin theta+costheta/sintheta -costheta+sintheta-costheta/sintheta+costheta=2sec2/tan2 theta -1

sleet_krkn [62]

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$\dfrac{sin^2\theta+2cos\thetasin\theta+cos^2\theta}{sin^2\theta-cos^2\theta}+\dfrac{sin^2\theta-2cos\thetasin\theta+cos^2\theta}{sin^2\theta-cos^2\theta}$