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3 years ago

Find the lower bound for the following lengths:

Mathematics

1 answer:

ikadub [295]3 years ago

7 0

Answer:

a) Lower bound = 39.5

b) Lower bound = 82.75

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It is known that the population variance equals 484. With a .95 probability, the sample size that needs to be taken to estimate

Hitman42 [59]

Answer:

The minimum sample size is n = 75 so that the desired margin of error is 5 or less.

Step-by-step explanation:

We are given the following in the question:

Population variance = 484

Standard deviation =

$\sigma^2 = 484\\\sigma =\sqrt{484} = 22$

Confidence level = 0.95

Significance level = 0.05

Margin of error = 5

Formula:

Margin of error =

$E = z\times \dfrac{\sigma}{\sqrt{n}}\\\\n = (\dfrac{z\times \sigma}{E})^2$

$z_{critical}\text{ at}~\alpha_{0.05} = 1.96$

Putting values, we get

$E\leq 5\\\\1.96\times \dfrac{22}{\sqrt{n}} \leq 5\\\\\sqrt{n} \geq 1.96\times \dfrac{22}{5}\\\\n \geq (1.96\times \dfrac{22}{5})^2\\\\n \geq 74.373$

Thus, the minimum sample size is n = 75 so that the desired margin of error is 5 or less.

3 0

3 years ago

The perimeter of a semicircle is 5.14 feet. What is the semicircle’s area?

hammer [34]

$\bf \textit{circumference of a semi-circle}\\\\
C=\pi r\qquad 
\begin{cases}
r=radius\\
-----\\
C=5.14
\end{cases}\implies 5.14=\pi r\implies \boxed{\cfrac{5.14}{\pi }=r}\\\\
-------------------------------\\\\
\textit{area of a semi-circle}\\\\
A=\cfrac{\pi r^2}{2} \implies A=\cfrac{\pi }{2}r^2\implies A=\cfrac{\pi }{2}\left( \boxed{\cfrac{5.14}{\pi }} \right)^2
\\\\\\
A=\cfrac{\pi }{2}\implies \cfrac{5.14^2}{\pi ^2}\implies A=\cfrac{26.4196}{2\pi }\implies A=\cfrac{13.2098}{\pi }$

5 0

3 years ago

The difference between a number and 10 is multiplied by 2. The answer is 6. What is the equation that represents this informatio

Rashid [163]

The expression is 10 - 7 x 2 = 6.

5 0

3 years ago

3<6c+13<5 (Enter your answer in INTERVAL notation, using U to indicate a union of intervals; or enter DNE if no solution e

laiz [17]

Answer:

(-5/3, -4/3)

Step-by-step explanation:

3 < 6c +13 < 5 . . . . given

-10 < 6c < -8 . . . . . subtract 13

-10/6 < c < -8/6 . . . divide by 6

We can express the interval using reduced fractions as ...

(-5/3, -4/3)

8 0

3 years ago

I need to determine each angles measure. M 4<br><br> M 6

Ulleksa [173]

By geometrical inspection we have:
M4 = 30
Then the angle M6 can be determined from the fact that you have a rectangle triangle (345) that has an angle of 90 and another of 30. The missing angle measures:
180-90-30 = 60 = M3
Then to find M6 we have
M3 + 60 + M6 = 180
M6 = 180-60-M3
M6 = 180-60-60
M6 = 60
answer:
M4 = 30
M6 = 60

7 0

3 years ago