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max2010maxim [7]
3 years ago
14

Radius OB measures x units. Which expression represents

Mathematics
1 answer:
777dan777 [17]3 years ago
7 0

Answer:

Circumference of the smaller circle = 2.1x units

Step-by-step explanation:

Given question is incomplete; here is the complete question.

Two similar circles are shown. The circumference of the larger circle, with radius OB, is 3 times the circumference of the smaller circle, with radius OA. Radius OB measures x units. Which expression represents the circumference of the smaller circle with radius OA ?

Radius of the larger circle OB = x units

Radius of the smaller circle OA = y units

Circumference of larger circle = 2πx units

Circumference of smaller circle = 2πy units

Since circumference of larger circle is 3 times the circumference of smaller circle,

2πx = 3(2πy)

2πx = 6πy

x = 3y

y = \frac{x}{3}

Therefore, circumference of the smaller circle = 2\pi (\frac{x}{3}) units

                                                                             = \frac{2\pi x}{3} units

                                                                             = 2.094x

                                                                             ≈ 2.1x

Circumference of the smaller circle circle = 2.1x units

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4. A parking lot contains 21 sedans. Sedans are found at a ratio of 7:5 to SUVs in the parking lot. How many
Mice21 [21]

Answer:

they are both divisible by 3

7 x 3 = 21

5 x 3 = 15

Step-by-step explanation:

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6 0
3 years ago
In a random sample of 80 teenagers, the average number of texts handled in a day is 50. The 96% confidence interval for the mean
Nastasia [14]

Answer:

a) \bar X =\frac{46+54}{2}=50

And the margin of error is given by:

ME= \frac{54-46}{2}= 4

The confidence level is 0.96 and the significance level is \alpha=1-0.96=0.04 and the value of \alpha/2 =0.02 and the margin of error is given by:

ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}

We can calculate the critical value and we got:

z_{\alpha/2} = 2.05

And if we solve for the deviation like this:

\sigma = ME * \frac{\sqrt{n}}{z_{\alpha/2}}

And replacing we got:

\sigma =4 *\frac{\sqrt{80}}{2.05} =17.45

b) ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}=2.05 *\frac{17.45}{\sqrt{160}}=2.828

And as we can see that the margin of error would be lower than the original value of 4, the margin of error would be reduced by a factor \sqrt{2}

Step-by-step explanation:

Previous concepts  

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

\bar X represent the sample mean  

\mu population mean (variable of interest)  

\sigma represent the population standard deviation  

n=80 represent the sample size  

Solution to the problem

Part a

The confidence interval for the mean is given by the following formula:  

\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}} (1)  

For this case we can calculate the mean like this:

\bar X =\frac{46+54}{2}=50

And the margin of error is given by:

ME= \frac{54-46}{2}= 4

The confidence level is 0.96 and the significance level is \alpha=1-0.96=0.04 and the value of \alpha/2 =0.02 and the margin of error is given by:

ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}

We can calculate the critical value and we got:

z_{\alpha/2} = 2.05

And if we solve for the deviation like this:

\sigma = ME * \frac{\sqrt{n}}{z_{\alpha/2}}

And replacing we got:

\sigma =4 *\frac{\sqrt{80}}{2.05} =17.45

Part b

For this case is the sample size is doubled the margin of error would be:

ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}=2.05 *\frac{17.45}{\sqrt{160}}=2.828

And as we can see that the margin of error would be lower than the original value of 4, the margin of error would be reduced by a factor \sqrt{2}

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3 years ago
Tammy estimated the product of 4.2 and 5.9, then calculated the exact product. Analyze her work and decide if she made an error.
nataly862011 [7]

Answer:

C.Tammy’s estimate is right, but the actual product should be 24.78.

Step-by-step explanation:

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Read 2 more answers
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Answer:

5

Step-by-step explanation:

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2 years ago
A parachutist's speed during a free fall reaches 50 meters per second. What is this speed in feet per second? At this speed, how
BigorU [14]

50m ≅164 ft (3s.f.)

50m/s≅164 ft/s

distance after 20s:

d=164 ft/s ⋅20s

=3280ft

Hope This Helps!

7 0
1 year ago
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