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4vir4ik [10]
3 years ago
7

Suppose the radius of a circle is 3 units what is the circumference

Mathematics
1 answer:
HACTEHA [7]3 years ago
8 0

Answer:

6\pi or approximately 18.85 units

Step-by-step explanation:

The formula for finding the circumference of a circle is C=2\pi r, where C = circumference and r = radius. In this case, r=3, so after plugging that into C=2\pi r, we get:

C=2\pi r\\  = 2*\pi *3\\=6\pi

Since \pi is approximately 3.1415, 6\pi =6*3.1415=18.849, which rounds to 18.85. Therefore, the circumference of the circle is 6\pi, or approximately 18.85 units. Hope this helps!

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The speeds of vehicles traveling on a highway are normally distributed with an unkown population mean and standard deviation. A
Maksim231197 [3]

Answer:

The 90% confidence interval would be given by (60.09;69.91)    

We are 90% confident that the true mean for the speeds of vehicles traveling on a highway is between 60.09 and 69.91 miles per hour.

Step-by-step explanation:

1) 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 =65 represent the sample mean for the sample  

\mu population mean (variable of interest)

s=9 represent the sample standard deviation

n=11 represent the sample size  

2) Confidence interval

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

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

In order to calculate the critical value t_{\alpha/2} we need to find first the degrees of freedom, given by:

df=n-1=11-1=10

Since the Confidence is 0.90 or 90%, the value of \alpha=0.1 and \alpha/2 =0.05, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,10)".And we see that t_{\alpha/2}=1.81

Now we have everything in order to replace into formula (1):

65-1.81\frac{9}{\sqrt{11}}=60.09    

65+1.81\frac{9}{\sqrt{11}}=69.91

So on this case the 90% confidence interval would be given by (60.09;69.91)    

We are 90% confident that the true mean for the speeds of vehicles traveling on a highway is between 60.09 and 69.91 miles per hour.

3 0
3 years ago
1 5/8 * 3 2/3 in simplest form
Tanzania [10]

Answer:

20

Step-by-step explanation:

If you need the step-by-step explanation please reach out to me!

8 0
2 years ago
Read 2 more answers
Is the relation a function? Why?
Anvisha [2.4K]

No! 11, the input, has two outputs which makes it not a function! :)

7 0
3 years ago
Read 2 more answers
Lee watches tv 3hours per day. Lee tv consumes 200 watts when on. Electricity cost 12 cents 1 kilowatt-hour how much does Lee's
Alik [6]

Answer: $2.16

Lee watches TV 3 hours per day and TV consumes 200 watts.

Cost of electricity = 12 cents/(1-kilowatt-hour)

200w×3 hours

600 watt-hours

1000 watt-hours=1kwh

1 watt-hours= 1/1000 kwh

600 watt-hours 600/1000=0.6 kwh

0.6×12=7.2cents

1 day=7.2 cents

30 days

7.2×30

216 cents

$2.16

3 0
3 years ago
Read 2 more answers
Can I get some help on this one and if you could show its done I would appreciate it. Thank you.
Andreyy89
<h3>Answer: 5.5 which is choice B</h3>

Have a look at the diagram I posted below. I marked on your image to add in another angle. This angle is also 20 degrees because of congruent alternate interior angles (horizontal lines are parallel). This angle I add in is the reference angle of the triangle

opposite the reference angle is the vertical side x

adjacent to the reference angle is the horizontal side 15

We'll use the tangent rule. Make sure your calculator is in degree mode.

tan(angle) = opposite/adjacent

tan(20) = x/15

15*tan(20) = x <<-- multiply both sides by 15

x = 15*tan(20)

x = 5.45955 <<--- use calculator; this is approximate

x = 5.5 <<--- round to one decimal place

5 0
3 years ago
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