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krok68 [10]
3 years ago
8

Shirley wants to find the distance her unicycle moves on the sidewalk when the tire makes one complete revolution. If the diamet

er of her unicycle tire is 14 inches, find the distance the unicycle moves in one complete revolution. Use as an approximation for pi.
Mathematics
1 answer:
Evgesh-ka [11]3 years ago
6 0

Answer:

44 in

Step-by-step explanation:

The circumference of the tire will be the same as the distance the unicycle moves in one complete revolution.

Find the circumference with the formula C = \pid, where d is the diameter

Plug in the values:

C = \pi(14)

C = approx. 44 in

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A pencil cup is a cylinder made of plastic with one base missing. The cup is 5 inches tall and has a radius of 1.75 inches. Appr
wariber [46]

Answer:

74.22

Step-by-step explanation:

a pencil cup is like a cylinder

A=2πrh+2πr2=2·π·1.75·5+2·π·1.752≈74.22013

hope this helps

correct me if this is wrong

3 0
3 years ago
Researchers are interested if a school breakfast program leads to taller children. Assume that the population of all 5 year-old
DedPeter [7]

Answer:

39-1.96\frac{1}{\sqrt{25}}=38.608    

39+1.96\frac{1}{\sqrt{25}}=39.392    

So on this case the 95% confidence interval would be given by (38.608;39.392)    

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=39 represent the sample mean for the sample  

\mu population mean (variable of interest)

\sigma=1 represent the population standard deviation

n=25 represent the sample size  

Solution to the problem

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

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

The margin of error is given by:

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

Since the Confidence is 0.95 or 95%, the value of \alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that z_{\alpha/2}=1.96

And replacing we got:

ME= 1.96 *\frac{1}{\sqrt{25}}= 0.392

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

39-1.96\frac{1}{\sqrt{25}}=38.608    

39+1.96\frac{1}{\sqrt{25}}=39.392    

So on this case the 95% confidence interval would be given by (38.608;39.392)    

7 0
3 years ago
The diagonal of a square is 8 cm.
VladimirAG [237]

the length of the side of this square is 4\sqrt{2} \:or \:5.65cm

Answer:

Solutions Given:

let diagonal of square be AC: 8 cm

let each side be a.

As diagonal bisect square.

let it forms right angled triangle ABC .

Where diagonal AC is hypotenuse and a is their opposite side and base.

By using Pythagoras law

hypotenuse ²=opposite side²+base side²

8²=a²+a²

64=2a²

a²=\frac{64}{2}

a²=32

doing square root on both side

\sqrt{a²}=\sqrt{32}

a=±\sqrt{2*2*2*2*2}

a=±2*2\sqrt{2}

Since side of square is always positive so

a=4\sqrt{2} or 5.65 cm

6 0
2 years ago
Read 2 more answers
Select the representation that does not change the location of the given point. (4, 110°)
miss Akunina [59]

Answer:

(4,470°)

Step-by-step explanation:

The representation that does not change the location of (4, 110°) in polar coordinates are all points that are coterminal with the given point.

The only point among the given options that is coterminal with (4, 110°) is (4, 470)°

The two points have the same magnitude and 470°-360°=110°.

Since 110° is coterminal with 470° and the two points have the same magnitude with the same sign, the two points represent the same location in polar coordinates.

The correct choice is (4,470°)

3 0
3 years ago
HELP!!! NEED HELP!!!!
blsea [12.9K]

Answer:

C

Step-by-step explanation:

6 0
3 years ago
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