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Nataly [62]
3 years ago
15

A circle has a radius of 5 meter. What is the length of the arc that is captured by a central angle that measures 120 degrees? R

ound your answer to the nearest tenth.
a) 3.33 meters
b) 31.42 meters
c) 10.47 meters
d) 2.09 meters

Mathematics
2 answers:
ivanzaharov [21]3 years ago
7 0
Well, the formula for the length of an arc is;
<u>  n⁰  </u>   × 2πr<u>
</u>360
<u></u>   Where; n⁰ is the angle
               π is pie, which is 22/7 or 3.143 approximately
                and r is the radius
  
  Anyway, according to the question;
n⁰ is 120⁰
and r is 5 meters. And as you know, the pie is 22/7. So that will be

120⁰/360 x 2 x 22/7 x 5
 And that will give you 10.47metres. Which is approximately 11 metres. Hope i helped, have a nice day 
Irina-Kira [14]3 years ago
3 0
I'd solved the question in attachment. Please watch out the pic..

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Answer:

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2a²b + 6ab²​

Factor out 2ab

2ab(a + 3b)

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A researcher compares the effectiveness of two different instructional methods for teaching electronics. A sample of 138 student
yan [13]

Answer:

The 98% confidence interval for the true difference between testing averages for students using Method 1 and students using Method 2 is (-8.04, 0.84).

Step-by-step explanation:

The (1 - <em>α</em>)% confidence interval for the difference between population means is:

CI=(\bar x_{1}-\bar x_{2})\pm z_{\alpha/2}\times \sqrt{\frac{\sigma^{2}_{1}}{n_{1}}+\frac{\sigma^{2}_{2}}{n_{2}}}

The information provided is as follows:

n_{1}= 138\\n_{2}=156\\\bar x_{1}=61\\\bar x_{2}=64.6\\\sigma_{1}=18.53\\\sigma_{2}=13.43

The critical value of <em>z</em> for 98% confidence level is,

z_{\alpha/2}=z_{0.02/2}=2.326

Compute the 98% confidence interval for the true difference between testing averages for students using Method 1 and students using Method 2 as follows:

CI=(\bar x_{1}-\bar x_{2})\pm z_{\alpha/2}\times \sqrt{\frac{\sigma^{2}_{1}}{n_{1}}+\frac{\sigma^{2}_{2}}{n_{2}}}

     =(61-64.6)\pm 2.326\times\sqrt{\frac{(18.53)^{2}}{138}+\frac{(13.43)^{2}}{156}}\\\\=-3.6\pm 4.4404\\\\=(-8.0404, 0.8404)\\\\\approx (-8.04, 0.84)

Thus, the 98% confidence interval for the true difference between testing averages for students using Method 1 and students using Method 2 is (-8.04, 0.84).

5 0
3 years ago
A certain region currently has wind farms capable of generating a total of 2200 megawatts (2.2 gigawatts) of power. Assuming win
sveta [45]

Answer:

<u>The correct answer is A. 4,818'000,000 kilowatt-hours per year and B. 481,800 households.</u>

Step-by-step explanation:

1. Let's review the information provided to us for solving the questions:

Power capacity of the wind farms = 2,200 Megawatts or 2.2 Gigawatts

2. Let's resolve the questions A and B:

Part A

Assuming wind farms typically generate 25​% of their​ capacity, how much​ energy, in​ kilowatt-hours, can the​ region's wind farms generate in one​ year?

2,200 * 0.25 = 550 Megawatts

550 Megawatts = 550 * 1,000 Kilowatts = 550,000 Kilowatts

Now we calculate the amount of Kilowatts per hour, per day and per year:

550,000 Kw generated by the farms means that are capable of produce 550,000 kw per hour of energy

550,000 * 24 = 13'200,000 kilowatt-hours per day

<u>13'200,000 * 365 = 4,818'000,000 kilowatt-hours per year</u>

Part B

Given that the average household in the region uses about​ 10,000 kilowatt-hours of energy each​ year, how many households can be powered by these wind​ farms?

For calculating the amount of households we divide the total amount of energy the wind farms can generate (4,818'000,000 kilowatt-hours) and we divide it by the average household consumption (10,000 kilowatt-hours)

<u>Amount of households =  4,818'000,000/10,000 = 481,800</u>

8 0
3 years ago
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MrRa [10]

Since the distance of MN is 31 and we have a distance of ML of h -15 and LN of 2h – 8, therefore

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LN = 2h – 8

LN = 2(18) – 8

LN = 28

 

Therefore the length of the segment LN is 28 units

7 0
3 years ago
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