A circle with a circumference 120, degrees central angle.What is the length of the arc?

Mathematics

1 answer:

Mrrafil [7]3 years ago

8 0

Answer: $arc\ length=6$

Step-by-step explanation:

The complete exercise is: "A circle with circumference 18 has an arc with a 120° central angle. What is the length of the arc?"

For this exercise you need to remember the folloowing:

1. The circumference of a circle can be found with this forrmula:

$C=2\pi r$

Where "r" is the radius of the circle

2. The Arc length can be calculated with the following formula:

$arc\ length=2\pi r(\frac{C}{360})$

Where "r" is the radius.

In this case, you know that the circumference of this circle is 18. Then, yoy can identify that:

$2\pi r=18$

So, knowing that the central angle measures 120 degrees, you can substitute values into the formula for calculate the arc length and then you must evaluate.

Therefore, applying this procedure, you get the following result:

$arc\ length=18(\frac{120}{360})\\\\arc\ length=6$

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The probability of passing the math class of Professor Jones is 64%, the probability of passing Professor Smith's physics class

alexgriva [62]

Answer:

The probability of using one or the other is 36%

Step-by-step explanation:

For solving this problem it is easy if we see it in a ven diagram, for this first we are going to name the initial conditions with some variables:

Probability of passing Professor Jones math class = 64% =0,64

P(J) = 0.64

Probabiliry of passing Professor Smith's physics class = 32% =0.32

P(S) = 0.32

Probability of passing both is = 30% = 0.30

P(JnS) = 0.30 (Is is an intersection so it is in the middle of the ven diagram

We need to know which is the probability of pasing one or the other for this we need to take out the probability of passing both for this we have to add the probability of passing Professor Jones math class with the probabiliry of passing Professor Smith's physics class and substract the probability of passing both for each one:

P(JuS) = (P(J) - P(JnS)) + (P(S) - P(JnS)) = (0.64 - 0.30) + (0.32 - 0.30) = 0.34 + 0.02 = 0.36 = 36%

If you check the ven diagram you can see that if we add all what is in red we will have the probability of passing Professor Jones math class and if we add all what is in blue we wiill have the probability of passing Professor Smith's physics class, and if we add just what is in each corner we will get the same value that is the probabilty of passsing one or the other.