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Korvikt [17]
3 years ago
11

What is the area of the shaded region to the nearest tenth?

Mathematics
1 answer:
Aleks04 [339]3 years ago
5 0

Answer:

15.1

Step-by-step explanation:

We know that the area of the circle is \pi r^{2}, but we are looking for the portion of the circle, this means we multiply it by the portion of the circle that is shaded.

Area of shaded region = \pi r^{2} (\frac{x}{360} )

where r = 4 and x = 108, the 360 comes from the fact that the total degrees around the circle is 360, so dividing the total amount of degrees by the angle will give us the portion we are looking for.

Area of shaded region = \frac{108}{360} \pi 4^{2} = 15.1

Another way to think about it is that the area of the total circle is \pi r^{2}, multiplying it by a fraction, a number less than 1, would give us a smaller value.

Hope this helps.

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According to the empirical (69-95-99.7) rule, if a random variable z has a standard normal distribution, then approximately 95%
Dmitry_Shevchenko [17]

Using z-scores, it is found that the value of z is z = 1.96.

-----------------------------

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula, which for a measure X, in a distribution with mean \mu and standard deviation \sigma, is given by:  

Z = \frac{X - \mu}{\sigma}

  • It measures how many standard deviations the measure is from the mean.
  • Each z-score has an associated p-value, which is the percentile.

  • The normal distribution is symmetric, which means that the middle 95% is between the <u>2.5th percentile and the 97.5th percentile</u>.
  • The 2.5th percentile is Z with a p-value of 0.025, thus Z = -1.96.
  • The 97.5th percentile is Z with a p-value of 0.975, thus Z = 1.96.
  • Thus, the value of Z is 1.96.

A similar problem is given at brainly.com/question/16965597

7 0
2 years ago
Two burritos cost $14.00. Complete the table to show the cost for 4, 5, and 10 burritos at that rate. Next, find the cost for a
Annette [7]

Answer:

4:28

5:35

10:70

Step-by-step explanation:

8 0
3 years ago
20. Based on student records, 25% of the students at a large high school have a
Elenna [48]

Answer:

(E) 0.71

Step-by-step explanation:

Let's call A the event that a student has GPA of 3.5 or better, A' the event that a student has GPA lower than 3.5, B the event that a student is enrolled in at least one AP class and B' the event that a student is not taking any AP class.

So, the  probability that the student has a GPA lower than 3.5 and is not taking any AP  classes is calculated as:

P(A'∩B') = 1 - P(A∪B)

it means that the students that have a GPA lower than 3.5 and are not taking any AP  classes are the complement of the students that have a GPA of 3.5 of better or are enrolled in at least one AP class.

Therefore, P(A∪B) is equal to:

P(A∪B) = P(A) + P(B) - P(A∩B)

Where the probability P(A) that a student has GPA of 3.5 or better is 0.25, the probability P(B) that a student is enrolled in at least one AP class is 0.16 and the probability P(A∩B) that a student has a GPA of 3.5 or better and is enrolled  in at least one AP class is 0.12

So, P(A∪B) is equal to:

P(A∪B) = P(A) + P(B) - P(A∩B)

P(A∪B) = 0.25 + 0.16 - 0.12

P(A∪B) = 0.29

Finally, P(A'∩B') is equal to:

P(A'∩B') = 1 - P(A∪B)

P(A'∩B') = 1 - 0.29

P(A'∩B') = 0.71

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3) same logic. but there are only 2 black 7 cards which means that odds are:
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