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Fantom [35]
2 years ago
3

A circle has a central angle measuring StartFraction 3 pi Over 4 EndFraction radians that intersects an arc of length 45 in. Wha

t is the length of the radius of the circle? Round your answer to the nearest tenth. Use 3.14 for Pi.
Mathematics
2 answers:
olga_2 [115]2 years ago
5 0

Answer:

r = 19.1 in

Step-by-step explanation:

Given:-

- The central angle of a circle, θ = 3π / 4

- The arc length, s = 45 in

Find:-

What is the length of the radius (r) of the circle?

Solution:-

- The arc length (s) of a sector of circle with a radius (r) subtended by a central angle ( θ ) is expressed by the given relation:

                                 s = r* θ

- Plug in the values and solve for radius (r)

                                 r = s / θ

                                 r = 45 / (3π / 4) = (45*4) / (3*3.14)

                                 r = 19.1 in

avanturin [10]2 years ago
3 0

Answer: The radius measures 19.1 inches (approximately)

Step-by-step explanation: The central angle in the sector has been given as 3Pi/4 radians. We start by converting the radians to degrees.

1 radian = 180/Pi (or 57.296 degrees)

Hence 3Pi/4 converted to degrees becomes,

= 3Pi/4 x 180/Pi

= (3 x 180)/4

= 135

Having determined the central angle to be 135 degrees, and the length of the arc is 45 inches, the radius can be calculated by substituting for the values into the formula for length of an arc.

Length of an arc = (X/360) x 2Pi x r

45 = (135/360) x 2(3.14) x r

45 = (3/4) x 3.14 x r

By cross multiplication we now have

(45 x 4)/3 x 3.14 = r

180/9.42 = r

19.1083 = r

Therefore, the radius rounded to the nearest tenth equals 19.1 inches.

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Natalija [7]

Answer:

This sample is not representative of all UF students, since those who are not local are not considered.

Step-by-step explanation:

This is a common statistics practice, when we want to study something from a population, we find a sample of this population.

However, the sample has to be representative

For example:

I want to estimate the proportion of New York state residents who are Buffalo Bills fans. So i ask, lets say, 1000 randomly selected Buffalo residents wheter they are Buffalo Bills fans, and expand this to the entire population of New York State residents. This is not representative of all New York State residents, just Buffalo residents.

In this problem, we have that:

They conduct a phone survey (with local numbers selected at random from the student directory) calling people during "dead week". Will this sample be representative of all UF students?

They only call those students with local numbers.

However, in an university, it is expected that there will be a good percentage of non local students.

So this sample is not representative of all UF students, since those who are not local are not considered.

8 0
2 years ago
suppose that a company claims that its boxes of breakfast cereal contain 15 ounces of cereal on average, with a standard deviati
olga nikolaevna [1]

Answer: 15 ounces


Step-by-step explanation:

It is given that a company claims the average cereal in boxes of breakfast cereal = 15 ounces

And we know that the mean amount is nothing but the average amount of any data.

Mean is synonym word of average .

The statistical mean is the mean or average that is used to find the central tendency of the data in any question.

Thus, the expected mean amount of cereal per box = 15 ounces.

8 0
2 years ago
What is the multiplicative rate of change of the exponential function represented in the table? 1.5 2.25 3.0 4.5
Sati [7]
Use the geometric sequence formula to solve for rate:
an=a1r^(n-1)

6.75=4.5r^(2-1)
6.75=4.5r
6.75/4.5=r
r= 1.5
and if you want to make sure just multiply each number by 1.5 and see if it gets you the next number
4.5 4.5×1.5=6.75 (holds true)
6.75 6.75×1.5=10.125 (holds true)
10.125 10.125×1.5=15.1875 (holds true)
15.1875

1.5 is the multiplicatice rate hope that helps :)
8 0
2 years ago
Read 2 more answers
Billy had 55 stamps in his collection. billy’s older brother tommy had 73 stamps in his collection. how many stamps did the two
Rudik [331]
No.of stamps Billy had = 55

Number of stamps Billy's older brother had = 73

So total number of stamps two brother have together = 73 + 55
                                                                                     = 128

6 0
2 years ago
Yolanda dug a hole in the ground that is deeper than -10 inches . She says the depth of the hole is greater than 10 inches. Is Y
denpristay [2]
No, she is not right
8 0
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