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the circumference of the circle shown below is 54 centimeters. which expression gives the length in centimeters of XY?

g100num [7]

Answer:

The correct option is C

Step-by-step explanation:

Given the circumference of circle which is 54 cm and also the measure of arc XY is 120°

we have to find the expression for arc length of XY

The arc length can be calculated by the formula

$\frac{\theta}{360}\times 2\pi r$

$\frac{\theta}{360}\times circumference$

$\frac{120}{360}\times 54$

Hence, option C is correct

4 0

3 years ago

Read 2 more answers

In a game called taxation and evasion, a player rolls a pair of dice. if on any turn the sum is 7, 11, or 12, the player gets au

bezimeni [28]

The probability that she gets audited no more than 2 times is 0.896482...

As, a pair of dice are rolling here, so the number of total possible outcome = (6×6) = 36

For Sum = 7 , the favorable outcomes are: (1,6) (2,5) (3,4) (4,3) (5,2) and (6,1)

For Sum = 11 , the favorable outcomes are: (5,6) and (6,5)

For Sum = 12 , the favorable outcome is: (6,6)

Probability = (Number of favorable outcomes)÷(Number of total outcomes)

So, $P(7)= \frac{6}{36} =\frac{1}{6}$

$P(11) = \frac{2}{36} = \frac{1}{18}$

$P(12) = \frac{1}{36}$

P( 7 or 11 or 12) = $\frac{1}{6}+\frac{1}{18}+\frac{1}{36} = \frac{6+2+1}{36}=\frac{9}{36} = \frac{1}{4}$

Here the total number of trials = 5 and the probability of getting audited = $\frac{1}{4}$

According the binomial distribution formula:

P(X) = (ⁿCₓ )(P)ˣ (1-P)ⁿ⁻ˣ

where P(X) is the probability of x successes out of n trials

Here, n= 5 and P = 1/4 and we need to find the probability of getting audited no more than 2 times. This means she can gets audited 0, 1 or 2 times.

So,

$P(X=0)+P(X=1) +P(X=2)\\\\= [^5C^0 (\frac{1}{4})^0 (1-\frac{1}{4})^5^-^0 ]+[^5C^1 (\frac{1}{4})^1 (\frac{3}{4})^5^-^1]+[^5C^2 (\frac{1}{4})^2 (\frac{3}{4})^5^-^2]\\\\= (\frac{3}{4})^5+ (5) (\frac{1}{4}) (\frac{3}{4})^4 +(10)(\frac{1}{4})^2 (\frac{3}{4})^3\\\\=0.237304... +0.395507...+0.263671...\\\\ = 0.896482...$

So, the probability that she gets audited no more than 2 times is 0.896482...

5 0

3 years ago

On day 3 of a canned food drive, the students had collected 80 cans and were 40% of the way to their goal. What was their goal f

Over [174]

Answer:

200 cans

Step-by-step explanation:

use rate method

80 40

x 100

40x=8000

x=8000/40

x=200

5 0

3 years ago

A government may create and regulate natural monopolies because:

MAXImum [283]

The government may wish to regulate monopolies to protect the interests of consumers. For example, monopolies have the market power to set prices higher than in competitive markets. The government can regulate monopolies through: Price capping – limiting price increases.

7 0

4 years ago

How many different types of Ice Cream Sundays are possible if each contain one type of 5 different types of ice cream, one type

kykrilka [37]

The answer is B, or 30. 1/5 x 1/2 x 1/3 = 1/30, which means one out of 30 total options will be chosen

5 0

3 years ago