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3 years ago

The diameter of a circle is 20 miles. What is the angle measure of an arc bounding a sector with area 10 square miles?

1 answer:

8 0

A=(απr^2)/360=(απd^2)/1440 (r^2=d^2/4)

α=1440A/(πd^2)

s=απd/360 (where s=arc length) so

s=(1440Aπd)/(360πd^2)

s=4A/d and since A=10mi^2 and d=20mi

s=(4*10)/20

s=2 miles

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3 years ago

Find the interquartile range of the data.

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The correct answer is D.14.
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By arranging the numbers in the stem and leaf plot from lowest to highest value, you get an even set of data (31,33,35,41,43,46,48,49,49,50). By dividing the set into two, you get a lower half of your data (31,33,35,41,43) and an upper half (46,48,49,49,50). The lower quartile is the median or the midpoint of the lower half of your data while upper quartile is for the upper half. The lower quartiles is 35 and upper quartile is 49. The difference between the two is 14.

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4 years ago

A sequence of Bernoulli trials consists of choosing components at random from a batch of components. A selected component is eit

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Answer:

a) 0.0287 = 2.87% probability that three non-defective components in a batch of seven components.

b) 0.0336 = 3.36% probability that 8 non-defective components are drawn before the first defective component is chosen.

Step-by-step explanation:

A sequence of Bernoulli trials composes the binomial distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

The probability that a selected component is non-defective is 0.8

This means that $p = 0.8$

a) Three non-defective components in a batch of seven components.

This is P(X = 3) when n = 7. So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 3) = C_{7,3}.(0.8)^{3}.(0.2)^{4} = 0.0287$

0.0287 = 2.87% probability that three non-defective components in a batch of seven components.

b) 8 non-defective components are drawn before the first defective component is chosen.

Now the order is important, so the we just multiply the probabilities.

8 non-defective, each with probability 0.8, and then a defective, with probability 0.2. So

$p = (0.8)^8*0.2 = 0.0336$

0.0336 = 3.36% probability that 8 non-defective components are drawn before the first defective component is chosen.

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3 years ago

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A negative balance of money could represent debt or money owed.

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4 years ago

The diameter of a circle is 20 miles. What is the angle measure of an arc bounding a sector with area 10​ square miles?

The diameter of a circle is 20 miles. What is the angle measure of an arc bounding a sector with area 10 square miles?