Segment A'B' is parallel to segment AB.<br>What is the length of segment AB?

Find the area created by the overlapping circles given the following information.

lara31 [8.8K]

The area of a circular sector of central angle α (in radians) in a circle of radius r is given by

... A = (1/2)r²×(α - sin(α))

Your area is expected to be computed as the sum of the areas of a sector with angle π/3 in a circle of radius 8 and a sector with angle π/2 in a circle of radius 6.

... A = (1/2)8²×(π/3 - sin(π/3)) + (1/2)6²×(π/2 - sin(π/2))

... A ≈ 16.07

Radii are in inches so the units of area will be in². The appropriate choice is

... 16.10 in²

_____

It should be noted that the geometry described is impossible. Chord CD of circle A will have length 6√2 ≈ 8.4853 inches. Chord CD of circle B will have length 8 inches. They cannot both be the same chord.

5 0

3 years ago

Read 2 more answers

Consider a parent population with mean 75 and a standard deviation 7. The population doesn’t appear to have extreme skewness or

Aleks04 [339]

Answer:

a) $\bar X \sim N(\mu=375, \sigma={\bar X}=\frac{7}{\sqrt{40}}=1.107)$

b) Since the sample size is large enough n>30 and the original distribution for the random variable X doesn’t appear to have extreme skewness or outliers, the distribution for the sample mean would be bell shaped and symmetrical.

c) $P(\bar X \leq 77)=P(Z$

d) See figure attached

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

Let X the random variable of interest. We know from the problem that the distribution for the random variable X is given by:

$E(X) = 75$

$sd(X) = 7$

We take a sample of n=40 . That represent the sample size

Part a

From the central limit theorem we know that the distribution for the sample mean $\bar X$ is also normal and is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

$\bar X \sim N(\mu=375, \sigma={\bar X}=\frac{7}{\sqrt{40}}=1.107)$

Part b

Since the sample size is large enough n>30 and the original distribution for the random variable X doesn’t appear to have extreme skewness or outliers, the distribution for the sample mean would be bell shaped and symmetrical.

Part c

In order to answer this question we can use the z score in order to find the probabilities, the formula given by:

$z=\frac{\bar X- \mu}{\frac{\sigma}{\sqrt{n}}}$

And we want to find this probability:

$P(\bar X \leq 77)=P(Z$

We can us the following excel code: "=NORM.DIST(1.807,0,1,TRUE)"

Part d

See the figure attached.

8 0

3 years ago

1)How many ways can the letters in the word BOOKKEEPER be arranged? (Must show set-up )

sergeinik [125]

Question 1

There are 5 letters (B, O, K, E, R) and there is a total of 10 letters to make up the word.
There are $\frac{10!}{(10-6)!6!}$ ways of arranging the letters, which equal to 210 ways

Question 2

There are seven swimmers in total.
There are $\frac{7!}{(7-1)!1!}$ ways of choosing the first winner, which is 7 ways
There are $\frac{6!}{(6-1)!1!}$ ways of choosing the second winner, which is 6 ways
There are $\frac{5!}{(5-1)!1!}$ ways of choosing the third winner, which is 5 ways
There are 7×6×5=210 ways of choosing first, second, and third winner

Question 3

The probability of eating an orange and a red candy is $\frac{15}{31}$ × $\frac{9}{30}$ , which equals to $\frac{9}{62}$

The probability of eating two green candies is $\frac{7}{31}$ × $\frac{6}{30}$ which equals to $\frac{7}{155}$

3 0

4 years ago

What is the value of x?

LiRa [457]

Answer:

98°

Step-by-step explanation:

x = 53° + 45° { exterior angle of a triangle is equal to the sum of two opposite interior angles }

x = 98°

5 0

3 years ago

Compare the decimals 16.30 and 16.3

pshichka [43]

16.30 and 16.3 equal. If you ever have a problem like that then you just add on a zero.

Example:
19.4500 = 19.45 Just add two zeros on the end
19.45 + two zeros = 1.4500

8 0

3 years ago

Segment A'B' is parallel to segment AB.What is the length of segment AB?