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4 years ago

The radius of a circle is 15. Using π, which equation expresses the ratio of the circumference to the diameter of a circle?

Mathematics

1 answer:

Kobotan [32]4 years ago

6 0

Answer:

The equation which expresses the ratio of the circumference to the diameter of a circle is $\frac{C}{30}=\pi$ ⇒ D

Step-by-step explanation:

π is the ratio between the circumference of the circle and the length of its diameter

$\frac{C}{d}=\pi$ , where

C is the circumference of the circle
d is the diameter of the circle

∵ The circumference of the circle is C

∵ The radius of the circle is 15 units

∴ r = 15 units

- Find the diameter of the circle

∵ The diameter of the circle d = 2 r

∴ d = 2(15) = 30 units

∴ The diameter of the circle is 30 units

∵ $\frac{C}{d}=\pi$

∵ d = 30 units

∴ $\frac{C}{30}=\pi$

The equation which expresses the ratio of the circumference to the diameter of a circle is $\frac{C}{30}=\pi$

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Critical Thinking: Empirical/Quantitative Skills

aliya0001 [1]

Answer:

1. 0.0910 = 9.10% probability that exactly 180 passengers show up for the flight.

2. 0.4522 = 45.22% probability that at most 180 passengers show up for the flight.

3. 0.5478 = 54.78% probability that more than 180 passengers show up for the flight.

Step-by-step explanation:

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.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

Assume that there is a 0.905 probability that a passenger with a ticket will show up for the flight.

This means that $p = 0.905$

Also assume that the airline sells 200 tickets

This means that $n = 200$

Question 1:

Exactly, so we can use the P(X = x) formula, to find P(X = 180).

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

$P(X = 180) = C_{200,180}.(0.905)^{180}.(0.095)^{20} = 0.0910$

0.0910 = 9.10% probability that exactly 180 passengers show up for the flight.

2. When 200 tickets are sold, calculate the probability that at most 180 passengers show up for the flight.

Now we have to use the approximation.

Mean and standard deviation:

$\mu = E(X) = np = 200*0.905 = 181$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{200*0.905*0.095} = 4.15$

Using continuity correction, this is $P(X \leq 180 + 0.5) = P(X \leq 180.5)$ , which is the p-value of Z when X = 180.5. Thus

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

$Z = \frac{180.5 - 181}{4.15}$

$Z = -0.12$

$Z = -0.12$ has a p-value of 0.4522.

0.4522 = 45.22% probability that at most 180 passengers show up for the flight.

3. When 200 tickets are sold, calculate the probability that more than 180 passengers show up for the flight.

Complementary event with at most 180 passengers showing up, which means that the sum of these probabilities is 1. So

$p + 0.4522 = 1$

$p = 1 - 0.4522 = 0.5478$

0.5478 = 54.78% probability that more than 180 passengers show up for the flight.

4 0

3 years ago

I'm behind on hw and I'm going to fail if I don't get help.

Reil [10]

Number two is A........hope this helps

6 0

3 years ago

A college is selling tickets for a winter fund-raiser. One day, Krissa sold 14 adult tickets and 8 student tickets for a total o

FromTheMoon [43]

The statement which explains Krissa’s error is "She switched the prices of the tickets" ⇒ A

Step-by-step explanation:

A college is selling tickets for a winter fund-raiser

One day, Krissa sold 14 adult tickets and 8 student tickets for a total of $376
The next day, she sold 7 adult tickets and 11 student tickets for a total of $272
The price of one adult ticket is a
The price of one student ticket is s
She wrote and solved the following system of equations. 14a + 8s = 376 and 7a + 11s = 272
She found that the price of one student ticket is $20 and the price of one adult ticket is $12

We need to find which statement explains Krissa’s error

∵ The system of equations is:

14a + 8s = 376 ⇒ (1)

7a + 11s = 272 ⇒ (2)

Multiply equation (2) by -2 to eliminate x

∵ -14a - 22s = -544 ⇒ (3)

Add equations (1) and (3)

∴ -14s = -168

Divide both sides by -14

∴ s = 12

Substitute the value of s in equation (2) to find a

∵ 7a + 11(12) = 272

∴ 7a + 132 = 272

Subtract 132 from both sides

∴ 7a = 140

Divide both sides by 7

∴ a = 20

∵ a represents the price of one adult ticket

∴ The price of one adult ticket is $20

∵ s represents the price of one student ticket

∴ The price of one student ticket is $12

∵ She found that the price of one student ticket is $20 and

the price of one adult ticket is $12

- She switched the prices of the tickets

∴ Her error is, she switched the prices of the tickets

The statement which explains Krissa’s error is "She switched the prices of the tickets"

Learn more:

You can learn more about the system of equations in brainly.com/question/2115716

#LearnwithBrainly

5 0

3 years ago

Read 2 more answers

Which is the value of this expression when j=-2

Nuetrik [128]

Answer:

Step-by-step explanation:

(jk^-2/j^-1k^-3)^3

(-2)(-1)^-2

------------- ^3

(-2)^-1(-1)^-3

switch negative exponenst to other side

(-2)(-2)(-1)^3

__________

(-1)^2

4(-1)

-----

= -4

REMEMBER all to the 3rd power!

(-4)^3

-64

3 0

3 years ago

While eating a big bowl of pho (Vietnamese soup), you discover that the diameter of the bowl is 9 inches. What is the circumfere

Sever21 [200]

Circumference = π × diameter
π × 9 = 28.274333882
To 1dp = 28.3
Circumference = 28.3 inches

7 0

3 years ago