MATHEMATICS COLLEGE

A municipal bond service has three rating categories (A, B, and C). Suppose that in the past year, of the municipal bonds issued throughout the United States, 70% were rated A, 20% were rated B, and 10% were rated C. Of the municipal bonds rated A, 50% were issued by cities, 40% by suburbs, and 10% by rural areas. Of the municipal bonds issued B, 60% were issued by cities, 20% by suburbs, and 20% by rural areas. Of the municipal bonds rated C, 90% were issued by cities, 5% by suburbs, and 5% by rural areas. a. If a new municipal bond is to be issued by a city, what is the probability that it will receive an A rating? b. What proportion of municipal bonds are issued by cities? c. What proportion of municipal bonds are issued by suburbs?

Answers

Answer 1

Answer:

a) The probability that a new municipal bond issued by a city will receive an A rating is 0.625 or 62.5%.

b) 56% of municipal bonds are issued by cities.

c) The proportion of municipal bonds issued by suburbs is 0.325 or 32.5%.

Let's solve each part of the problem:

a. If a new municipal bond is to be issued by a city, what is the probability that it will receive an A rating?

Use conditional probability here.

Using conditional probability notation, we have:

P(A | City)

To calculate this, use the following formula:

P(A | City) = P(A and City) / P(City)

We are given:

- P(A) = 0.70 (probability of an A rating)

- P(B) = 0.20 (probability of a B rating)

- P(C) = 0.10 (probability of a C rating)

For bonds issued in cities:

- P(City | A) = 0.50 (probability that it's a city if it's rated A)

- P(City | B) = 0.60 (probability that it's a city if it's rated B)

- P(City | C) = 0.90 (probability that it's a city if it's rated C)

Now, let's calculate:

P(A and City) = P(A) * P(City | A)

P(City) = P(A) * P(City | A) + P(B) * P(City | B) + P(C) * P(City | C)

Substitute the values:

P(A and City) = 0.70 * 0.50

= 0.35

P(City) = (0.70 * 0.50) + (0.20 * 0.60) + (0.10 * 0.90)

= 0.35 + 0.12 + 0.09

= 0.56

Now, calculate the conditional probability:

P(A | City) = P(A and City) / P(City)

= 0.35 / 0.56

= 0.625

So, the probability is 0.625 or 62.5%.

b. What proportion of municipal bonds are issued by cities?

56% of municipal bonds are issued by cities.

c. What proportion of municipal bonds are issued by suburbs?

To find the proportion of municipal bonds issued by suburbs, use a similar approach:

P(Suburb) = P(A) * P(Suburb | A) + P(B) * P(Suburb | B) + P(C) * P(Suburb | C)

We are given:

- P(Suburb | A) = 0.40

- P(Suburb | B) = 0.20

- P(Suburb | C) = 0.05

Now, calculate:

P(Suburb) = (0.70 * 0.40) + (0.20 * 0.20) + (0.10 * 0.05)

= 0.28 + 0.04 + 0.005

= 0.325

So, the proportion of municipal bonds issued by suburbs is 0.325 or 32.5%.

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Answer 2

Answer:

Final answer:

The probability that a municipal bond issued by a city will receive an A rating is 35%. The proportion of all municipal bonds issued by cities is 56%. The proportion of all municipal bonds issued by suburbs is 32.5%.

Explanation:

This question requires an understanding of probability and conditional probability.

a) To find the probability that a new municipal bond issued by a city will receive an A rating, we must first determine the likelihood that an A-rated municipal bond is issued by a city. Given that 50% of A-rated bonds are issued by cities and that 70% of all bonds receive an A rating, we can calculate this probability as (0.50)*(0.70) = 0.35, or 35%.

b) To find the proportion of municipal bonds issued by cities, we must add up the bonds issued by cities across all ratings. So, (0.70*0.50) + (0.20*0.60) + (0.10*0.90) = 0.35 + 0.12 + 0.09 = 0.56, or 56%.

c) To calculate the proportion of municipal bonds issued by suburbs, we do the same calculation as in part b) but for suburbs. So, (0.70*0.40) + (0.20*0.20) + (0.10*0.05) = 0.28 + 0.04 + 0.005 = 0.325, or 32.5%.

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Answers

Answer: Lyrics B

Step-by-step explanation:

The investigation about the operating time of cordless toothbrushes is in first place associated to two tails experiment since investigation call for evalution of values under and above any given value (mean value). On the other side investigation of two different manufactures implies totally independent samples, unless these two companies have a commercial relationship which is not express in the problem ststement. Therefore the answer is lyrics B

A group of friends has gotten very competitive with their board game nights. They have found that overall, they each have won an average of 18 games, with a population standard deviation of 6 games. If a sample of only 2 friends is selected at random from the group, select the expected mean and the standard deviation of the sampling distribution from the options below. Remember to round to the nearest whole number.

Answers

Answer: $\mu_x=18\text{ hours}$

$\sigma_x=4\text{ hours}$

Step-by-step explanation:

We know that mean and standard deviation of sampling distribution is given by :-

$\mu_x=\mu$

$\sigma_x=(\sigma)/(√(n))$

, where $\mu$ = population mean

$\sigma$ =Population standard deviation.

n= sample size .

In the given situation, we have

$\mu=18\text{ hours}$

$\sigma=6\text{ hours}$

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Then, the expected mean and the standard deviation of the sampling distribution will be :_

$\mu_x=\mu=18\text{ hours}$

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A particle moving along a line has position s(t) = t^4 − 20t^2 m at time t seconds. Determine: (a)- At which times does the particle pass through the origin? (b)- At which times is the particle instantaneously motionless.

Answers

The particle passes through the origin at t = 0 and t = ±√20. The particle is instantaneously motionless at t = 0 and t = ±√10.

(a) To determine the times at which the particle passes through the origin, we need to find when the position function equals zero. So, we set s(t) = 0 and solve for t.
t4 - 20t2 = 0
Factoring out a t2, we get:
t2(t2 - 20) = 0
Setting each factor equal to zero and solving for t gives us the following solutions:
t = 0 (giving us the initial position), and t = ±√20 (approximately t = ±4.47).

(b) To determine when the particle is instantaneously motionless, we need to find when the velocity of the particle is equal to zero. The velocity function of the particle is the derivative of the position function. So, we differentiate s(t) with respect to t to find the velocity function.
v(t) = s'(t) = 4t³ -40t
Setting v(t) = 0, we have:
4t³ -40t = 0
Factoring out a 4t, we get:
4t(t² - 10) = 0
Setting each factor equal to zero and solving for t gives us the following solutions:
t = 0 (giving us the initial velocity), and t = ±√10 (approximately t = ±3.16).

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Final answer:

The particle passes through the origin at t = 0 and t = √20 seconds. The particle is instantaneously motionless at t = 0 and t = ±√10 seconds.

Explanation:

The position of the particle at time t is given by the equation s(t) = t4 - 20t2. To determine the times when the particle passes through the origin, we set s(t) equal to zero and solve for t. This gives us the quadratic equation t4 - 20t2 = 0, which can be factored as t2(t2 - 20) = 0. The solutions to this equation are t = 0 and t = ±√20. Since t cannot be negative in this scenario, the particle passes through the origin at t = 0 and t = √20 seconds.

To determine the times when the particle is instantaneously motionless, we need to find the times when the velocity of the particle is equal to zero. The velocity of the particle can be found by taking the derivative of the position function with respect to time, v(t) = 4t3 - 40t. Setting this equation equal to zero and solving for t gives us the cubic equation 4t3 - 40t = 0. This equation can be factored as 4t(t2 - 10) = 0. The solutions to this equation are t = 0 and t = ±√10. Therefore, the particle is instantaneously motionless at t = 0 and t = ±√10 seconds.

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The difference between seven and triple the input

Answers

Answer: 3x - 7

x = some input number

3x = triple the input

3x - 7 = difference of triple the input and 7

Someone please answer!

Answers

Answer:

m=1/2

Step-by-step explanation:

y1= 1

y2=6

x1= -10

x2-0

m= slope

m= y2-y1/x2-x1

m=6-1/0 - - 10

m= 6-1/0+10

m=5/10

m=1/2

Studying mathematics in the night is better than the morning study and why?give me your opinion please share it with me i'm thinking to study math at night but idk guys help

Answers

Honestly, I believe you should study while you're still up (if it's not too late). Your brain isn't really awake that early in the morning and you might not even remember anything. If you have have a test later in the day, study through out your classes and lunch and you should be fine. Another tip is to go with you gut instinct. Don't second guess yourself because that can mess you up.

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