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:
(a) The probability that the new municipal bond issued will receive an A rating given that it was issued by a city is 0.196.
(b) Thus, the probability of municipal bonds issued by suburbs is 0.325.
Step-by-step explanation:
The data provided is as follows:
P (A) = 0.70
P (B) = 0.20
P (C) = 0.10
P (c | A) = 0.50
P (s | A) = 0.40
P (r | A) = 0.10
P (c | B) = 0.60
P (s | B) = 0.20
P (r | B) = 0.20
P (c | C) = 0.90
P (s | C) = 0.05
P (r | C) = 0.05
(a)
The Bayes' theorem states that the conditional probability of an event Y\(_{i}\) given that another event X has already occurred is:
\(P(Y|X)=\frac{P(X|Y)P(Y)}{\sum\limits_{i} {P(X|Y_{i})P(Y_{i})}}\)
Compute the probability that the new municipal bond issued will receive an A rating given that it was issued by a city as follows:
\(P(A|c)=\frac{P(c|A)P(A)}{P(c|A)P(A)+P(c|B)P(B)+P(c|C)P(C)}\)
\(=\frac{(0.50\times 0.70)}{(0.50\times 0.70)+(0.60\times 0.20)+(0.10\times 0.90)}\\\\=\frac{0.35}{0.56}\\\\=0.196\)
Thus, the probability that the new municipal bond issued will receive an A rating given that it was issued by a city is 0.196.
(b)
The law of total probability states that:
\(P(X)=\sum\limits_{i} {P(X|Y_{i})}\)
Compute the probability of municipal bonds issued by suburbs as follows:
\(P(s)=P(s|A)P(A)+P(s|B)P(B)+P(s|C)P(C)\)
\(=(0.40\times 0.70)+(0.20\times 0.20)+(0.10\times 0.05)\\\\=0.28+0.04+0.005\\\\=0.325\)
Thus, the probability of municipal bonds issued by suburbs is 0.325.
Related Questions
From a recent study, it was found that 10% of students travel outside of the country during spring break. Is this an example of descriptive statistics or inferential statistics?
Answers
This is an example of descriptive statistics. Descriptive statistics is used to summarize, organize, and present data in a meaningful way.
Is this an example of descriptive statistics or inferential statistics?It involves the collection, analysis, interpretation, and presentation of data. In this case, the study found that 10% of students travel outside of the country during spring break. This is a summary of the data collected and presents it in a way that is easy to understand. It gives a percentage of students who travel outside of the country during spring break, which can be used to describe the behavior or characteristics of students.On the other hand, inferential statistics is used to make predictions or draw conclusions about a population based on a sample of data. It involves using statistical methods to make inferences about a population from a sample. For example, if a study found that 10% of students at a particular university travel outside of the country during spring break, inferential statistics would be used to make predictions or conclusions about the behavior or characteristics of students at other universities.To learn more about inferential statistics refer to:
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PART BGiven 10 < 12, write the inequality obtained by(a) Adding 2 to each side of the given inequality(b) Subtracting 12 from each side of the given inequality.(c) Multiplying each side of the given inequality by 2(d) Multiplying each side of the given inequality by-3Add 2 to each side of the given inequality.Subtract 12 from each side of the given inequality
Answers
INFORMATION:
The next inequality is given
\(10<12\)And we must subtract 12 from each side
STEP BY STEP EXPLANATION:
To solve the problem, we need to subtract 12 from each side of the given inequality
\(10-12<12-12\)Finally, simplifying we obtain
\(-2<0\)ANSWER:
-2 < 0
please help A video game box is shaped like a rectangular prism with the following dimensions Length = 20 in • Width = 8.25 in. • Height = 4.5 in. What is the volume of the box in cubic inches?
Answers
Answer:
V= 742.4 in³
Step-by-step explanation:
V= L x W x H = (20)(8.25)(4.5) = 742.4 in³
for each problem, identify the variables, write the equations, and solve
Answers
Let the 4-passenger cars be represented with F
Let the 6-passenger cars be represented with S
Rocket Coaster has 15 cars
So that F + S = 15 ----- Equation 1
Also, we were told that the total room for 72 passenger
so that 4F + 6S = 72 ----- Equation 2
Solving the two equations simultaneously using the substitution method,
Step 1
From equation 1:
Make F the subject of the formula
F = 15 - S ---- Equation 3
Step 2
substitute equation 3 into equation 2
4 (15 - S) + 6S = 72
Step 3
60 - 4S + 6S = 72
6S - 4S = 72 - 60
2S = 12
divide both sides by 2
S = 12/ 2
S= 6
Step 4
Substitute the value of S = 6 into equation 3
F = 15 - 6
F = 9
So the number of 4-passenger cars = 9
the number of 6-passenger cars = 6
Marcia Gadzera wants to retire in San Diego when she is 65 years old. Marcia is now 50 and believes she will need $90,000 to retire comfortably. To date, she has set aside no retirement money. If she gets interest of 10% compounded semiannually, how much must she invest today to meet her goal of $90,000?
Answers
Answer:
Step-by-step explanation:
We can use the formula for the future value of an annuity to determine how much Marcia needs to invest today to meet her retirement goal of $90,000. The formula for the future value of an annuity is:
FV = PMT x [(1 + r/n)^(n*t) - 1] / (r/n)
where:
FV = future value of the annuity
PMT = payment (or deposit) made at the end of each compounding period
r = annual interest rate
n = number of compounding periods per year
t = number of years
In this case, we want to solve for the PMT (the amount Marcia needs to invest today). We know that:
Marcia wants to retire in 15 years (when she is 65), so t = 15
The interest rate is 10% per year, compounded semiannually, so r = 0.10/2 = 0.05 and n = 2
Marcia wants to have $90,000 in her retirement account
Substituting these values into the formula, we get:
$90,000 = PMT x [(1 + 0.05/2)^(2*15) - 1] / (0.05/2)
Simplifying the formula, we get:
PMT = $90,000 / [(1.025)^30 - 1] / 0.025
PMT = $90,000 / 19.7588
PMT = $4,553.39 (rounded to the nearest cent)
Therefore, Marcia needs to invest $4,553.39 today in order to meet her retirement goal of $90,000, assuming an interest rate of 10% per year, compounded semiannually.
Aleks topic please help
Answers
Answer:
Item price now= 3.95
Step-by-step explanation:
To find out the price now, we will subtract 79 (original price) by 95% of 75. That will equal the discounted price. Finding the percentage of anything, we can use the formula, Total amount•percentage/100. The total amount is 79, and the percentage is 95. 79•95=7505, 7505/100=75.05. Now, 95% of 79 is 75.05, 79-75.05=3.95. $3.95 is the price now of the item. Though, I am unsure what a ALEKS calculator is. Have a nuce time, and joyful day
Which of the following inequalities matches the graph?
A. -2x + 3y > 7
B. 2x - 3y < 7
C. -3x + 2y ≥ 7
D. 3x - 2y ≤ 7
Answers
What is an equation of the line that passes through
the point (-2,3) and is parallel to the line whose
equation is y = {x – 4?
Answers
Answer:
B
Step-by-step explanation:
For the perpendicular of an equation you need to flip the fraction and change the sign from positive to negative or if it's negative to positive. 3/2 is changed to -2/3 which when multiplied by -2 gives you 4/3 and 4/3+5/3 is equal to 3.
I need some help with this
Answers
\(\pink{\underline{{\boxed{\bf{QUESTION: }}}}}\)
-6(x+4) = _____
\(\pink{\underline{{\boxed{\bf{OPTIONS:}}}}}\)
6x - 4❌-6x + 4❌-6x - 24✔️6x + 24❌\(\pink{\underline{{\boxed{\bf{ ANSWER: }}}}}\)
-6(x+4) = -6x - 24
Hope It's helped! :)James enjoys spending money at the hardware store. He bought a wrench for $9.14, a nail gun for $54.48, and a pound of nails for $6.98. How much change did James get if he paid with a hundred-dollar bill? *
Answers
Answer:
$29.40
Step-by-step explanation:
29.40 dollars as 100 - the sum of the cost = 29.4
the sunshine cleaning service can vaccum 8 square yards of flooring every 4 minutes. Which graph includes ordered pairs that represent this relationship?
Answers
Graph of a proportional relationship
A proportional relationship can be written as
y = kx
Where k is a constant.
In the problem, the horizontal axis represents the time in minutes it takes for the sunshine cleaning service to vacuum a carpet's square yards of area, represented in the y-axis.
We know the service vacuums 8 square feet of carpet every 4 minutes. This means the point (4,8) must belong to the graph.
If the service works at a constant rate, then in 2 minutes (half the time) it would vacuum half the area of 4 square feet. This is the point (2,4).
The only graph that has both points and is a straight line passing through the origin is the graph marked with the letter B.
Identify the volume of the pyramid.
21 in.
8 in.
7 in.
Answers
Answer
392in³
Step-by-step explanation:
Volume=base X height divided by 3 OR length X width X height divided by 3
length=8in
width=7in
height=21in
So, Volume = 8x7x21
1,176in³
Now divide by 392in³
What is the slope of the line that contains these points?
x 39 40 41 42
y 36 29 22 15
Answers
Answer: -7
Step-by-step explanation:
Use this formula for finding the slope:
Δy/Δx=y1-y2/x1-x2
Now get 2 points, (39, 36); (40, 29)
36-29/39-40= 7/-1= -7
So the slop is -7
Hope this helps!
In circle F with m/EFG = 62°, find the angle measure of minor arc EG.
Answers
The angle measure of the minor arc is 62°
What is a circle?A circle is the locus of a point such that its distance from a fixed point (center) is always constant.
The diameter is the length of the line that passes through the center circle touching two points on the circle's circumference.
The arc of a circle is the part or segment of the circumference of a circle.m∠EFG = minor arc EGminor arc EG = 62°
The measure of the arc is 62°
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Find the distance between the pair of points.(-5, -8) and (4,4). What is the distance?
Answers
Answer:
label a graph doing -5,-8, and 4,4 use the formula which is
d = ( x 2 − x 1 )^2 + ( y 2 − y 1 )^2
x2-x1 = 4–2= 2 Y2–Y1 = 1–3 = -2 d=√(2)^2+(-2)^2 =√4+4 = √8 d= 2√2
so this is the same thing the person above me did but I've been typing this out so long I want to go ahead and submit anyway
the density of the copper is 9.86g/cm\(x^{3}\)
![the density of the copper is 9.86g/cm[tex]x^{3}[/tex]](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/kBdJoEKedYKgyZmbWgXrufRB5h52H33f.png)
Answers
The mass of the cubic cuboid is 1.479 kilograms.
What is the mass of a copper cuboid?
Dimensionally speaking, density (ρ), in kilograms per cubic meter, is mass (m), in kilograms, per unit volume (V), in cubic meters. By the assumption of uniform density within the copper cuboid, the mass of the solid is equal to:
m = ρ · V
Where V is the volume of cuboid, in cubic meters.
And the volume of cuboid is:
V = w · h · l
Where:
w - Width, in meters. h - Height, in meters.l - Length, in meters.Please notice that a kilogram equals 1000 grams and a meter equals 100 centimeters.
First, calculate the volume of the cuboid:
V = (0.05 m) · (0.03 m) · (0.10 m)
V = 1.5 × 10⁻⁴ m³
Second, determine the mass of the cuboid:
m = (9.86 g / cm³) · (1 kg / 1000 g) · (1000000 cm³ / m³) · (1.5 × 10⁻⁴ m³)
m = 1.479 kg
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Is 3/4 greater than 3/5
Answers
Answer:
Yes.
Explanation:
3/4 is 75% of a whole, 3/5 is 60%.
In May 1958, King led a civil rights march to Washington D.C. There were 37,000 people there. If they broke into 9 groups •when they arrived, how many people would be in each group?
Answers
Answer:
37,000÷9=4,111 it actually came out to a deimcal but I rounded to the nearest whole number.
Name a linear pair.
Answers
Answer:
It is C. Linear pairs make a 180 degree turn. Hope this helps!
Step-by-step explanation:
Answer:
C. ∠GQI, ∠IQM
Step-by-step explanation:
linear pairs must add up to 180°
∠GQI and ∠IQM make a straight line which is 180°
Y-4x=9 in standard form
Answers
Answer: y - 4x = 9 in standard form is -y + 4x = -9
A fish descends 4 meters per minute for 2 minutes. Then it ascends 3 meters per minute for 3 minutes. What is the total distance, in meters, the fish traveled?
Answers
The fish's total distance traveled is 17 meters in 5 minutes based on multiplication and addition operations.
How is the total distance traveled determined?The total distance the fish traveled can be determined using mathematical operations, especially multiplication and addition.
We know that distance is the product of speed and time, i.e. d = st, where s is speed, t is time, and d is distance.
In this situation, we separately find the distance the fish traveled during its descent and ascent by multiplying time and speed.
The results are added to obtain the total distance the fish traveled for both activities.
The fish's descent speed = 4 meters per minute (MPM)
The total time for the descent = 2
The total distance for the descent = 8 miles (4 x 2)
The fish's ascent speed = 3 meters per minute (MPM)
The total time during ascent = 3 minutes
The total distance for the ascent = 9 miles (3 x 3)
The total distance the fish traveled for descent and ascent = 17 meters (8 + 9)
Thus, we can mathematically conclude that the fish traveled 17 meters.
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The 7 times the sum of a
number and 6 IS 63
Answers
Answer:
Missing number = 3
Step-by-step explanation:
Let \(x\) be the missing number. We have the following:
\(7\cdot (6+x)=63,\\6+x=9,\\x=\boxed{3}\)
An acute angle, θ, is in a right triangle such that cos θ = 12/13. What is the Value of csc θ? (100 Points!)
13/12
13/5
5/13
5/12
Answers
Answer:
csc θ = 13/12
Step-by-step explanation:
cos θ = 12/13
Formula: cos θ = 1/cscθ
Its just the reciprocal.
solve:
1/csc θ = 12/13
csc θ = 13/12
Answer:
\(\textsf{a)} \quad \text{cosec}\:\theta=\dfrac{13}{12}\)
Step-by-step explanation:
Given cosine trigonometric identity:
\(\boxed{\cos\theta=\dfrac{12}{13}}\)
To find the value of cosec θ, use the trigonometric identity:
\(\boxed{\text{cosec}\; \theta=\dfrac{1}{\cos\theta}}\)
Substitute the given value of cos θ into the cosec θ identity:
\(\implies \text{cosec}\:\theta=\dfrac{1}{\frac{12}{13}}\)
\(\implies \text{cosec}\:\theta=1 \div \dfrac{12}{13}\)
\(\implies \text{cosec}\:\theta=1 \times \dfrac{13}{12}\)
\(\implies \text{cosec}\:\theta=\dfrac{13}{12}\)
Therefore, the value of cosec θ is:
\(\boxed{\text{cosec}\:\theta=\dfrac{13}{12}}\)
*NEED ANSWER ASAP* *GIVING AWAY 10 POINTS*
A horseshoe weighs 8.2 ounces. The nails make up 0.2 of that weight. What is the weight of the horseshoe without the nails?
A. 1.64 oz
B. 6.56 oz
C. 9.84 oz
D. 16.4 oz
Answers
Answer: A horseshoe weighs 8.2 ounces The nails in the horseshoe weigh 0.12 ounces.
Step-by-step explanation: B should be your answer have a great day :)
Answer:
B
Step-by-step explanation:
i did 8.2 divided by 20 percent ( .2)
then subtracted
equal 6.56
Simplify (a÷b)³×(b÷c)×(c÷a)³ when a=3,b=a²,c=a³
Answers
Answer:
To simplify the expression (a÷b)³×(b÷c)×(c÷a)³ when a=3, b=a², c=a³, we can substitute the given values and perform the calculations.
Substituting the values of a, b, and c:
a = 3
b = a² = 3² = 9
c = a³ = 3³ = 27
Now let's simplify the expression:
(a÷b)³×(b÷c)×(c÷a)³
(3÷9)³×(9÷27)×(27÷3)³
Simplifying each term:
(3÷9) = 1/3
(9÷27) = 1/3
(27÷3) = 9
Now we can substitute the simplified values back into the expression:
(1/3)³×(1/3)×9
Simplifying further:
(1/27)×(1/3)×9
1/9
Therefore, the simplified expression is 1/9.
As part of their employee benefits , all workers at Middletown Electronics receive a pension that is calculated by multiplying the number of years worked times 1.56% of the average of their three highest years’ salary. Maureen has worked for Middletown for 30 years and is retiring. Her highest salaries are $107,000, $107,800, and $108,198. Calculate Maureen’s pension.
Answers
Maureen's pension would be $50,035.20.
What is Percentage?
To compute a percentage, divide the value by the entire amount and multiply the result by 100. A percentage is a quantity or ratio that is stated as a fraction of one hundred. The percent sign, "%," is frequently used to represent it.
First, we need to calculate the average of Maureen's three highest salaries:
Average = (107,000 + 107,800 + 108,198) / 3
Average = 322,998 / 3
Average = 107,666
Next, we need to calculate 1.56% of this average:
Percentage = 1.56% * 107,666
Percentage = 1,667.84
Finally, we multiply this percentage by the number of years worked to find the pension:
Pension = 30 * 1,667.84
Pension = 50,035.20
So, Maureen's pension would be $50,035.20.
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Mrs. Buchanan is planning marching routines for the school band. The band has 36 members. Band
members can march in any number of rows as long as each row has the same number of members. The
marching path, however, limits members to 6 per row.
this assignment is worth so much and it’s gonna lock soon so can someone please help?
Answers
Answer:
Down below
Step-by-step explanation:
9 rows - 4 members
6 rows - 6 members
18 rows - 2 members
12 rows - 3 members
36 rows - 1 member
I hope you get it in time!!
9/4 divided by 3/8
PLEASE HELP
Answers
Answer:
6
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
9/4 ÷ 3/8
= 9/4 × 8/3
= 72/12
= 6
An online music store sells songs for $0.90 each.a. Write a function that you can use to find the cost C of buying s songs. b. What is the cost of buying 5 songs?
Answers
Let C be the total cost for buying s songs, then since the cost of each song is $0.90 we can set the following equation:
\(C=0.90s\text{.}\)Now, if we substitute s=5 in the above equation we get:
\(C=0.90(5)=\frac{9}{2}=4.5.\)Answer:
a)
\(C=0.90s\text{.}\)b) $4.5.
Which equation is equivalent to 2 Superscript 4 x Baseline = 8 Superscript x minus 3?
2 Superscript 4 x Baseline = 2 Superscript 2 x minus 3
2 Superscript 4 x Baseline = 2 Superscript 2 x minus 6
2 Superscript 4 x Baseline = 2 Superscript 3 x minus 3
Answers
The equivalent exponential equations are given as follows:
\(2^{4x} = 2^{3(x - 3)}\)
How to obtain the equivalent exponential expression?The exponential expression for this problem is defined as follows:
\(2^{4x} = 8^{x - 3}\)
The number eight is the third power of 3, that is:
8 = 2³.
The power of a power rule is used when a single base is elevated to multiple exponents.
Then the simplified expression is obtained keeping the base, while the exponents are multiplied.
Meaning that the equivalent expression on the right side of the equality in this problem is given as follows:
\(8^{x - 3} = (2^3)^{x - 3} = 2^{3(x - 3)}\)
Meaning that the correct option is given by the fourth option.
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