An investment firm recommends that a client invest in bonds rated AAA, A, and B. The average yield on AAA bonds is 4%, on A bonds 6%, and on B bonds 11%. The client wants to invest twice as much in AAA bonds as in B bonds. How much should be invested in each type of bond under the following conditions?
A. The total investment is $26,000, and the investor wants an annual return of $1,620 on the three investments.
B. The values in part A are changed to $38,000 and $2,360, respectively
A. The client should invest $(?) in AAA bonds, $(?)in A bonds, and $(?)in B bonds.

Answers

Answer 1

Part A.

1) Variables:

X: amount invested in AAA bonds

Y: amount invested in A bonds

Z: amount invested in B bonds.

2) Return:

4%* X + 6% * Y + 11% * Z = 1620

3) Investment:

X + Y + Z = 26,000

4) Ratio between AAA and B bonds.

X = 2*Z

5) Solution of the system of equations:

Replace X with 2Z in the two first equations:

2Z * 4% + Y * 6% + Z * 11% = 1620

=> 0.08Z + 0.06Y + 0.11Z = 1620

=> 0.19Z + 0.06Y = 1620

2Z + Y + Z = 26,000

=> 3Z + Y = 26,000 => Y = 26,000 - 3Z

Replace Y with 26,000 - 3Z

0.19Z + 0.06(26,000 - 3Z) = 1620

0.19Z + 1560 - 0.18Z = 1620

0.01Z = 1620 - 1560

0.01Z = 60

Z = 60 / 0.01 = 6000

=> X = 2*6000 = 12,000

=> Y = 26,000 - 12,000 - 6,000 = 8,000

Answer: 12,000 in bonds AAA, 8,000 in bonds A, and 6000 in bonds B.

Part B.

2) Return:

0.04X + 0.06 Y + 0.11Z = 2360

3) Investment:

X + Y + Z = 38,000

4) Ratio between AAA and B bonds.

X = 2Z

5) Solution of the system of equations:

Replace X with 2Z in the two first equations:

=> 0.08Z + 0.06Y + 0.11Z = 2360

=> 0.19Z + 0.06Y = 2360

2Z + Y + Z = 38,000

=> 3Z + Y = 38,000 => Y = 38,000 - 3Z

Replace Y with 38,000 - 3Z

0.19Z + 0.06(38,000 - 3Z) = 2360

0.19Z + 2280 - 0.18Z = 2360

0.01Z = 2360 - 2280

0.01Z = 80

Z = 80 / 0.01 = 8000

=> X = 2*8000 = 16,000

=> Y = 38,000 - 16,000 - 8000 = 14,000

Answer: 16,000 in AAA bonds, 14,000 in A bonds, and 8,000 in B bonds.

Related Questions

5/8 of the 64 musicians in a music contest are guitarist. Some of the guitarist play jazz solos, and the rest play classical solos. The ratio of the number of guitarist playing jazz solos to the total number of guitarist in the contest is 1:4. How many guitarist play classical solos in the contest?

Answers

5/8 x 64= 40 x 1/4 =10 40 - 10 = 30 classical solos

Kyra typed 140 words in 5 minuets. Then, she typed 196 words in 7 minutes. Was her rate of words per minute constant? If so, what is the constant of proportionality?

Answers

Hello lamdravenox! There are a few ways to tell if the rate of words per minute are constant but we can divide 140/5 and 196/7 to tell if the rate of words per minute are constant.

First divide 140 / 5 = 28 words per min
Second divide 196 / 7 = 28 words per min

So we can see the rate of words per minute is constants and her rate is at 28 words per min so the constant of proportionality is 28 words per minute.

How to find the graph of a parabola?

Answers

This question is so general that a thorough answer would be quite long. Could you be more specific about what you want to know?

y = a(x-h)^2 + k is an equation for a parabola with vertex at (h,k). the graph opens up if a is + and down if a is -.

y = ax^2 + bx + c is another common form.
The y-intercept of the graph is (0,c). The graph opens up if a is + and down if a is -. The x-coordinate of the vertex is x = -b/(2a). Substitute that into the given function to calculate the associated y-value.

Again, what specifically would you like to learn?

Final answer:

Graphing a parabola starts by identifying the vertex from the equation of the parabola, determining whether the parabola opens upwards or downwards, plotting the vertex and other points and then joining these points with a smooth curve.

Explanation:

Graphing a parabola involves understanding the equation of the parabola which takes the form y = ax² + bx + c, where 'a', 'b', and 'c' are constants. To find the graph of the parabola from this equation, follow these steps:

Find the vertex of the parabola. The vertex is given by the point (h, k), where h = -b/2a and k can be found by substituting h into the equation.Depending on the sign of 'a', determine if the parabola opens upwards ('a' positive) or downwards ('a' negative).Plot the vertex on a graph. The vertex is the lowest point on the graph if the parabola opens upwards, and the highest point if the parabola opens downwards.Use the equation to find other points on the parabola. Substitute different x-values into the equation to find corresponding y-values.Connect the dots to form a smooth curve.

Remember, parabolas are a type of conic sections, formed through the intersection of a plane with a cone.

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What is the answer to this problem

Answers

4x10^4 because 10 is multiplied 4 times
10 x 10 x 10 x 10 =10,000 because 10 x 10 =100 x 10= 1,000 x 10 = 10,000
6 x 10^5 = 6 x 1000,000 because its is moved 5 times
6x 10^5 =6000000 because it has 5 sapces shope tat help and im not copying the experts answer

10x10x10x10=10^4
10x10x10x10=10,000

6x10^5=6x100000
6x10^5=600000

A model for the population in a small community after t years is given by P(t)=P0e^kt.
a)If the initial population doubled in 5 years, how long will it take to have tripled its initial population?
b)In addition, if the population of the community is 10,000 in 3 years, what was its initial population?

Answers

[tex]\bf \textit{Amount of Population Growth}\\\\ A=Ie^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ I=\textit{initial amount}\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{elapsed time}\\ \end{cases}[/tex]

a)

so, if the population doubled in 5 years, that means t = 5. So say, if we use an amount for "i" or P in your case, to be 1, then after 5 years it'd be 2, and thus i = 1 and A = 2, let's find "r" or "k" in your equation.

[tex]\bf \textit{Amount of Population Growth}\\\\ A=Ie^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\to &2\\ I=\textit{initial amount}\to &1\\ r=rate\\ t=\textit{elapsed time}\to &5\\ \end{cases} \\\\\\ 2=1\cdot e^{5r}\implies 2=e^{5r}\implies ln(2)=ln(e^{5r})\implies ln(2)=5r \\\\\\ \boxed{\cfrac{ln(2)}{5}=r}\qquad therefore\qquad \boxed{A=e^{\frac{ln(2)}{5}\cdot t}} \\\\\\ \textit{how long to tripling?}\quad \begin{cases} A=3\\ I=1 \end{cases}\implies 3=1\cdot e^{\frac{ln(2)}{5}\cdot t}[/tex]

[tex]\bf 3=e^{\frac{ln(2)}{5}\cdot t}\implies ln(3)=ln\left( e^{\frac{ln(2)}{5}\cdot t} \right)\implies ln(3)=\cfrac{ln(2)}{5} t \\\\\\ \cfrac{5ln(3)}{ln(2)}=t\implies 7.9\approx t[/tex]

b)

A = 10,000, t = 3

[tex]\bf \begin{cases} A=10000\\ t=3 \end{cases}\implies 10000=Ie^{\frac{ln(2)}{5}\cdot 3}\implies \cfrac{10000}{e^{\frac{3ln(2)}{5}}}=I \\\\\\ 6597.53955 \approx I[/tex]

How is multiplying and dividing numbers in scientific notation different from adding and subtracting numbers in scientific notation?

Answers

When you multiply or divide in scientific notation, you just add or subtract the exponents. When you add or subtract in scientific notation, you have to make the exponents the same before you can do anything else.

Final answer:

In scientific notation, multiplication involves multiplying the numbers before the exponents and adding the exponents, while division involves dividing the numbers before the exponents and subtracting the exponents. Addition and subtraction require the numbers to have the same exponent.

Explanation:

Multiplying and dividing numbers in scientific notation is different from adding and subtracting It's useful to know how to use scientific notation, especially in fields like astronomy where large numbers are common. Numbers in scientific numeration are written with one number to the left of the decimal point. For example, 500,000,000 will be expressed as 5 × 10⁸.

When we multiply two numbers in scientific notation, we multiply the numbers out front and then add the exponents. For instance, if we are multiplying (3 × 10⁵) × (2 × 10¹⁰), our answer will be 6 × 10¹⁵.

On the other hand, to divide two numbers in scientific notation, we divide the numbers out front and then subtract the exponents. For example, if we are dividing 1.2 x 10⁶ by 2 x 10³, our answer will be 0.6 x 10³ or 6 x 10².

When working with addition and subtraction in scientific notation, the numbers must have the same exponent in order for the operation to be performed.

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The probability that a dvd player produced by vca television is defective is estimated to be 0.06. a sample of ten players is selected at random. (round your answers to four decimal places.) (a) what is the probability that the sample contains no defective units? correct: your answer is correct. (b) what is the probability that the sample contains at most two defective units?

Answers

Absolute MonarchA monarchial form of government in which the monarch exercises ultimate governmental authority.Divine RightIt is the belief that the ruler's authority comes directly from his, or her, God. (Usually the country's main religion.)Charles V (From Spain)Spanish Emperor who ruled the Holy Roman Empire.Philip II (From Spain)King of Spain from 1556 and of Portugal from 1581.Spanish ArmadaA spanish fleet of warships.Huguenot...

Simplify. Assume that all variables represent positive real numbers. sqrt y^9

Answers

See picture for answer.

Cassie and Maria and Kirk and Jim raked 7/8 of all the leaves. How much raking did Cassie do?

Answers

If they all contributed equal amount of work into raking, then Cassie did 7/32 raking.

The point-slope form of the equation of the line that passes through (–5, –1) and (10, –7) is y + 7 = (x – 10). What is the standard form of the equation for this line?

Answers

That point slope equation given does not pass through those points, the point slope equation y + 7 = -0.4(x - 10) does, though. The standard form of that would be

2x + 5y = -15

You can get that by distributing the -0.4 out

y + 7 = -0.4x + 4

You can then add 0.4x to both sides, and subtract 7 from both sides to get

0.4x + y = -3

Now some teachers may accept this, but in correct standard form the coefficient of x is a whole number, so you have to multiply both sides by 5 to get rid of the decimal, and you get

Kent caught an 8 pound 3 ounce trout in Pike Lake. The season's record catch so far is 129 ounces. Did Kent's fish beat the record?

Answers

Yes Kent Did beat the record. There are sixteen ounces in one pound. 16•8=128+3 sooooo..131

Garrett has deposited $519 in a savings account that earns interest at a rate of 4.2% compounded daily. What will the account balance be in 17 years?

Answers

The formula is
A=p (1+r/k)^kt
A future value?
P present value 519
R interest rate 0.042
K compounded daily 365
T time 17 years
A=519×(1+0.042÷365)^(365×17)
A=1,059.83

Hope it helps!

Evaluate the integral f*dr where f(x,y)=<-y,x^2> and c consists of te arc of the parabola y=2x^2 from (-1,2) to (1,2)

Answers

[tex]y=2x^2\implies\mathbf r(x)=\langle x,2x^2\rangle[/tex]

[tex]\displaystyle\int_C\mathbf F\cdot\mathrm d\mathbf r=\int_{t=-1}^{t=1}\langle-2x^2,x^2\rangle\cdot\langle1,4x\rangle\,\mathrm dx[/tex]
[tex]=\displaystyle\int_{-1}^1(8x^3-2x^2)\,\mathrm dx[/tex]
[tex]=-\dfrac43[/tex]

George exercises 15 minutes a day, every day of the year. How many minutes a year does George exercise? Write and solve an equation to find the answer.

Answers

equation : total = 15x

let x = number of days

1 year = 365 days

x = 365

total = 15(365) = 5475 minutes

How to find a ratio with the denominator of 1 without using a diagram

Answers

Actually, any number over 1 is "a ratio with the denom. of 1."

29
---
1

is such a ratio, for example.

1/4x + 1/3 = 1/6x - 1/4

Answers

1/4x + 1/3 = 1/6x - 1/4

We simply want to isolate x.

So, we must get x onto it's own side of the equal sign.

To do that, we subtract 1/3 from both sides.

1/4x = 1/6x - 1/4 - 1/3

Then, subtract 1/6x from both sides.

1/4x - 1/6x = -1/4 - 1/3

Simplify.

1/4x → 3/12x ; -1/6x → -2/12x ; -1/4 → -3/12 ; -1/3 → -4/12

Plug these into our equation.

3/12x - 2/12x = -3/12 - 4/12

Simplify.

1/12x = -7/12

Multiply everything by 12.

12 · 1/12x = -7/12 · 12

Simplify.

x = -7

~Hope I helped!~

What system of linear inequalities is shown in the graph? Enter your answers in the boxes.

Answers

First, find the equation of the lines:

y=-2x+2 and y=1/3x+2

We see that the shaded part is below the y=1/3x+2 graph, so it becomes y<1/3x+2 (It's not ≤ since it's a dotted line)

For the y=-2x+2, the shaded part is under the line as well, so it becomes y≤-2x+2 (Here, we include the ≤ since it's a solid line)

So your answer is y<1/3x+2 and y≤-2x+2.

Step 1

Find the slope of the dotted line A

Let

[tex]A(-3,1)\\B(0,2)[/tex]

Find the slope m

[tex]m=\frac{(y2-y1)}{(x2-x1)}[/tex]

substitute in the formula

[tex]m=\frac{(2-1)}{(0+3)}[/tex]

[tex]m=\frac{(1)}{(3)}[/tex]

[tex]mA=\frac{1}{3}[/tex]

Step 2

Find the equation of the line A

we know that

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]mA=\frac{1}{3}[/tex]

[tex]B(0,2)[/tex]

substitute

[tex]y-2=\frac{1}{3}(x-0)[/tex]

[tex]y=\frac{1}{3}x+2[/tex]

Step 3

Find the equation of the inequality A

we know that

the solution is below the dotted line A

the inequality A is

[tex]y<\frac{1}{3}x+2[/tex]

Step 4

Find the slope of the solid line B

Let

[tex]B(0,2)\\C(1,0)[/tex]

Find the slope m

[tex]m=\frac{(y2-y1)}{(x2-x1)}[/tex]

substitute in the formula

[tex]m=\frac{(0-2)}{(1-0)}[/tex]

[tex]m=\frac{(-2)}{(1)}[/tex]

[tex]mB=-2[/tex]

Step 5

Find the equation of the line B

we know that

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]mB=-2[/tex]

[tex]B(0,2)[/tex]

substitute

[tex]y-2=-2(x-0)[/tex]

[tex]y=-2x+2[/tex]

Step 6

Find the equation of the inequality B

we know that

the solution is below the solid line B

the inequality B is

[tex]y\leq -2x+2[/tex]

therefore

The system of linear inequalities is

[tex]y<\frac{1}{3}x+2[/tex]

[tex]y\leq -2x+2[/tex]

using a graphing tool

the solution is the shaded area

see the attached figure

Object moving in the xy-plane is acted on by a conservative force described by the potential-energy function u(x,y)=α(1/x2+1/y2), where α is a positive constant

Answers

It seems like the problem is asking for us to derive an expression for the force F⃗ stated in terms of the unit vectors i^ and j^.

The solution for this is:

U(x,y) = α (x^-2 + y^-2)

F = - dU(x,y)

F = - (dU/dx + dU/dy)

F = - (-2αx^-3 - 2αy^-3)

F = 2α (x^-3 + y^-3)

F = 2α (1/x^3 i + 1/y^3 j)

Final answer:

A conservative force is related to the potential-energy function. In this particular context, the force exerted on an object in an xy-plane is calculated using the negative gradient of the potential energy function u(x,y) given.

Explanation:

The question presents a potential-energy function for an object moving in the xy-plane, with the function u(x,y)=α(1/x2+1/y2) where α is a positive constant. This case refers to the action of a conservative force.

A conservative force is characterized by the fact that the work done by the force is only dependent on the start and end points of the motion. In turn, this gives the freedom to define a potential energy for any conservative force. In the context of this potential-energy function, the conservative force acting on the object can be calculated from the negative gradient of the potential energy.

To express it quantitatively, given a potential energy function U(x), the force F acting on the object at a position x is given by F=-dU/dx. If we extend this to two dimensions in the xy-plane, the force F = - ∇U, where ∇ is the gradient operator.

Applying these concepts to your given potential energy function u(x,y)=α(1/x2+1/y2), the force acting on the object in the x and y directions can be calculated by differentiating this function with respect to x and y respectively, applying the opposite sign.

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What is 2 tens 13 ones

Answers

2 tens = 20
13 ones = 13

20 + 13 = 33

33 is your answer

hope this helps

two tens is 20,so 10 ones equals 1 ten so 3 tens plus 3=33

Enter the correct unit of measurement to complete the conversion
10,000 grams equals 10 what
1/5000,000 liter eqaul 2 what
1 nanosecond equal one what of a what
1 hectometer equal what meters
1 milliampere equl one waht of an ampere
1 megaton equal 1 what tons
THANK YOU SO MUCH

Answers

Hi. Here you go, hope it helps.

10,000 grams = 10 kilograms
1/500,000 liters equal = 2 microliters
1 nanosecond = 1 billionth of a second
1 hectometer = 100 meters
1 milliampere = 0.001 ampere
1 megaton = 1,000,000 tons

Take care,
Diana

Answer:

As per list given

Step-by-step explanation:

Given are some measurements and we have to convert them into suitable units.

i) 10,000 grams = 10 kilograms

1/500,000 liters equal = 2 microliters

1 nanosecond = 1 billionth of a second

1 hectometer = 100 meters

1 milliampere = 0.001 ampere

1 megaton = 1,000,000 tons

15 sided polygon what is the degree of rotation

Answers

Just divide 360 by 15.
360/15 = ?

Hamza bought 8 gallons of brown paint to paint his kitchen and dinning room. Unfortunately, when hamza started painting, he thought the paint was too dark for his house,so he wanted he wanted to make it lighter. The store manager would not let hamza return the paint but did inform that if he used 1 4 of a gallon of white paint mixed with 2 gallons of brown paint, he would get the shade of brown he desires. If hamza decided to take this approach, how many gallons of white paint would hamza have to buy to lighten the 8 gallons of brown paint?

Answers

I believe he would need 56 gallons of white paint.

Is that supposed to be 1, 4 or 14 gallons of white paint? There is a space between the 1 and the 4, but I went with 14 originally.

ANSWER: 56 gallons of white paint

Why?

14 gallons of white paint for every 2 gallons of brown paint
8 divided by 2 = 4 times the amount of white paint needed for 2
4 x 14 = 56 gallons of white pains

IF it was supposed to be 1 or 4 gallons of white paint per 2 gallons of brown

For 1 gallon of white paint for every 2 gallons of brown the answer would be
4 x 1 = 4.

If it should say 4 gallons of white for every 2 gallons of brown the answer would be 4 x 4 = 16.

rewrite 4/21 and 2/9 so that they have a common denominator, then use <, > or =

Answers

4/21 = 12/63 and 2/9 = 14/63

12/63 < 14/63

2 over 3.5

which means... 5.5

hope it helped!

Use the elimination method to solve the system

5x − 14y = 74
−x − 6y = 38

Answers

[tex]\bf \begin{array}{llll} 5x-14y=74&\implies &~~5x-14y=74\\ -x-6y=38&\boxed{\times 5}\implies &-5x-30y=190\\ &&--------\\ &&~~0x-44y=264 \end{array} \\\\\\ -44y=264\implies y=\cfrac{264}{-44}\implies \boxed{y=-6}\\\\ -------------------------------\\\\ 5x-14y=74\implies 5x-14(-6)=74\implies 5x+84=74 \\\\\\ 5x=-10\implies x=\cfrac{-10}{5}\implies \boxed{x=-2}[/tex]

a 204 inch board is cut into two pieces. one piece is five times the length of the other.find the lengths of the two pieces

Answers

Solution along with work is included in attachment.

The difference of a number divided by 7 and 9 is equal to 2. use the variable C what the unknown

Answers

Given that the number is C.
The number divided by 7 is C/7
Difference means we will subtract 9 from C/7.
Therefore, the equation will be:
C/7 - 9 = 2 (multiply all terms by 7 to get rid of the fraction)
C - 63 = 14
C = 14 + 63 = 77

write words to match the expression
3+(4×12)

Answers

3 plus the quotient of 4 and 12. Hope this helps!

At the city park there were 15 blue jays, 6 cardinals, and 9 mockingbirds. For each of the following questions set up a proportion equation and solve for the unknown. 1. If there were 6 mockingbirds, how many cardinals would there be at the park? 2. If there were 5 blue jays, how many cardinals would there be at the park? 3. If there were 20 cardinals, how many mockingbirds would there be at the park?

Answers

1. 4 cardinals because: 6 mockingbirds : x cardinals = 9 mockingbirds : 6 cardinals 6*6 / 9 = 4 2. 2 cardinals because: 5 blue jays : x cardinals = 15 blue jays : 6 cardinals 5*6 / 15 = 2 3. 30 mockingbirds because; 20 cardinals : x mockingbirds = 6 cardinals : 9 mockingbirds 20*9 / 6 = 30

It is estimated that light takes 110,000 years to travel the full distance across our galaxy

In the picture please read the rest of the question.

Answers

[tex]\bf \stackrel{light~speed}{3.0\times 10^8}ms^{-1}\implies \stackrel{light~speed}{3.0\times 10^8}~\frac{m}{s}\implies 300,000,000~\frac{m}{s}\\\\ -------------------------------\\\\ \textit{how many seconds in a minute?}\qquad 60 \\\\\\ \textit{how many seconds in }\stackrel{1~hr}{60~minutes?}\qquad 60\cdot 60 \\\\\\ \textit{how many seconds in }\stackrel{1~day}{24~hrs}?\qquad 60\cdot 60\cdot 24 \\\\\\ \textit{how many seconds in }\stackrel{1~year}{365~days}?\qquad 60\cdot 60\cdot 24\cdot 365[/tex]

now, it takes 1 second for light to travel 300,000,000 meters.

if we know it takes light 1 second to go 300 million meters, then in 365 days or a year, or 60*60*24*365 seconds, it will then travels

300,000,000 * 60 * 60 * 24 * 365 meters in 1 year,

how about in 110,000 years, how many meters has it travelled?

300,000,000 * 60 * 60 * 24 * 365 * 110,000 that many meters.

we know she travels the Milky Way in 110,000 years or 60 * 60 * 24 * 365 * 110,000 seconds

and we know that 110,000 years is 3468960000000 seconds, so

if it travels 300000000 meters in only 1 second, in 3468960000000 seconds, it will travel then (300000000) * (3468960000000) meters

or 1040688000000000000000 meters.

The circular base of a cone has a radius of 5 centimeters. The height of the cone is 12 centimeters, and the slant height is 13 centimeters. What is the approximate surface area of the cone? Use 3.14 for π and round to the nearest whole number. 267 cm2 283 cm2 456 cm2 487 cm2

Answers

Answer:

Option B. is the correct option.

Step-by-step explanation:

The circular base of a cone has a radius of 5 cm. The height of the cone is 12 cm. Slant height of the cone is 13 cm.

We have to calculate the approximate surface area of the cone.

Since we know Surface area of a cone = Area of circular base + lateral area of the cone

Now Surface area of a cone = πr² + πrl = πr(r + l)

By putting the values of the dimensions of a cone in the formula.

S.A. = π (5² + 5×13) = 3.14×(25 + 65) = 3.14×(90) = 282.60 ≈ 283 cm²

Therefore, Option B is the correct option.

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