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.
Final answer:
To meet the client's investment goals with an investment return of $1,620 on a total of $26,000, the client should invest $8,000 in AAA bonds, $14,000 in A bonds, and $4,000 in B bonds. This is derived from setting up and solving a system of linear equations based on the conditions provided.
Explanation:
Part A: Investment Calculations
To solve for the amount to invest in each type of bond, we can set up a system of equations based on the given conditions. Let x be the amount invested in AAA bonds, y be the amount invested in A bonds, and z be the amount invested in B bonds. We are told that the client wants to invest twice as much in AAA bonds as in B bonds, which gives us the equation x = 2z. The total investment is $26,000, so we have x + y + z = $26,000. The desired annual return is $1,620, and this gives us another equation based on the yields: 0.04x + 0.06y + 0.11z = $1,620.
By solving this system of equations, we can find the amounts to invest in each bond.
From x = 2z, we can substitute for x in the other equations.
The total investment equation becomes 2z + y + z = $26,000, simplifying to 3z + y = $26,000.
The return equation becomes 0.08z + 0.06y + 0.11z = $1,620, simplifying to 0.19z + 0.06y = $1,620.
We can now solve these two new equations for y and z, and then find x using x = 2z.
After solving, we get:
z (B bonds) = $4,000
x (AAA bonds) = 2z = $8,000
y (A bonds) = $26,000 - x - z = $14,000
Part B: Investment Calculations with Updated Values
The process for part B is similar, but with the updated total investment of $38,000 and a desired return of $2,360. The equations are adjusted accordingly, and after solving, we would get the new investment amounts for AAA, A, and B bonds.
The client should invest $8,000 in AAA bonds, $14,000 in A bonds, and $4,000 in B bonds for the conditions in part A.
How much time does it take light to travel from the moon to the earth, a distance of 384000?
V = speed of light = 3 x 108 m/s
d = distance = 384000 x 103 m = 3.84 x 108 m
time taken = t = d/V = 3.84 x 108 /(3 x 108 ) = 1.28 sec
What is the equation of the line (8,-6) 8x-3y=7
2t+8>-4(t+1)
T>___
**The sign is meant to be more than or equal to.**
Martha, Lee, Nancy, Paul, and Armando have all been invited to a dinner party. They arrive randomly and each person arrives at a different time In how many ways can they arrive?
a football game had 20 and 2/3 minutes of commercials in the first 1 1/4 hours it was on at that rate how many minutes of commercials will be shown in three and a half hours
Jamar is factoring 90x-15. Find his mistake and correct it
Answer: 15(6x - 1)
Step-by-step explanation: Jamar had a great start, by figuring out the factors of both 90 and 15; of which he picked 15.
What he got wrong was failing to do same to the value 15 exactly what he did to 90x.
To put it right, here is how to go about it:
90x - 15
Factor of both 90 and 15 is 15
Therefore:
15 (6x - 1)
This is correct. You can as well expand the result to check.
The correct factorization will be: 15(6x - 1)
Given,
90x-15
Here,
Jamar had a great start, by figuring out the factors of both 90 and 15; of which he picked 15.
What he got wrong was failing to do same to the value 15 exactly what he did to 90x.
To make it correct:
90x - 15
Factor of both 90 and 15 is 15
Therefore:
15 (6x - 1)
Hence the correct factorization is achieved .
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Find the difference between the product of 26.22 and 3.09 and the sum of 3.507, 2.08,
11.5, and 16.712.
A. 4.489
B. 6.511
C. 47.2208
D. 58.3108
(3.6)^x=45 solve the exponential equation?
y varies jointly as x and z. y equals 80y=80 when x equals 5x=5 and z equals 4z=4. Find y when x equals 4x=4 and z equals 6z=6.
Find the slope of the line that passes through (8, 10) and (1, 1). Simplify your answer and write it as a proper fraction, improper fraction, or integer.
The slope of the line that passes through (8, 10) and (1, 1) is 9/7.
Explanation:To find the slope of a line that passes through two given points, (x1, y1) and (x2, y2), we use the formula:
m = (y2 - y1) / (x2 - x1)
Using the given points (8, 10) and (1, 1), we substitute the coordinates into the formula:
m = (1 - 10) / (1 - 8) = -9 / -7 = 9/7
Therefore, the slope of the line that passes through (8, 10) and (1, 1) is 9/7.
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The slope of the line that passes through the points (8, 10) and (1, 1) is calculated using the slope formula and it comes out to be 9/7, which is an improper fraction.
To find the slope of a line passing through two points, you use the slope formula:
Slope (m) = (change in y) / (change in x) = (y2 - y1) / (x2 - x1)
For the points (8, 10) and (1, 1), we calculate the slope as follows:
m = (1 - 10) / (1 - 8)
m = (-9) / (-7)
m = 9/7
Therefore, the slope of the line that passes through (8, 10) and (1, 1) is 9/7, which is an improper fraction.
x(7x-3)(x^2+81)=0x (7x-3)(x2+81)=0
A 5000 seat theater has tickets at $27 and $40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of $158,400
This math problem can be solved by setting up a system of linear equations. Designate the number of $27 tickets as x and the number of $40 tickets as y. You then form two equations, one for the total number of tickets (x + y = 5000) and one for the total revenue (27x + 40y = 158400). Solve these equations to determine how many of each ticket should be sold.
Explanation:The subject of this question is a problem in algebra, specifically a system of linear equations. Let's denote the number of $27 tickets as x and the number of $40 tickets as y. The total number of tickets sold will be 5000. So, we have our first equation: x + y = 5000. The total revenue is $158,400. The revenue from $27 tickets will be $27x and the revenue from $40 tickets will be $40y. So, we have our second equation: 27x + 40y = 158400. Now, we have a system of linear equations which can be solved to find the number of each ticket type that should be sold. Solve these equations to get the desired quantity of ticket type for generating the required total revenue.
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Will give brainliest!
How long will it take the tool to fall to the ground?
The function for objects dropped from a height where t is the time in seconds, h is the height in feet at time t, and h0 is the initial height is h(t)=-16t^2+h0. The building I already figured to be 162 feet.
Thank You!!
2x + 5y = −13 3x − 4y = −8
A box of packaged snacks contains 6 individual bags and costs $5.40. Each individual bag contains 18 crackers. What is the cost per cracker?
The cost per cracker from a box of 6 individual bags costing $5.40, with each bag containing 18 crackers, is $0.05.
Explanation:In the process of calculating the cost per cracker, the initial step involves determining the cost per bag. This is accomplished by dividing the total cost of the box, which amounts to $5.40, by the number of bags contained within, totaling 6 bags. Consequently, the cost per bag is determined to be $0.90. Subsequently, to ascertain the cost per individual cracker, the cost per bag is further divided by the number of crackers present in each bag, which is 18. Following this calculation, it is established that each cracker costs $0.05. In essence, the cost analysis method involves dividing the total box cost by the number of bags to derive the cost per bag, and then dividing this value by the number of crackers per bag to determine the precise cost per cracker, amounting to 5 cents per cracker.
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On Thursday, a local hamburger shop sold a combined total of 258 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the numbers of hamburgers sold. How many hamburgers were sold on Thursday?
The local drugstore is offering 15% off the normal price for a 16-pack of AAA batteries. If a 16-pack of AAA batteries is normally $9.99, what would be the sale price for the batteries after the discount?
Answer:
D: $8.95
Step-by-step explanation:
step 1
Calculate what 15% of the normal price is.
15% as a decimal is 0.15. Multiply this by $9.99.
0.15⋅$9.99 = $1.4985
step 2
Subtract $9.99 by $1.4985 and round the difference to the nearest cent.
$9.99 − $1.4985 = $8.4915 ≈ $8.49
step 3
Match your solution to the correct answer choice.
Answer choice D is the only answer choice that matches your solution. Select answer choice D and move on to the next question.
20 POINTS PLEASE HELP, need it tonight
A system of equations is graphed on the coordinate plane.
2y=3x−14
y=6x−2
A. No solution
B. One solution
C. Infinitely many solutions
Answer:
A
Step-by-step explanation:
A wedding dress is on sale for $225.00,which is 25% off of the original price. What was the original price. how do you solve this?
Answer:
$300
Step-by-step explanation:
Write an equation for the the sale price in terms of the original price. Then solve for the original price.
sale price = (original price) - (percent off) × (original price)
Factoring out the (original price), we have ...
sale price = (original price) × (1 - percent off)
We can find the original price by dividing this equation by (1 - percent off).
(sale price)/(1 -percent off) = original price
Putting in the numbers, we get ...
$225/(1 -25%) = original price
$225/(1 - 25/100) = $225/(1 -0.25) = $225/0.75 = original price = $300
What is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point (−4, −3)?
a; y + 3 = −4(x + 4)
b; y + 3 = –1/4(x + 4)
c; y + 3 = 1/4(x + 4)
d; y + 3 = 4(x + 4)
Solve: The quantity 2 x minus 10 divided by 4 = 3x
Suzan sees a bag of marbles, she grabs a handful at random. She has seen a bag containing four red marbles, four green ones, two white ones, and two purple ones. She grabs eight of them. Find the probability of the following event, expressing it as a fraction in lowest terms. She does not have all the red ones.
I need help answering this question.
12 ch 5 warm up: people's weights (java) (1) prompt the user to enter five numbers, being five people's weights. store the numbers in an array of doubles. output the array's numbers on one line, each number followed by one space. (2 pts) ex: enter weight 1: 236.0 enter weight 2: 89.5 enter weight 3: 142.0 enter weight 4:
Final answer:
The code provided guides the user through entering five weights using a Scanner object, stores them in a double array, and then prints them all on one line separated by spaces.
Explanation:
To address the question of prompting the user to enter five people's weights and storing them in an array of doubles in Java, we need to provide a short piece of code executing this task.
The code will look something like this:
import java.util.Scanner;
class Main {
public static void main(String[] args) {
Scanner scanner = new Scanner(System.in);
double[] weights = new double[5];
for(int i = 0; i < weights.length; i++) {
System.out.println("Enter weight " + (i+1) + ": ");
weights[i] = scanner.nextDouble();
}
System.out.println("The entered weights are:");
for(double weight : weights) {
System.out.print(weight + " ");
}
}
}
This code initializes a Scanner to take user input, creates an array of doubles to store the weights, and uses a for loop to iterate over the array, prompting the user to enter a weight for each element. It then prints out each weight followed by a space.
Roberto Anaya and his wife plan to rent a condominium for $725 per month. They pay a $125 monthly fee for all of the maintenance work. Their annual expenses are insurance $468, lost interest, $129; and utility bills, $3,000. What are their average monthly expenses to the nearest cent?
Answer:
The average monthly expenses is $ 1,149.75
Step-by-step explanation:
Given,
The monthly rent of the condominium = $ 725,
Also, monthly fee for maintenance work = $ 125,
And, Their annual expenses are insurance $468, lost interest, $129; and utility bills, $3,000,
⇒ The total annual expenses in insurance, lost interest and utility bill = $ 468 + $ 129 + $ 3,000
= $ 3597,
⇒ The monthly expenses in insurance, lost interest and utility bills = [tex]\frac{3597}{12}[/tex]
= $ 299.75,
Hence, the average monthly expenses = monthly rent of the condominium + monthly fee for maintenance work + monthly expenses in insurance, lost interest and utility bills
= $ 725 + $ 125 + $ 299.75
= $ 1,149.75
In 10 minutes a heart can beat 700 times. At what rate can a heart beat?
Heart will beat 140 times in 2 minutes.
Heart beats at a rate of 70 beats per minute.
(How it's done down below)
In 0 minutes heart beats 700 times
hence in 1 minute it will beat 700/10=70 times
and heart will beat 140 times in 140/70=2 minutes
Heartbeats at a rate of 70 beats per minute.
Explanation:hence in 1 minute it will beat 700 ÷ 10=70 times
What temperature is ten degrees higher than -7°C ?
Suppose the constant rate of change of y with respect to x is 8.5, and the value of y is 5 when the value of x is 11. what is the value of y when the value of x is 19? what is the value of y when the value of x is –1? what is the value of x when the value of y is 7?
Answer:
(x, y) = (19, 73)(x, y) = (-1, -97)(x, y) = (11 4/17, 7)Step-by-step explanation:
You are given a point and a slope, so you can write the linear equation relating x and y using the point-slope form of the equation for a line. That form for slope m and point (h, k) is ...
y = m(x -h) +k
For your given values, m = 8.5, and (h, k) = (11, 5), the equation relating x and y can be written ...
y = 8.5(x -11) +5
___
Evaluating this for several different x-values can be done with a spreadsheet or calculator. I like to write the function into a graphing calculator and let it do the tedious arithmetic. (See the attachment.)
However, to show you what is involved in doing this by hand, we can ...
let x = 19, then ...
y = 8.5(19 -11) +5 = 8.5·8 +5 = 73
__
let x = -1, then ...
y = 8.5(-1-11) +5 = 8.5·(-12) +5 = -97
____
To find the value of x for y=7, we can realize that to make y go up by 2 (from the given point of 5), we need to have x go up by 2/8.5 (from the given point of 11). That is ...
for y = 7 ...
x = 11 + 2/8.5 = 11 + 4/17 = 11 4/17
To determine values for y based on x in a linear function, use the equation derived. For x = 19, y equals 73; for x = -1, y equals -97. Solving for x when y is 7 gives approximately 11.24.
To solve the given problem, we use the concept of a linear function which states that the change in y with respect to x is constant. Here, the constant rate of change (slope) is given as 8.5.
We can express the linear relationship in the form of the equation:
y = 8.5x + b
We are also given a point on the line: (11, 5). Plugging these values into the equation to find b:
5 = 8.5(11) + b
5 = 93.5 + b
Subtract 93.5 from both sides:
b = 5 - 93.5 = -88.5
So, the equation becomes:
y = 8.5x - 88.5
Now, let's find the values of y for the given x values:
When x = 19: y = 8.5(19) - 88.5 = 161.5 - 88.5 = 73When x = -1: y = 8.5(-1) - 88.5 = -8.5 - 88.5 = -97To find the value of x when y = 7, we can rearrange the equation:
7 = 8.5x - 88.5
Add 88.5 to both sides:
95.5 = 8.5x
Divide by 8.5:
x = 95.5 / 8.5 = 11.2353 (approximately)
8-(x+3)=11 solve for x
please help solve this equation