Susan invested $6,000 in municipal bonds and $13,000 in certificates of deposit. For the bond investment scenario, given the increase in market interest rate to 9%, you would pay less than $10,000 for the bond. The calculation shows you would be willing to pay approximately $9,724.77.
Explanation:To solve Susan's investment problem, we can set up a system of equations using the information provided in the problem. Let x be the amount invested in municipal bonds and y be the amount invested in certificates of deposit (CDs). We can then set up the following equations:
x + y = $19,000 (Total investment amount)
0.07x + 0.09y = $1,590 (Total annual income from investments)
Now, we solve the system of equations. Multiplying the second equation by 100 to get rid of decimals:
7x + 9y = 159,000
Next, we can multiply the first equation by 7 to help us eliminate one variable:
7x + 7y = 133,000
Subtracting the modified first equation from the second equation:
9y - 7y = 159,000 - 133,000
2y = 26,000
y = $13,000
Using y = $13,000 in the first equation:
x + 13,000 = 19,000
x = $6,000
Therefore, Susan invested $6,000 in municipal bonds and $13,000 in certificates of deposit.
Regarding the bond investment scenario:
a. Since the market interest rate has risen to 9%, higher than the bond's 6% interest rate, you would expect to pay less than $10,000 for the bond.
b. To calculate the price you would be willing to pay, you need to find the present value of the expected payment from the bond one year from now:
The expected payment is $10,000 (the face value) plus $600 (the final interest payment), which totals $10,600.
Using the market interest rate of 9%, the present value (PV) formula is:
PV = Payment / (1 + market interest rate)
PV = $10,600 / (1 + 0.09)
PV = $10,600 / 1.09
PV ≈ $9,724.77
Therefore, you would be willing to pay approximately $9,724.77 for the bond.
The number of pizzas eaten at the class party is equal to one-fourth the number of students, plus two more pizzas for the adults. If nine pizzas are eaten, how many students are there?
The area of desert a is eight times the area of desert
b. if the sum of their areas is 900,000 square miles, find the area of each desert
What is the solution set of 2x2 7x 5=0??
77/8 as a mixed number
An office building casts a 90 foot shadow. At the same time of day, a 5 foot woman standing near the building casts an 8 foot shadow. What is the approximate height of the building to the nearest foot?
Jason considered two similar televisions at a local electronics store. The generic version was based on the brand name and was three fourths the size of the brand name. If the generic television set is 12 inches by 24 inches, what are the dimensions of the brand name television?
18 inches by 36 inches
6 inches by 12 inches
16 inches by 32 inches
9 inches by 18 inches
Answer: The answer is 16 by 32.
Step-by-step explanation:
I took the test and this was correct. Explanation is easy because 12 is 3/4 of 16 and 24 is 3/4 of 32.
If the generic television set is 12 inches by 24 inches, the dimensions of the brand name television is, 16 inches by 32 inches
What is a fraction?Fraction is a mathematical term, which represents the portion or sub-parts of the whole thing. Basically, It has two parts: numerator and denominator.
Numerator is a number which lies on the top side, it indicates the number of equal parts taken and denominator is on the bottom side, it indicates the equal parts of the whole number.
Given that,
Jason considered two similar televisions at a local electronics store
The generic version was three fourths the size of the brand name
The generic television set is 12 inches by 24 inches
The dimensions of the brand name television = ?
Suppose, the dimensions of the brand name are a inches by b inches
So,
3/4 a = 12
a = 16
Similarly,
3/4 b = 24
b = 32
Hence, the dimensions are 16 inches by 32 inches
To know more about Fraction check:
https://brainly.com/question/8482939
#SPJ2
Catie is making bracelets for her friends using small rubber bands. She has 364 rubber bands and she wants to make 6 bracelets. How many rubber bands will she use for each bracelet? How many rubber bands will be left over?
Haley is at the store buying some supplies for an art project. She decides to buy some colored pencils for $3.95 and a drawing tablet. The total cost of the supplies before sales tax is $6.94.
Which equation could not be used to find the cost of the drawing tablet?
$3.95 + x = $6.94
$6.94 + x = $3.95
x = $6.94 - $3.95
$6.94 - x = $3.95
(3x^2a - 4y^a z^3a) ^2 ...?
Find a polynomial function with integer coefficients that has given zeros. (There are many correct answers)
0, 0, 4, 1+i
#1: The theoretical yield of a reaction is 5.00 moles of potassium permanganate (KMnO4). If the reaction actually produces 695.2 g KMnO4, what is the percent yield of the reaction?
A. 78%
B. 83%
C. 88%
D. 120%
Final answer:
To calculate the percent yield, the actual yield in moles of potassium permanganate was found to be 4.40 moles from 695.2 g, using the molar mass of KMnO4. Then, the percent yield was calculated using the theoretical yield of 5.00 moles, resulting in 88%.
Therefore, the correct answer is C. 88%
Explanation:
To calculate the percent yield of the reaction, we first need to know the moles of potassium permanganate (KMnO4) that correspond to 695.2 g. We use the molar mass of KMnO4 which is 158.04 g/mol to convert grams to moles.
Actual yield in moles = mass (g) / molar mass (g/mol) = 695.2 g / 158.04 g/mol = 4.40 moles of KMnO4
Now, with the theoretical yield of 5.00 moles, we can find the percent yield using the formula:
Percent yield = (actual yield / theoretical yield) × 100%
Percent yield = (4.40 moles / 5.00 moles) × 100% = 88%
Therefore, the correct answer is C. 88%
what is 0.9 as a percentage
0.9 as a percentage is 90 percent.
Explanation:To convert a decimal to a percentage, you need to multiply the decimal by 100. In this case, 0.9 times 100 equals 90. Therefore, 0.9 as a percentage is 90 percent.
Learn more about Conversion decimal to percentage here:https://brainly.com/question/30775491
#SPJ12
True or false.
1) Adjacent angles are supplementary?
2) Same-side interior angles are supplementary?
3) Vertical angles are congruent?
What is the volume of a cone with a radius of 18 cm and a height of 10 cm? Use 3.14 for pi. Round your answer to the nearest tenth
The correct answer is 3391.2cm^3
a piggy bank contains only nickels and quarters. The total value in the back is $3.80. Write an equation in standered form that models the possible combinations of nickels and quarters in the piggy bank
Simplify 5 log2 k – 8 log2 m + 10 log2 n
...?
Answer:
your answer is log2 k to the fifth power n to the tenth power over m to the eighth power
Step-by-step explanation:
Identify the maximum and minimum values of the function y = 10 cos x in the interval [-2π, 2π].
Line PQ is parallel to BC and splits AB into lengths of x + 8 and x. The other side, AC, is split into lengths of x + 13 and x + 1. What is the length of AC? Image Not to Scale.
Answer:
AC = 18.Step-by-step explanation:
The problem is about proportions, because we have two parallels line being intercepted by two transversal. So, the proportion would be:
[tex]\frac{x+8}{x}= \frac{x+13}{x+1}[/tex]
Solving for [tex]x[/tex]:
[tex]\frac{x+8}{x}= \frac{x+13}{x+1}\\(x+1)(x+8)=x(x+13)\\x^{2} +8x+x+8=x^{2} +13x\\9x+8=13x\\8=13x-9x\\4x=8\\x=\frac{8}{4}=2[/tex]
Now, to find the length of AC, we just have to use the value found and replace it in the proper expression:
[tex]AC=x+13+x+1=2x+14=2(2)+14=4+14=18[/tex]
Therefore, the length of AC is 18.
Lily forgot the security code for her apartment building. the code is two different numbers followed by a letter. how many different possible codes are ther?
What is 24.051 rounded to the nearest hundredth? How did you solve it?
If the average cost of hotel stay per night is about $85 plus 18% of hotel tax, estimate the total stay. Round answer to the hundredths place
A bookstore charges a standard rate for paperback or hardback books. The cost of a paperback book is 11 dollars less than the cost of a hardback book. Recently one day of sales totaled $784.10. That day the bookstore sold 53 paperback books and 45 hardback book. Write a system representing the situation. Use the graph test made the solution of the system. What does the solution mean to the situation? How much does each type of book cost? You substitution to verify your solution.
The required price of the paperback book and hardback book is $2.95 and $13.95 respectively.
Given that,
The cost of a paperback book is 11 dollars less than the cost of a hardback book. Recently one day of sales totaled $784.10. That day the bookstore sold 53 paperback books and 45 hardback book.
Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.
Here,
Let the price of paperback be x and price of hardback books be y,
According to the question,
x = y - 11 - - - (1)
53x + 45y = 784.10 - - - (2)
From equation 1
53 [y - 11] + 45y = 784.10
y = $13.95
Now,
y = 13.95 - 11
y = $2.95
Thus, the required price of the paperback book and hardback book is $2.95 and $13.95 respectively.
Learn more about simultaneous equations here:
https://brainly.com/question/16763389
#SPJ5
A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 2 feet per second. (Do not use mixed numbers. Round your answers to three decimal places.)
(a) How fast is the top of the ladder moving down the wall when the base is given below?
15 feet away from the wall
_____ ft/sec
20 feet away from the wall
_____ ft/sec
24 feet away from the wall
_____ ft/sec
...?
last one. i can do the first part. put x = distance from top of ladder to the floor, y = distance from base of ladder to the wall (draw a picture) then pythagoras sez
x2+y2=25calculus says
2xx′+2yy′=0and you are told that
y′=2so you know
2xx′+4y=0or
x′=−2yxIn a circus a tightrope is stretched from the top of a 10 ft. pole to the top of a 25 ft pole. The poles are 36 feet apart and vertical. How long is the tightrope?
Show your work.
Final answer:
To find the length of the tightrope between two poles of different heights and a known distance apart in a circus using the Pythagorean theorem.
Explanation:
The length of the tightrope can be calculated using the Pythagorean theorem.
Given:
Height of the first pole = 10 ftHeight of the second pole = 25 ftDistance between the poles = 36 ftUsing the Pythagorean theorem:
Length of the tightrope = √(36^2 + (25-10)^2)
Length of the tightrope = √(1296 + 225)
Length of the tightrope = √1521
Length of the tightrope = 39 ft
Jason bought 8 new baseball trading cards to add to his collection. the next day his dog ate half of his collection. there are now only 40 cards left. how many cards did jason start with
Jason started with 72 baseball trading cards. To find out how many baseball trading cards Jason started with, let's break down the information given step by step.
1. Jason bought 8 new baseball trading cards: This implies that Jason's collection increased by 8 cards.
Let's denote the number of cards Jason had before buying the new ones as X . After buying the new cards, Jason would have X + 8 cards.
2. The next day his dog ate half of his collection: If his dog ate half of his collection, this means that the number of cards left after the incident is half of what Jason had before. So, after the dog ate half of the collection, Jason would have [tex]\( \frac{1}{2} \times (X + 8) \)[/tex] cards remaining.
3. There are now only 40 cards left: This information tells us that the number of cards left after the incident is 40. So, we have the equation:
[tex]\[ \frac{1}{2} \times (X + 8) = 40 \][/tex]
Now, let's solve for X:
[tex]\[ \frac{1}{2} \times (X + 8) = 40 \][/tex]
[tex]\[ X + 8 = 40 \times 2 \][/tex]
X + 8 = 80
X = 80 - 8
X = 72
So, Jason started with 72 baseball trading cards.
To verify, let's check the steps:
1. Jason initially had 72 cards.
2. He bought 8 new cards, totaling 72 + 8 = 80 cards.
3. After his dog ate half of his collection, he was left with [tex]\( \frac{1}{2} \times 80 = 40 \)[/tex] cards, which matches the given information.
Therefore, Jason started with 72 baseball trading cards.
The complete question is:
Jason bought 8 new baseball trading cards to add to his collection. the next day his dog ate half of his collection. there are now only 40 cards left. how many cards did jason start with?
one pipe fills a storage pool in 8 hours. A second pipe fills the same pool in 4 hours when a third pipe is added and all three are used to fill the pool,it takes only 2 hours. find how long it takes the third pipe to do the alone.
Why is investing in a mutual fund less risky than investing in a particular company’s stock?
two ninths of the eighteen people in the bakery are eating cookies how many people are eating cookies
Final answer:
To find out how many people are eating cookies, you multiply the total number of people in the bakery, which is 18, by two-ninths. The result is four, meaning four people are eating cookies.
Explanation:
If two-ninths of the eighteen people in the bakery are eating cookies, we need to calculate 2/9 of 18 to find out how many people are eating cookies. This is a basic fraction multiplication problem.
To solve this, we multiply 18 (the total number of people) by the fraction 2/9:
18 × (2/9) = (18 × 2) / 9
18 × 2 = 36
36 / 9 = 4
Therefore, four people in the bakery are eating cookies.
Order these numbers from least to greatest. 8 7/11 , 8.17 , 8.174 , 173/20
The numbers are ordered from least to greatest by first converting them all to decimals, resulting in the order: 8.17, 8.174, 8 7/11 (8.6363), and 173/20 (8.65).
First, we need to convert all the numbers to similar formats, either as decimals or fractions, to compare them accurately. Here's what we have:
8 7/11 = 8 + 7/11 = 8.6363 (rounded to four decimal places)8.17 (already a decimal)8.174 (already a decimal)173/20 = 8.65 (as a decimal)Now, we can easily order these from least to greatest:
8.178.1748 7/11 (8.6363)173/20 (8.65)Will give brainliest answer. If explained..
A parallelogram and some of its dimensions are shown below.
What is the area of the parallelogram?
A. 100 sq.in.
B. 200 sq.in.
C. 300 sq.in.
D. 600 sq.in.