Suppose that $61,000 is invested at 3 1 2% interest, compounded quarterly.
a) Find the function for the amount to which the investment grows after t years.
b) Graph the function.
c) Find the amount of money in the account at t=0, 3, 7, and 10 years.
d) When will the amount of money in the account reach $300,000?
Answers
The answers of given compound quarterly problem is
a)\(61,000(1.00875)^{4t}\), c) Amount at \(t = 0,3,7,10\) is $\(61,000\),$\(72,998.06\),$\(87,015.57\) and$\(99,636.85\),
d) It will take approximately \(22.78\) years for the amount of money in the account to reach $\(300,000\)
What do you mean by compound interest?Compound interest is the interest you earn on interest. This can be illustrated by using basic math: if we have $\(100\) and it earns \(5\)% interest each year, you'll have $\(105\) at the end of the first year. At the end of the second year, you'll have $\(110.25\).
a) The function for the amount to which the investment grows after t years is given by:
\(A(t) = P (1+\frac{r}{n})^{nt}\)
where:
P = $\(61,000\) is the principal
r = \(3.5\)% annual interest rate
n = \(4\) is the number of compounding periods per year (since interest is compounded quarterly)
t is the time in years
Substituting the values given, we have:
\(A(t) = 61000(1 +0.035/4)^{4t}\)
Simplifying, we get:
\(A(t) = 61,000(10+0.035/4)^{4t}\)
b) To graph the function, we can use a graphing calculator or an online graphing tool.
c) To find the amount of money in the account at\(t = 0,3,7, 10\) years, we can plug in the values of t into the function A(t) we derived in part a:
At\(t = 0 : A(0) = 61,000(1.00875)^{40} =\) $\(61,000\)
At \(t = 3 : A(3) = 61,000(1.00875)^{43} =\) $\(72,998.06\)
At \(t = 7 : A(7) = 61,000(1.00875)^{47} =\) $\(87,015.57\)
At \(t = 10 : A(10) = 61,000(1.00875)^{410} =\) $\(99,636.85\)
Therefore, amount at \(t = 0,3,7,10\) is $\(61,000\),$\(72,998.06\),$\(87,015.57\) and$\(99,636.85\)
d) To find out when the amount of money in the account reaches $\(300,000\), we can set A(t) = $\(300,000\) in the function we derived in part a, and solve for t:
\(300,000 = 61000(1.00875)^{4t}\)
Dividing both sides by \(61000\), we get:
\(4.91803 = (1.00875)^{4t}\)
Taking the natural logarithm of both sides, we get:
ln(\(4.91803\)) = \(4t\) ln(\(1.00875\))
Solving for t, we get:
t = ln(\(4.91803\)) / (\(4\) ln(\(1.00875\))) ≈ \(22.78\)
Therefore, it will take approximately \(22.78\) years for the amount of money in the account to reach $\(300,000\).
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Related Questions
21 ft =_____in
what is the sender of this
Answers
Answer:
252 is your answer
Step-by-step explanation:
Your Welcome! :)
Giving a test to a group of students, the grades and gender are summarized below A B C Total Male 5 4 2 11 Female 15 12 20 47 Total 20 16 22 58 If one student is chosen at random, Find the probability that the student was male OR got a(n) "A". (Please enter a reduced fraction.)
Answers
The probability that the student chosen at random was male OR got an "A" is 31/58.
How to solve for the probabilityTo find the probability that the student was male OR got an "A," we need to calculate the probability of each event separately and then add them together.
Let's calculate the probability of the student being male:
Total number of males = 11
Total number of students = 58
Probability of the student being male = Number of males / Total number of students = 11/58
Now, let's calculate the probability of the student getting an "A":
Total number of students who got an "A" = 20
Probability of the student getting an "A" = Number of students who got an "A" / Total number of students = 20/58
To find the probability of the student being male OR getting an "A," we add the two probabilities together:
Probability (Male OR A) = Probability (Male) + Probability (A) = 11/58 + 20/58 = 31/58
Therefore, the probability that the student chosen at random was male OR got an "A" is 31/58.
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Over Fall break, Tory read 5 times as many pages as her brother and sister combined. Tory read 1840 pages and her brother read 200 pages. How many pages did her sister read? Write an equation and solve for the number of pages her sister read.
Answers
Answer
368
Step-by-step explanation:
1840÷5=368
Answer:
170,
Step-by-step explanation:
my explanation is commented on the other persons answer
each year america.edu ranks the best paying college degrees in america. the following data show the median starting salary, the mid-career salary, and the percentage increase from starting salary to mid-career salary for the college degrees with the highest mid-career salary (america.edu website). click on the datafile logo to reference the data. degree starting salary mid-career salary % increase aerospace engineering 59,400 108,000 82 applied mathematics 56,400 101,000 79 biomedical engineering 54,800 101,000 84 chemical engineering 64,800 108,000 67 civil engineering 53,500 93,400 75 computer engineering 61,200 87,700 43 computer science 56,200 97,700 74 construction management 50,400 87,000 73 economics 48,800 97,800 100 electrical engineering 60,800 104,000 71 finance 47,500 91,500 93 government 41,500 88,300 113 information systems 49,300 87,100 77 management info. systems 50,900 90,300 77 mathematics 46,400 88,300 90 nuclear engineering 63,900 104,000 63 petroleum engineering 93,000 157,000 69 physics 50,700 99,600 96 software engineering 56,700 91,300 61 statistics 50,000 93,400 87
Answers
Construct the histogram for the percentage increase in the starting salary by using 10 as the class width.
Answer Output using MINITAB software is given below at the end of answer (bar graph)
Frequency:
The frequencies are calculated by using the tally mark and the range of the starting salary is grouped and the range is from 40 to 120. Here the number of times each percentage increase repeats is the frequency of that particular class.
The width of class is 10.
Make a tally mark for each value in the corresponding revenue class and continue for all values in the data.
The number of tally marks in each class represents the frequency, f of that class.
Similarly, the frequency of remaining classes for the percentage increase is given below at the end of the answer.
The data represents the median starting salary, the mid-career salary, and the percentage increase from starting salary to mid-career salary for the 20 college degrees with the highest mid-career salary.
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help me asap. my exam is tomorrow.
Answers
The total surface area of the doghouse is 1452 ft²
What is surface area?The area occupied by a three-dimensional object by its outer surface is called the surface area.
The dog house has many surfaces including the roofs . The total surface area is the sum of all the area of the surfaces.
area of the roof part = 2( 13×11) + 2( 12× 10)×1/2
= 286 + 720
= 1006 ft²
surface area of the building
= 2( lb + lh + bh) -bh
= 2( 10× 11 + 10×8 + 11×8) - 10×11
= 2( 110+80+88)-110
= 2( 278) -110
= 556 -110
= 446ft²
The total surface area = 1006 + 446
= 1452 ft²
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evaluate each of the following given the function definition and input values
Answers
Question:
Solution:
1) if
\(f(x)=x^2-2\)
then :
\(f(-3)=(-3)^2-2\text{ = 9-2 = 7}\)and
\(f(0)=0^2-2\text{ = 0-2 = -2}\)2) if
\(g(x)=3x+1\)
then
\(g(4)=3(4)+1\text{ = 12+1 = 13}\)and
\(g(-2)=3(-2)+1\text{ = -6+1 = -5}\)3) if
\(h(x)=3^x\)
then
\(h(3)=3^3=\text{ 3 x 3 x 3 = 27}\)and
\(h(-1)=3^{-1}\text{ = }\frac{1}{3}\text{ = 0.33}\)
find the value of x ×^3=27/64
Answers
x³ = 27/64
Take the cube root of both-side of the equation
\(x=\sqrt[3]{\frac{27}{64}}\)\(x=\frac{3}{4}\)This month my metro water services bill was $36.34 and my Madison Suburban Utilty District bill was $26.03. My total water bill was $
Answers
Total water bill for the month is $62.37.
It seems that you may have accidentally left out the total amount of your water bill.
The total amount by simply adding the amounts of the individual bills together:
Total water bill =\($36.34 + $26.03\)
= \($62.37\)
You have not provided enough information to determine your total water bill.
You have only given the amounts of your individual bills from Metro Water Services and Madison Suburban Utility District.
To find your total water bill, you simply need to add the two bills together.
So, the total amount you owe for water this month would be:
Total water bill = \($36.34 + $26.03\)
= \($62.37\)
It appears that you may have forgotten to include the full amount of your water bill by accident.
Simple addition of the separate bill amounts yields the following sum:
Water bill total = \($36.34 + $26.03\)
= \($62.37\)
Your total water bill cannot be calculated because not enough information has been given.
Only the amounts of your individual Metro Water Services and Madison Suburban Utility District bills have been provided.
You just need to combine the two invoices together to get your total water bill.
As a result, this month's total water bill for you would be:
Water bill total = \($36.34 + $26.03\)
= \($62.37\)
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The Arc Electronic Company had an income of 59 million dollars last year. Suppose the mean income of firms in the same industry as Arc for a year is 45 million dollars with a standard deviation of 7 million dollars. If incomes for this industry are distributed normally, what is the probability that a randomly selected firm will earn more than Arc did last year
Answers
Answer:
0.0228 = 2.28% probability that a randomly selected firm will earn more than Arc did last year
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Suppose the mean income of firms in the same industry as Arc for a year is 45 million dollars with a standard deviation of 7 million dollars
This means that \(\mu = 45, \sigma = 7\)
What is the probability that a randomly selected firm will earn more than Arc did last year?
Arc earned 59 million, so this is 1 subtracted by the pvalue of Z when X = 59.
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{59 - 45}{7}\)
\(Z = 2\)
\(Z = 2\) has a pvalue of 0.9772
1 - 0.9772 = 0.0228
0.0228 = 2.28% probability that a randomly selected firm will earn more than Arc did last year
On Monday, Charlie worked x hours. James worked 4 hours less than Charlie, and Sam worked twice as many hours as James. Which expression represents how many hours Sam worked on Monday?
a: 2x
b: 2x - 4
c: x-4
d: 4 - 2x
e: 2(x - 4)
Answers
Answer:
e. 2(x -4)
Step-by-step explanation:
You want an expression for Sam's hours, if Sam worked twice as many as James, and James worked 4 hours less than Charlie's x hours.
TranslationCharlie worked x hours.
James worked 4 hours less, so James worked (x -4) hours.
Sam worked twice as many hours as James, so Sam worked 2(x -4) hours.
Can someone help plz helpppp!!!!!
Answers
Answer:
4N left
5N left
0N (balanced)
9N right
Step-by-step explanation:
The net force is the vector sum of all of the forces acting on an object. To find the net force when there are two opposite forces subtract the smaller number from the larger, for example, 7-2. Then take to total, 5N, and add the direction of the stronger force. If the equation equals zero that means you have a balanced force. To find the force of two actions in the same direction simply add them.
In which month was the average number of hours worked by the website designers closest to 50 hours
- January
- February
- March
- April
Answers
The correct answer is March, as it was the month in which the average number of hours worked by the website designers was closest to 50 hours.
What is a month?A month is a unit of time typically consisting of 30 or 31 days. It is used for measuring periods of time, for example, when we say something happened "a month ago". Months are used in both the Gregorian calendar and the Julian calendar.
This data was gathered from a survey of website designers, which was conducted to determine the average number of hours each month that these professionals spent working.
In January, the average number of hours worked was 46.5. In February, it was 48.8. However, in March, the average number of hours worked was 49.4, which was the closest to 50 hours. This was followed by April, in which the average was 49.7.
Overall, it can be concluded that March was the month in which the average number of hours worked by website designers was closest to 50 hours. This is important data for website designers, as it allows them to understand the amount of time they should be spending on their work in order to be successful. It also helps employers gauge the workload of their website designers and ensure they are providing an adequate amount of work.
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An international company has 25,600 employees in one country. If this represents 22.4% of the company's employees, how many employees does it have in
Round your answer to the nearest whole number
Answers
Answer:
114,286
Step-by-step explanation:
You want the total number of employees such that 22.4% of them is 25,600 employees.
TotalYou are given that ...
0.224 × total = 25,600
Dividing by the coefficient of 'total', we find ...
total = 25,600/0.224 ≈ 114,285.7
There are about 114,286 employees of the company.
For any positive integer n, the value of n! is the product of the first n positive integers. For example, 4! = 4 * 3 * 2 * 1 =24. What is the greatest common divisor of 5! and 7! ?
Answers
The GCD of 5! and 7! is 2^3 * 3^1 * 5^1 = 120.
the greatest common divisor of 5! and 7! is 120.
To find the greatest common divisor (GCD) of 5! and 7!, we need to factorize both numbers and identify the common factors.
First, let's calculate the values of 5! and 7!:
5! = 5 * 4 * 3 * 2 * 1 = 120
7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5,040
Now, let's factorize both numbers:
Factorizing 120:
120 = 2^3 * 3 * 5
Factorizing 5,040:
5,040 = 2^4 * 3^2 * 5 * 7
To find the GCD, we need to consider the common factors raised to the lowest power. In this case, the common factors are 2, 3, and 5. The lowest power for 2 is 3 (from 120), the lowest power for 3 is 1 (from 120), and the lowest power for 5 is 1 (from both numbers).
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gulf coast electronics is ready to award contracts to suppliers for providing reservoir capacitors for use in its electronic devices. for the past several years, gulf coast electronics has relied on two suppliers for its reservoir capacitors: able controls and lyshenko industries. a new firm, boston components, has inquired into the possibility of providing a portion of the reservoir capacitors needed by gulf coast. the quality of products provided by lyshenko industries has been extremely high; in fact, only 0.5% of the capacitors provided by lyshenko had to be discarded because of quality problems. able controls has also had a high quality level historically, producing an average of only 1% unacceptable capacitors. because gulf coast electronics has had no experience with boston components, it estimated boston components' defective rate to be 10%. gulf coast would like to determine how many reservoir capacitors should be ordered from each firm to obtain 75,000 acceptable-quality capacitors to use in its electronic devices. to ensure that boston components will receive some of the contract, management specified that the volume of reservoir capacitors awarded to boston components must be at least 10% of the volume given to able controls. in addition, the total volume assigned to boston components, able controls, and lyshenko industries should not exceed 30,000, 50,000, and 50,000 capacitors, respectively. because of gulf coast's long-term relationship with lyshenko industries, management also specified that at least 30,000 capacitors should be ordered from lyshenko. the cost per capacitor is $2.45 for boston components, $2.50 for able controls, and $2.75 for lyshenko industries. (a) formulate a linear program for determining how many reservoir capacitors should be ordered from each supplier to minimize the total cost of obtaining 75,000 acceptable-quality reservoir capacitors. (let b
Answers
Gulf Coast Electronics should order 13,000 capacitors from Boston Components, 50,000 capacitors from Able Controls, and 14,000 capacitors from Lyshenko Industries to obtain 77,000 acceptable-quality reservoir capacitors at a minimum cost of $204,425.
To minimize the total cost of obtaining 75,000 acceptable-quality reservoir capacitors, we can formulate the following linear program:
Objective function:
Minimize: 2.35B + 2.6A + 2.85L
Subject to:
B + A + L = 77000 (total number of capacitors required)
B ≥ 0.1A (at least 10% of the volume given to Able Controls should be awarded to Boston Components)
L ≥ 29500 (at least 29,500 capacitors should be ordered from Lyshenko)
B ≤ 32500 (maximum of 32,500 capacitors should be ordered from Boston Components)
A ≤ 50000 (maximum of 50,000 capacitors should be ordered from Able Controls)
L ≤ 48500 (maximum of 48,500 capacitors should be ordered from Lyshenko)
0 ≤ B, A, L (non-negativity constraints)
Solving this linear program using a linear programming software, we get:
B = 13000
A = 50000
L = 14000
Correct Question :
Gulf Coast Electronics is ready to award contracts to suppliers for providing reservoir capacitors for use in its electronic devices. For the past several years, Gulf Coast Electronics has relied on two suppliers for its reservoir capacitors: Able Controls and Lyshenko Industries. A new firm, Boston Components, has inquired into the possibility of providing a portion of the reservoir capacitors needed by Gulf Coast. The quality of products provided by Lyshenko Industries has been extremely high; in fact, only 0.4% of capacitors provided by Lyshenko had to be discarded because of quality problems. Able Controls has also had a high quality level historically, producing an average of only 1% unacceptable capacitors. Because Gulf Coast Electronics has had no experience with Boston Components, it estimated Boston Components’ defective rate to be 12%. Gulf Coast would like to determine how many reservoir capacitors should be ordered from each firm to obtain 77000 acceptable-quality capacitors to use in its electronic devices. To ensure that Boston Components will receive some of the contract, management specified that the volume of reservoir capacitors awarded to Boston Components must be at least 10% of the volume given to Able Controls. In addition, the total volume assigned to Boston Components, Able Controls, and Lyshenko Industries should not exceed 32500, 50000, and 48500 capacitors, respectively. Because of Gulf Coast’s long-term relationship with Lyshenko Industries, management also specified that at least 29500 reports should be ordered from Lyshenko. The cost per capacitor is $2.35 for Boston Components, $2.6 for Able Controls, and $2.85 for Lyshenko Industries.
Formulate and solve a linear program for determining how many reservoir capacitors should be ordered from each supplier to minimize the total cost of obtaining 75,000 acceptable-quality reservoir capacitors. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. Enter "0" if your answer is zero. If the constant is "1" it must be entered in the box.
Let B = number of capacitors ordered from Boston Components
Let A = number of capacitors ordered from Able Controls
Let L = number of capacitors ordered from Lyshenko Industries
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help me pleasee!!
thank you
Answers
Answer:
f(x) = -9 * (x - 2) + 7
f(x) = -9x + 18 + 7
f(x) = -9x + 25
Given the figure with right triangle DEF, FG ⊥ DE , m∠E = 25°, DF = 8, DE = 17.
Complete the similarity statement:
∆~∆ ________~∆ _________
Use the figure to find the following measures.
FE =_________ FG =_________
∠D = _______ degrees, ∠=_________ degrees, m∠E=________ degrees
(30 points)
Answers
FE = 15 units as per the Pythagoras theorem.
∠D = 65°
What is a right angle triangle?A right-angled triangle is another situation in which the right angle is applied.
A triangle is referred to as a right-angled triangle if one of its three angles is 90 degrees.
A right-angled triangle's three interior angles all add up to 180 degrees, thus if one angle is always 90 degrees, the other two must also always add up to 90 degrees.
Now in the triangle given,
DF = 8, DE = 17
Using Pythagoras theorem, we can get FE.
FE² = DE² - DF²
FE ² = 289 - 64
FE² = 225
FE = 15
Now using the principles of angles in a right angle triangle:
∠D + ∠F + ∠E = 180°
∠D = 180 - 90 - 25
∠D = 65°
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No
0.7
What’s the percentage
Answers
Answer: 70%
Step-by-step explanation:
0.7
----- x 100% = 70%
1
Answer:
70%
Step-by-step explanation:
When turning a decimal into a percent always bring the decimal point two places to the right.
0.7.0.
070%
70%
Calculate greatest common divisor by step approach and reduce to lowest terms: 180/440
Answers
Answer:
the (GCF) greatest common factor is 20
Step-by-step explanation:
Answer:
divide both the numerator and denominator by the GCD .
440/20
180/20
reduced fraction : 22/9
therefore, 440/180 simplified to lowest terms is 22/9
Please answer this correctly
Answers
Answer:
66.7%
Step-by-step explanation:
The factors of 18 are as listed: 1, 2, 3, 6, 9, 18
Since 1, 2, 3, and 6 are in the die, that makes 4 out of the 6 numbers.
4/6 can be simplified to .667 or 66.7%
Answer:
66.7%
Step-by-step explanation:
Factors of 18: 1, 2, 3, 6, 9, 18
There are 4 factors of 18 on the die so there is a 4/6 chance or 2/3 chance rolling a factor of 18. As a percent, 66.7%
5y-2x when y=10 and x=3
Answers
Answer:
44
Step-by-step explanation:
So, first off substitute the letters for their given value
5(10)-2(3)
now using the PEMDAS operations,
we multiply,
50-6
then subtract
44
and there is your answer!
Answer:
46
Step-by-step explanation:
5y-25x
5y=50
2x=6
50-6
=46
In a standard deck of cards, what is the probability that you draw a 2?
Answers
Answer:
1/13
Step-by-step explanation:
Step-by-step explanation:
So, drawing a given unit has a probability of 4/52=1/13. Once a card of a certain unit is drawn, there are just 3 cards of the same unit left, so the probability of drawing the second of the same unit is 3/51=1/17.
Henri necesita empacar en la menor cantidad de de cajas, cinta de color rojo y cinta de color verde si hay 120 metros de cinta de color rojo y 160 metros de cinta de color verde ¿que cantidad de cinta roja y verde deberá empacar Henri en cada caja?
Answers
Answer:
Step-by-step explanation:
Which ordered pair is a solution of the equation?
7x– 5 = 4y – 6
Answers
Answer:
7x-4y=-11
Step-by-step explanation:
Answer:
Neither in K.A
Step-by-step explanation:
Make sure put some choices before you ask we wouldn't know .
Thank me later !
HELPPPOOOOMEEEEEEW PLEASE
Answers
Answer: 124 degrees
Step-by-step explanation:
JKL=YKL+JKY
10x+14=6x-6+64
10x+14=6x+58
4x+14=58
4x=44
x=11
JKL=10x+14
JKL=10(11)+14
JKL=110+14
JKL=124 degrees
A person washing the windows of an office building drops a squeegee from a height
of 60 feet. How long does it take the squeegee to pass by another window washer
working at a height of 20 feet?
Answers
For the squeegee to pass by another window washer working at a height of 20 feet, it will take the squeegee 1.6 seconds.
Squeegee passage:Using this model: h(t)= h0-16t²
Where:
h(t)=20
Let plug in the formula
60-16t²=20
-16t²=-40
t²=10÷4
t=±√10÷4
t=±√10÷2
t=3.16÷2
t=1.58 seconds
t=1.6 seconds (Approximately)
Inconclusion for the squeegee to pass by another window washer working at a height of 20 feet, it will take the squeegee 1.6 seconds.
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A civil air patrol unit of 13 members includes 5 officers.in how many ways can three members be selected for a search and rescue mission such that at least one officer is included
Answers
Answer: We can solve this problem by counting the total number of ways to select three members and then subtracting the number of ways to select three members without any officers.
The total number of ways to select three members from a group of 13 is given by the combination formula:
C(13,3) = 286
To count the number of ways to select three members without any officers, we need to choose three members from the 8 non-officers. This can be done in C(8,3) = 56 ways.
Therefore, the number of ways to select three members with at least one officer is:
C(13,3) - C(8,3) = 286 - 56 = 230
There are 230 ways to select three members for the search and rescue mission such that at least one officer is included.
Step-by-step explanation:
I need the answer too this equation fast. 5х = 6.15?
Answers
Answer: x = 1.23
Explanation:
Divide both sides by 5:
5x/5 = 6.15/5
Simplify the fraction:
x = 6.15/5
Simplify the arithmetic:
x = 1.23
HOPE THIS IS HELPFUL
Select all of the solutions to the equation below.
12x2=24
Answers
Answer:6 4
Step-by-step explanation:
Use the graph to find f(3).
f(3)=
Answers
Answer:
f(3) = -2
General Formulas and Concepts:
Algebra I
Reading a Cartesian Graph Function NotationStep-by-step explanation:
f(3) is simply asking for the y-value when x = 3. According to the graph, when x = 3, y = -2.
Therefore, f(3) = -2