Caroline puts $400 into a savings account that earns 6% annually. Write a function that represents this situation, where t is the time in years. Solve algebraically after how many years she will get $1200 in her account (round it to the nearest year).
Answers
Answer: 19 years
Step-by-step explanation:
Given
Amount invested \(\$400\)
Rate of interest \(R=6\%\)
after 1-year amount becomes
\(A=400\left (1+6\%\right)\\A=400\left (1+0.06\right)\\A=400\times 1.06\\A=\$424\)
After n years it is
\(A=400\left (1.06\right)^n\)
Sum accumulated is \(\$1200\)
\(\Rightarrow 1200=400\left(1.06\right)^n\\\Rightarrow 3=\left(1.06\right)^n\\\text{Taking log both sides}\\\Rightarrow n=\dfrac{\ln 3}{\ln 1.06}\\\\\Rightarrow n=18.85\approx 19\ \text{years}\)
Related Questions
Solve for x:
A: 3x - 7 = -19; x =
B: 2x + 3 = -11; x =
C: -3 + 1 = -26; x =
D: 6x + 3 = -15; x =
E: -9 + 7x = 33; x =
F: -2x + 8 = 4; x =
( URGENT PLEASE SOLVE !!! )
Answers
A: x = -4
B: x = -7
C: There is no solution for x since -2 does not equal -26.
D: x = -3
E: x = 6
F: x = 2
Suppose a computer manufacturer has the total cost function
C(x) = 76x + 3600
(in dollars) and the total revenue function
R(x) = 376x
(in dollars).
(a) What is the equation of the profit function P(x) (in dollars) for this commodity?
Answers
The equation of the profit function P(x) (in dollars) for this commodity is given by P(x) = 300x - 3600
It is given in the problem that,
The total cost function C(x) = 76x + 3600 (in dollars)
Also,
The total revenue function R(x) = 376x (in dollars)
We need to find the equation of the profit function P(x) (in dollars) for this commodity
First we need to understand the following terms
Cost is the price of a commodity which is paid or charged in exchange of something. Example - 1 kg of apple are of 3 Dollars
Revenue, which is determined by multiplying the average sales price by the quantity of units sold, is the money made from regular business operations.
So,
The equation of the profit is given by = Total Revenue - Total Cost
P(x) = R(x) - C(x)
Putting values, we get
P(x) = 376x - (76x + 3600)
P(x) = 376x - 76x - 3600
P(x) = 300x - 3600
Hence, the equation of the profit function P(x) (in dollars) for this commodity is given by P(x) = 300x - 3600
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Assumptions: Tax depreciation is straight-line over three years. Pre-tax salvage value is 25 in Year 3 and 50 if the asset is scrapped in Year 2. Tax on salvage value is 40% of the difference between salvage value and book value of the investment. The cost of capital is 20%.
Answers
Based on the given assumptions and calculations, the net present value (NPV) of the investment in the new piece of equipment is -$27,045.76, indicating that the investment is not favorable.
To calculate the after-tax cash flows for each year and evaluate the investment decision, let's use the following information:
Assumptions:
Tax depreciation is straight-line over five years.
Pre-tax salvage value is $10,000 in Year 5 and $15,000 if the asset is scrapped in Year 4.
Tax on salvage value is 30% of the difference between salvage value and book value of the investment.
The cost of capital is 12%.
Given:
Initial investment cost = $50,000
Useful life of the equipment = 5 years
To calculate the depreciation expense each year, we divide the initial investment by the useful life:
Depreciation expense per year = Initial investment / Useful life
Depreciation expense per year = $50,000 / 5 = $10,000
Now, let's calculate the book value at the end of each year:
Year 1:
Book value = Initial investment - Depreciation expense per year
Book value \(= $50,000 - $10,000 = $40,000\)
Year 2:
Book value = Initial investment - (2 \(\times\) Depreciation expense per year)
Book value \(= $50,000 - (2 \times$10,000) = $30,000\)
Year 3:
Book value = Initial investment - (3 \(\times\) Depreciation expense per year)
Book value = $50,000 - (3 \(\times\) $10,000) = $20,000
Year 4:
Book value = Initial investment - (4 \(\times\) Depreciation expense per year)
Book value \(= $50,000 - (4 \times $10,000) = $10,000\)
Year 5:
Book value = Initial investment - (5 \(\times\) Depreciation expense per year)
Book value \(= $50,000 - (5 \times $10,000) = $0\)
Based on the assumptions, the salvage value is $10,000 in Year 5.
If the asset is scrapped in Year 4, the salvage value is $15,000.
To calculate the tax on salvage value, we need to find the difference between the salvage value and the book value and then multiply it by the tax rate:
Tax on salvage value = Tax rate \(\times\) (Salvage value - Book value)
For Year 5:
Tax on salvage value\(= 0.30 \times ($10,000 - $0) = $3,000\)
For Year 4 (if scrapped):
Tax on salvage value\(= 0.30 \times ($15,000 - $10,000) = $1,500\)
Now, let's calculate the after-tax cash flows for each year:
Year 1:
After-tax cash flow = Depreciation expense per year - Tax on salvage value
After-tax cash flow = $10,000 - $0 = $10,000
Year 2:
After-tax cash flow = Salvage value - Tax on salvage value
After-tax cash flow = $0 - $0 = $0
Year 3:
After-tax cash flow = Salvage value - Tax on salvage value
After-tax cash flow = $0 - $0 = $0
Year 4 (if scrapped):
After-tax cash flow = Salvage value - Tax on salvage value
After-tax cash flow = $15,000 - $1,500 = $13,500
Year 5:
After-tax cash flow = Salvage value - Tax on salvage value
After-tax cash flow = $10,000 - $3,000 = $7,000
Now, let's calculate the net present value (NPV) using the cost of capital of 12%.
We will discount each year's after-tax cash flow to its present value using the formula:
\(PV = CF / (1 + r)^t\)
Where:
PV = Present value
CF = Cash flow
r = Discount rate (cost of capital)
t = Time period (year)
NPV = PV Year 1 + PV Year 2 + PV Year 3 + PV Year 4 + PV Year 5 - Initial investment
Let's calculate the NPV:
PV Year 1 \(= $10,000 / (1 + 0.12)^1 = $8,928.57\)
PV Year 2 \(= $0 / (1 + 0.12)^2 = $0\)
PV Year 3 \(= $0 / (1 + 0.12)^3 = $0\)
PV Year 4 \(= $13,500 / (1 + 0.12)^4 = $9,551.28\)
PV Year 5 \(= $7,000 / (1 + 0.12)^5 = $4,474.39\)
NPV = $8,928.57 + $0 + $0 + $9,551.28 + $4,474.39 - $50,000
NPV = $22,954.24 - $50,000
NPV = -$27,045.76
The NPV is negative, which means that based on the given assumptions and cost of capital, the investment in the new piece of equipment would result in a net loss.
Therefore, the investment may not be favorable.
Please note that the calculations above are based on the given assumptions, and additional factors or considerations specific to the business should also be taken into account when making investment decisions.
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The complete question may be like :
Assumptions: Tax depreciation is straight-line over five years. Pre-tax salvage value is $10,000 in Year 5 and $15,000 if the asset is scrapped in Year 4. Tax on salvage value is 30% of the difference between salvage value and book value of the investment. The cost of capital is 12%.
You are evaluating an investment in a new piece of equipment for your business. The initial investment cost is $50,000. The equipment is expected to have a useful life of five years.
Using the given assumptions, calculate the after-tax cash flows for each year and evaluate the investment decision by calculating the net present value (NPV) using the cost of capital of 12%.
A picture frame is designed to take a 6cm x 8cm picture. The border is the exact same width all round and its area is 32 cm^2. How wide is the border?
Answers
What the answer fast
Answers
Answer:
HI = 13
Step-by-step explanation:
The triangle that is shown is a 45-45-90 triangle, so we know that GH = GJ = 9 and IJ = 13, we are able to solve for HI.
Technically, IJ = HI, since both triangles are congruent. Both IJ and HI will be 13.
what are the first 30 digits of pi? im trying to learn and i already know some, i just want to know more.
Answers
Answer:
3.14159265358979323846264338327
Step-by-step explanation:
Rebecca and Joslyn go strawberry picking one Saturday morning. Both girls pick strawberries at a steady rate. The table shows the amount of strawberries Joslyn picked after certain lengths of time. Rebecca picked at a rate of 2 5 cup per minute.
Answers
The table that shows the amount of strawberry picked by Joslyn is a linear function
Rebecca's rate is greater than Joslyn's rate
How to determine the faster rateFrom the table, we have the following values
(x,y) = (0,0) and (3,6)
The rate is then calculated as:
\(m = \frac{y_2 -y_1}{x_2 -x_1}\)
So, we have:
\(m = \frac{6 - 0}{3 - 0}\)
Evaluate
\(m = 2\)
This means that:
Joslyn's rate is 2 cups per minute
From the question, we have:
Rebecca's rate is 2.5 cups per minute
2.5 is greater than 2
This means that:
Rebecca's rate is greater than Joslyn's rate
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Identify the explanatory variable and the response variableA golfer wants to determine if the amount of practice every year can be used to predict the amount of improvement in his game.The explanatory variable is the _____The response variable is the _____
Answers
Answer:
the explanatory variable is "the amount of practice every year" while the response variable is "the improvement in his game"
Step-by-step explanation:
In simple terms, the difference between explanatory and random variable is that the response variable is usually the focus of a question in a study/experiment while an explanatory variable is a variable that explains changes in the response variable. Which means that the explanatory variable is simply any variable that may affect the response variable.
Now, in this question, the golfer wants to determine if the amount of practice every year can be used to predict the amount of improvement in his game.
This means that the amount of practice every year explains how much he improves every year.
Thus, the explanatory variable is "the amount of practice every year" while the response variable is "improvement in his game"
3. Verify that the function
satisfies the three
hypotheses of Rolle's
Theorem on the given
interval. Then find all
numbers c that satisfies the
conclusion of Rolle's
Theorem.
y=-x² + 8x – 17
[3,5]
Answers
sin¹(x)-cos¹ (x)/sin²(x)-cos² (x) =1
Answers
if Tn =5n +2 which term will have a value of 52
Answers
Answer:
10th term
Step-by-step explanation:
given \(T_{n}\) = 5n + 2 and \(T_{n}\) = 52 , then equate right sides and solve for n
5n + 2 = 52 ( subtract 2 from both sides )
5n = 50 ( divide both sides by 5 )
n = 10
that is the 10th term has a value of 52
Please help!!!!!!!!!
Answers
All we need to do is substitute and solve.
A = P(1 + rt)
A = 5,100(1 + 0.035*60)
A = 5,100(3.1)
A = 15,810
Therefore, the answer is [ $15,810 ]
Best of Luck!
An assembly worker is making 3-legged and 5-legged stools. She has 67 legs to use in all for the day's work. What is the largest number of 3- legged stools she can make and still use all the legs to make 5-legged stools with the rest of the legs?
Answers
Answer:
Step-by-step explanation:
let number of 5 legs=x
so 67-5x =multiple of 3
x=1,67-5=62 not divisible by 3
x=2,67-5×2=57 ÷3=19
so he can make 19 three -legged table and 2 five -legged table.
Please help me thank you
Answers
Answer:
I don't see the photo
Step-by-step explanation:
y = 5/2x -11 that is the correct answer mark me as brainliest
Dena is buying wallpaper. It costs $8.79 per meter. She needs 120 feet. How much will the wallpaper cost? Round to the nearest half dollar.
Answers
Answer:
321.50 dollars.
Step-by-step explanation:
Dena is buying wallpaper. It costs $8.79 per meter. She needs 120 feet. How much will the wallpaper cost? Round to the nearest half dollar.
This is a tricky math problem that requires some conversions and calculations. First, we need to convert feet to meters, because Dena lives in a country that uses the metric system. According to the search results , one foot is equal to 0.3048 meters. So, 120 feet is equal to 120 x 0.3048 = 36.576 meters.
Next, we need to multiply the length of the wallpaper by the price per meter to get the total cost. The total cost is 36.576 x 8.79 = $321.38.
Finally, we need to round the total cost to the nearest half dollar. This means we need to look at the cents part of the cost and see if it is closer to 0, 50 or 100. In this case, 38 cents is closer to 50 than to 0 or 100, so we round up the cost to $321.50.
Therefore, Dena will have to pay $321.50 for the wallpaper. That's a lot of money for some paper that will probably peel off in a few years! Maybe she should consider painting her walls instead.
What is the local max and min?
Answers
Answer:
Functions can have "hills and valleys": places where they reach a minimum or maximum value. It may not be the minimum or maximum for the whole function, but locally it is.
Step-by-step explanation:
hope this helps :)
April buys soil for her flowerpots. she uses 9 kilograms of soil for her violets and 4 kilograms of soil for her tulips. she has 3,000 grams of soil left for some daisies (1 kilogram = 1,000 grams) use the drop down menus to show how much soil she bought
Answers
April bought 16 kilograms of soil in total.
To show how much soil April bought
We need to add the amounts of soil she used for her violets and tulips. Since April used kilograms for violets and tulips, we need to convert the 3,000 grams to kilograms before we can add them up.
April bought:
9 kilograms of soil for violets
4 kilograms of soil for tulips
3 kilograms of soil for daisies (since 3,000 grams is 3 kilograms)
Therefore, April bought 16 kilograms of soil in total.
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^answer for me please ?
Answers
Answer:
a and b
Step-by-step explanation:
parallel lines are lines that do not intersect each other
Mrs. jack bought 150 t-shirts for $1920 from a factory. The t-shirts are sold at $19.99 each.
Answers
We need to know about profit and loss inorder to solve the problem. The cost of one shirt is $12.8, the amount of money Mrs. Jackson received after selling all t-shirts is $2998.50, the total profit made is $1078.50 and the profit percentage is 56.17%.
We know that Mrs. Jackson bought 150 t-shirts for $1920, we need to fisrt find the cost of one t-shirt, we can do that by dividing the total cost by the number of t-shirts.
cost of one =1920/150=$12.8
Next we need to find the total selling price of all the t-shirts given that each t-shirt is sold at $19.99
total selling price= 150x19.99= $2998.50
The total profit made by Mrs. Jackson can be calculated by subtracting the cost price from the selling price.
profit=2998.50-1920=$1078.50
The profit percentage with respect to the cost price can be calculated as
profit percentage= 1078.50/1920x100=56.17%
Therefore the cost of one t-shirt is $12.8, the amount Mrs. Jackson received on selling all the t-shirts is $2998.50, the profit made is $1078.50 and the profit percentage is 56.17%.
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Your question was incomplete. Please refer below for the entire question.
Mrs. Jackson bought 150 T-shirt for 1920 from a factory.
i) calculate the cost of one T-shirt
The T-shirt are sold at $19.99 each.
Calculate
ii) the amount of money Mrs Jackson received after selling All of T-shirt.
iii) the TOTAL profit made
iv) the profit made as a percentage of the cost price, giving your answer correct to the nearest whole number.
I really need help with this question
Answers
The length of each side of the wood is 5 centimetres.
How to use quadratic equation to find the length of each side of the wood?Doug has 8 square pieces of wood. Each piece of wood have a side length of s cm. The total area of all 8 pieces of wood is 200 cm².
Hence, using quadratic equation let's find the length of each side of the wood.
Therefore,
8s² = 200
Hence,
8s² = 200
divide both sides of the equation by 8
s² = 200 / 8
s² = 25
s = √25
s = 5 centimetres
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Maria's dog weighs 8 times as much as her rabbit. Together they weigh 81 pounds. How much does the dog Weigh?
Answers
I just plugged in numbers plus the number I multiplied by
So 8 times 9 :72 +9: 81
Graph the line with the equation y = -x - 6
Answers
here you go . i hope this helps
Evaluate the expression for n = 5.
9(n + 1) =
Answers
Answer:
\(\huge\boxed{\boxed{\underline{\textsf{\textbf{Answer}}}}}\)
╭⋟─────────────── ღ
Given,
\(\boxed{n = 5}\)
So, substitute the value of n as 5 in the equation 9(n + 1).
\(9(n + 1) \\ = 9(5 + 1) \\ = 45 + 9 \\ = 54\)
\(\boxed{Answer \ = \ 54}\)
ღ ───────────────⋞╯
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❦ \(RainbowSalt2222\)
n=5
Now, substituting the value of n is the given equation
9(n+1)
9(5+1)
9×6
54
Consider the following distribution: 5, 5, 8, 9, 10, 10, 11. Which of the following is a correct statement about this distribution?
The mode is 9.
The median is 7.
The distribution is bimodal.
The mean is 6.5.
Answers
The distribution is bimodal. - this is a correct statement.
According to the question, the following distribution is 5, 5, 8, 9, 10, 10, and 11.
In statistics, the mode is the value that is being occurred frequently in a given set.In the above distribution, there are two modes i,e 5 and 10.
In statistics and probability theory median is the value separating the higher half from the lower half of a data sample. It is the point above and below which half (50%) of the observed data falls and so represents the midpoint of the data.Median: Middle value
In the above distribution, the median is - 9.
A data set is called bimodal if it has two modes which means that there is not a single data value that occurs with the highest frequency. Instead, there are two data values that tie in having the highest frequency.In statistics mean is the sum of a collection of numbers divided by the count of the numbers.Mean = \(\frac{5 + 5 + 8 + 9 + 10 + 10 + 11}{7}\) = \(\frac{58}{7}\) = 8.28
Hence,
The distribution is bimodal. - this is a correct statement.
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Which values are solutions to the inequality?
5r≤6r−8
Select each correct answer.
Responses
r = 7
r = 8
r = 9
r = 10
Answers
Answer:
r=8, r=9, r=10
Step-by-step explanation:
5(7)≤6(7)-8
35≤42-8
35≤34
not true.
5(8)≤6(8)-8
40≤48-8
40≤40
true.
5(9)≤6(9)-8
45≤54-8
45≤46
true.
5(10)≤6(10)-8
50≤60-8
50≤52
true.
have a great day!
Find slope of a parallel line -16+5x=4y
Answers
Ans
solve x : 3 (x-1) +7= 4x +2 -3 (2-x)
Answers
Answer:
Step-by-step explanation:
x=2
remove the parentheses. cancel the equal terms. calculate. move the terms. calculate. divide both sides. x=2
which expression is equivalent to -1.3 - (1.9)?
Answers
Answer: 0.6
Step-by-step explanation:
4 ft 5 ft 2 ft 6 ft 6 ft 11 ft
Answers
Answer:
34 feet
Step-by-step explanation:
Solve the equation. -5(-4+2n)=-10(n-2)
Answers
Answer:
0 = 0 means that there are infinite solutions.
Step-by-step explanation:
Equation is -5(-4+2n)=-10(n-2)
1. Distribute the -5 and -10
20 -10n = -10n + 20
2. Subtract 20 from one side to the other to get only 1 variable on 1 side.
-10n = -10n
3. divide -10 to separate the variable from the constant.
n = n
This means there are infinite solutions.