Hannah wants to have $ 6500 to help pay for a new deck in 16 years. If she wants to put her money into an account earning 4.75% interest compounded continuously, how much should she invest now, so that she will have $ 6500 in 16 years?
Payment amount =

Answers

Answer 1

[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$6500\\ P=\textit{original amount deposited}\\ r=rate\to 4.75\%\to \frac{4.75}{100}\dotfill &0.0475\\ t=years\dotfill &16 \end{cases} \\\\\\ 6500=Pe^{0.0475\cdot 16} \implies \cfrac{6500}{e^{0.0475\cdot 16}}=P\implies 3039.83\approx P[/tex]


Related Questions

What is the complete factorization of the polynomial below?
x³-2x²+x-2
A. (x-2)(x + 1)(x-1)
B. (x + 2)(x + 1)(x-1)
C. (x + 2)(x-1)(x-1)
D. (x-2)(x-1)(x-1)

Answers

Answer:

(x-2)(x^2+1)

do not exist the answer, so check your question

Step-by-step explanation:

(x^3-2x^2)+(x-2) = x^2(x-2)+(x-2)

= (x-2)(x^2+1)

Consider the graph of the function.



Which best represents the graph of the function?

Responses

f(x)=x−8−−−−√+2
f
(
x
)

Answers

The equation of the function represented by the graph is (d) g(x) = √(x + 9) - 1

How to describe the transformed equation from the parent function?

From the question, we have the graph that can be used in our computation:

The parent function of the graph is a square root function

This is represented as

f(x) = √x

First, we have the transformation to be:

The function is translated left by 9 units

Next, we have:

The function is translated down by 1 unit

Mathematically, this can be represented as

g(x) = f(x - 9) - 1

When represented as an equation, it is

g(x) = √(x + 9) - 1

Hence, the transformation is (d) g(x) = √(x + 9) - 1

Read more about transformation at

brainly.com/question/27224272

#SPJ1

A person standing close to the edge on top of a 48-foot building throws a ball vertically upward.
The quadratic function
h(t) = 16t+52t + 48 models the ball's height about the ground, h(t) in feet, t seconds after it was thrown. What is the maximum height of the ball? (Write the answer to the nearest hundredth)

Answers

After solving, the maximum height of the ball is 90.25 feet.

In the given question,

A person standing close to the edge on top of a 48-foot building throws a ball vertically upward.

The quadratic function

h(t) = -16t^2+52t + 48 models the ball's height about the ground, h(t) in feet, t seconds after it was thrown.

We have to find the maximum height of the ball.

Height is given that;

h(t) = -16t^2+52t + 48

Now comparing the given equation by the standard equation ax^2+bx+c=0

Here b = 52, a = -16

For maximum height put t= -b/2a

t = -52/2(-16)

t = 52/32

t = 1.625

Maximum height

h(1.625) = -16(1.625)^2+52(1.625) + 48

h(1.625) = -42.25+ 84.5 + 48

h(1.625) = 90.25 feet

The maximum height of the ball is 90.25 feet.

To learn more about quadratic function link is here

brainly.com/question/27958964

#SPJ4

Andrea started out the day with 2 quects and sold some each hour. Lee started the day with 12 quects and sold some each hour. The graph below represents the number of quects each person has after x hours. Estimate the number of quects each person will have when they have the same amount.

Answers

Each person will have 3 quects when they have the same amount

How to estimate the number of quects each person will have when they have the same amount?

Given that:

Andrea started out the day with 2 quects and sold some each hour. Lee started the day with 12 quects and sold some each hour.

The equation of a line is of the form y = mx+c

where m is the slope and c is the y-intercept

For Lee

y =mx+c

c = 12

m = 12-8/0-1 = 4/( -1) = -4

y = -4x+12

For Andrea

y =mx+c

c = 2

m = 2-1/0-1.5 = 1/(-1.5) = -2/3

y = -2/3 x + 2

At the same amount y = -4x+12 is equal to y = -2/3 x + 2. Thus:

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

4x-2/3 x = 12-2

10/3 x = 10

10x = 30

x = 30/10 = 3

Therefore, at 3 quects each person will have when they have the same amount

Learn more about graph of a line on:

https://brainly.com/question/28953503

#SPJ1

What is the image of (7, 8) after a reflection over the line y = -x?

Answers

Answer:

If you connect the 2 dots it will give a X image.Both lines will cross each other forming the X

The revenue, R(x), of producing and selling x Awesome Hearing Aids is modeled by the function: R(x) = -3x^2 +53x
a. How many hearing aids need to be produced and sold in order to maximize the revenue? Round to the nearest whole number. ______ hearing aids must be produced and sold to maximize revenue.

b. What is the revenue? Use the fraction from (a) then round answer to the nearest dollar. The maximum revenue is $ ________.

Answers

Answer:

9 ; $234

Step-by-step explanation:

the maximum revenue is the vertex of the parabola


a) -53/(2*-3)

-53/-6

53/6

8.833333

9


b

-3(53/6)^2 + 53(53/6)

-3(2809/36) + 2809/6

-2809/12 + 2809/6

(-2809 + 5618)/12

2809/12

234.083333

234

can someone help me quick? don’t just put the answer, explain it please

Answers

Step-by-step explanation:

Riders must be at least 48 inches. "At least" means greater than or equal to. Therefore, the inequality is:

h ≥ 48

To graph this, we draw a solid dot at the 48 mark (because it can equal 48) and an arrow to the right (because it can be greater than 48).

At the July 1980 Olympics, the record for the women's shot put was 22.41 meters, which was 5.09 meters less than double the 1948 Olympic winning distance. What was the women's winning shot put distance in the 1948 Olympics?

Answers

22.41+5.09=27.5
27.5/2=13.75

On July ​, the billing​ date, Marvin Zug had a balance due of ​$265.72 on his credit card. His card charges an interest rate of​ 1.25% per month. The transactions he made are to the right.
​a) Find the finance charge on August ​, using the previous balance method.
​b) Find the new balance on August 7.

(see photo)

Answers

Answer:

475$

Step-by-step explanation:

If cos(θ)=-1/4 and θ is in the 3rd quadrant, find the exact value for
sin(θ).

Answers

cos (b) ^2+sin (b) ^2=1. So sine of b squared is equal to 1 minus 1/16 is equal to 15/16. And since b is in the third quadrant, sine of b is less than 0. So sine of b is equal to minus the square root of 15/16

If an object is dropped from a height of 85 feet, the function h(t) = -16t2 +85 gives the height
of the object after t seconds. Approximately, when will the object hit the ground?

Answers

Answer:

Step-by-step explanation: h(t)=-16t2+85

Let h(t)=0 to find when the object will hit the ground

0=-16t2+85

Solve for t=?

We need to get t term on its own

Take 85 from both sides

0-85=-16t2+85-85

-85=-16t2

To get t term on its own

Divide both sides by -16

-85/-16=-16t2/-16

5.3=t2

We have to solve for t squared that means we must take the square root of both sides

the square root of 5.3=gives + or - 2.3 seconds we can't have negative time so discard -2.3 seconds

Write a quadratic equation in a such that the sum of its roots is -8 and the product
of its roots is -15

Answers

The equation is x^2-8 x-15=0.

What is equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."

Given, sum of the roots of a quadratic equation is 8 and their product is 15 We know that the quadratic equation is given as [tex]$\mathrm{x}^2-$[/tex](Sum of the roots) [tex]$\mathrm{x}+$[/tex] (product of the roots)[tex]$=0$[/tex] [tex]$\Rightarrow x^2-8 x-15=0$[/tex]

Hence, the equation is x^2-8 x-15=0.

To learn more about equation visit:https://brainly.com/question/29657992

#SPJ1

Answer:

  x² +8x -15 = 0

Step-by-step explanation:

You want a quadratic such that the sum of the roots is -8 and their product is -15.

Coefficients

When the roots of a quadratic are p and q, its factored form is ...

  (x -p)(x -q) = 0

The expanded form of this is ...

  x² -(p+q)x +pq = 0

That is, the coefficient of x is the opposite of the sum of the roots, and the constant is the product of the roots.

Application

Here, we want the sum of roots to be -8, so the x-coefficient will be the opposite of that: 8. The constant will be the product of the roots: -15. That makes the desired quadratic be ...

  x² +8x -15 = 0

__

Additional comment

The attachment shows the quadratic, its roots, and their sum and product.

What is the y-intercept of the
grouph of the line whose equation is
y = -2/5 x +4?

Answers

Answer:

b = 4

Step-by-step explanation:

y = mx + b represents the equation of a line

m represents the slope

b represents the y-intercept

Based on what we're given, we could determine that 4 is our y-intercept or b.

A survey of 2000 subscribers to a certain news paper revealed that 1800 people subscribe to the daily morning edition and 1000 subscribe to both the daily and the sunday editions. how many subscribe to the Sunday edition? how many subscribe to the Sunday edition only?

Answers

1200 people subscribed Sunday edition and 200 people subscribed only sunday edition.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that A survey of 2000 subscribers to a certain news paper revealed that 1800  people subscribe to the daily morning edition  

And 1000 subscribe to both the daily and the sunday editions.  

Let x denote the number who subscribe to the Sunday edition.  

Then the addition rule with overlap tells us that is;

1800 + x – 1000 = 2000

800 + x = 2000  

x = 1200  

so, 1500 subscribe to the Sunday edition and 1200 – 1000 = 200 subscribe to the Sunday edition only.

Hence, 1200 people subscribed Sunday edition and 200 people subscribed only sunday edition.

Learn more about equations here;

https://brainly.com/question/25180086

#SPJ1

Find the value.
4³ =
A
12
с
B
81
64

Answers

The answer is:
4³ = 64

Answer: 64

Step-by-step explanation:

43 = (4)(4)(4)

=64

OR

4x4x4=64

Part of your job as manager is to count the cash for the daily bank deposit. When you count thecash, you have 47 ones, 22 fives, 9 tens and 17 twenties. You also have 67 pennies, 12 nickels, 9dimes and 15 quarters. What is the total amount of the deposit?

Answers

Answer:

$592.92

Step-by-step explanation:

Part of your job as manager is to count the cash for the daily bank deposit. When you count the cash, you have 47 ones, 22 fives, 9 tens and 17 twenties. You also have 67 pennies, 12 nickels, 9dimes and 15 quarters. What is the total amount of the deposit?

47 ones = $47

22 fives = $110

9 tens = $90

17 twenties = $340

67 pennies = $0.67

12 nickels = $ 0.60

9 dimes = $0.90

15 quarters = $3.75

$47 + $110 + $90 + $340 + $0.67 + $ 0.60 + $0.90 + $3.75 = $592.92

You have a student who says the sum of 3/4 and 5/6 is 4/5. Do you agree with them? Explain and solve this problem. Draw a model and explain how to solve this problem. Explain why we need common denominators.

Answers

The sum of 3/4 and 4/5 is 31/20 and To divide the common denominators by the individual denominators without using fractions or decimals, we need common denominators or the LCM of the two denominators.

What is a fraction?

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, are two fractions 3/4 and 4.5 and their sum is,

= 3/4 + 4/5.

= (15 + 16)/20.

= 31/20.

So, the answer of the student is wrong.

We need common denominators or LCM of the two denominators so that we can divide the common denominators by the individual denominators without having fractions or decimals.

learn more about fractions here :

https://brainly.com/question/10354322

#SPJ1

Systolic blood pressure for a group of women is normally distributed, with a mean of 115 and a standard deviation of 9. Find the probability that a woman selected at random has the following blood pressures. (Round your answers to four decimal places.) (a) greater than 130 (b) less than 108 (c) between 108 and 122

Answers

The probability that the blood pressure of woman is more than 130 by given normal distribution is 0.9505

What is z-value?

The standard score in statistics is the amount of standard deviations that a raw score deviates from or exceeds the mean of the phenomenon being observed or assessed. Standard scores are positive for raw scores above the mean.

We are given a normal distribution with a mean value 115 and standard deviation 9

And we are asked to find the probability that a woman selected at random has blood pressure greater than 130

We first find the z-value

z= (x-μ)/σ

z= (130-115)/9

z= 15/9

z= 1.6666

Now the corresponding value is

Probability is 0.95

Hence the probability is 95%

TO learn more about the probability please refer the following link

https://brainly.com/question/24756209

#SPJ4

trying to find the arc length of the arc for the polar curve r=8cosθ between 0 and π4

Answers

Answer:

Step-by-step explanation:

To find the arc length of the polar curve r = 8cosθ between 0 and π/4, we can use the formula for arc length:

L = ∫a^b √(r^2 + (dr/dθ)^2) dθ

Substituting in the values for r and dθ, we get:

L = ∫0^(π/4) √(8^2cos^2θ + (-8sinθ)^2) dθ

= ∫0^(π/4) √(64cos^2θ + 64sin^2θ) dθ

= ∫0^(π/4) √(64) dθ

= ∫0^(π/4) 8 dθ

= 8(π/4 - 0)

= 8π/4

= 2π

Therefore, the arc length of the polar curve r = 8cosθ between 0 and π/4 is 2π.

Drag and drop the range of each data set into the boxes.

Answers

Answer:

Data set 1: 20

Data set 2: 25

Step-by-step explanation:

Range is where you take the lowest value and subtract it from the highest value. So with data set 1, the highest number is 40 and the lowest is 20.cSo 40-20=20. Answer 20. Then with data set number 2, the highest number is 60 and the lowest is 35. So 60-35=25. Answer 25.

I hope this helps!!!

14,032.8/ 1,000 this is my q and a i nedd this to colm

Answers

Answer: 14.0328

Step-by-step explanation:

Answer: 14.032

Step-by-step explanation: you just have to move the decimal point

eg=72. if ef = 4x-3 and fg = 6x+9 then x+?

Answers

The value of x has been solved as 6.4

How to solve for x

We would have EG = EF + FG

where EG = 70

EF = 4x-3

FG =  6x+9

We would have to put these values in the equation that we have above, such that we would have, To the respective variables, connect the related terms:

70 = (4x-3) + (6x+9)

Separate the x variable. Because of the equal symbol, everything you do on one side also affects the other.

Open the brackets

70 = 4x + 6x -3 + 9

70 = 10x + 6

70 - 6 = 10x

64 = 10x

divide through by 10

x = 64 / 10

x = 6.4

Hence the value of x would be given as 6.4

Read more on expressions here: https://brainly.com/question/17407104

#SPJ

If y varies inversely as x2 and y=38 when x=18, find y if x=20.

Answers

The required value of y for the given inverse relation is 30.78

What is the inverse variation?

Inverse variation occurs when one variable varies inversely with respect to another. It represents the inverse relationship between two quantities are two quantities.

In mathematics, inverse variation refers to the relationships between variables that are expressed as y = k/x, where x and y are two variables and k is a constant value. It states that if the value of one quantity rises, the value of the other quantity falls.

Given, y varies inversely as [tex]x^{2}[/tex]

That is, y∝ 1/ [tex]x^{2}[/tex]

or, y = k/ [tex]x^{2}[/tex]

or,  [tex]x^{2}[/tex]y = k

And, y=38 when x=18

Then,  [tex]18^{2}[/tex]*38 = k

k = 12312

Now, if x=20 then y=?

[tex]x^{2}[/tex]y = 12312

or,  [tex]20^{2}[/tex]*y = 12312

or, 400y = 12312

or, y = 12312/400 = 30.78

Hence, the required value of y is 30.78

To learn more about inverse variation

https://brainly.com/question/19403855

#SPJ1

Help me plssss I dead don’t get this asap

Answers

Answer:

i don't know but its not B or D and my guess is A

Step-by-step explanation:

Alexa has $900 in a savings account that earns 2% annually. The interest is not compounded. How much will she have in total in 5 years? Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.​

Answers

Answer:

Alex will have a total of $990 in 5 years.

Step-by-step explanation:

Using the formula [tex]i=prt[/tex] we get [tex]i=900[/tex] × [tex]0.2[/tex] × [tex]5[/tex] which equals 90

[tex]900 + 90 = 990[/tex]

Ethan and his children went into a grocery store and he bought $6 worth of apples and bananas. Each apple costs $0.75 and each banana costs $0.30. He bought a total of 14 apples and bananas altogether. Determine the number of apples, x,x, and the number of bananas, y,y, that Ethan bought.

Answers

The number of apples x will be 10 and the number of bananas y will be 4.

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Ethan and his children went into a grocery store and he bought $6 worth of apples and bananas. Each apple costs $0.75 and each banana costs $0.30. He bought a total of 14 apples and bananas altogether.

The number of apples and bananas will be calculated as,

0.75x +0.30y = 6

x + y = 14 or x = 14 - y

0.75(14-y) = 0.30y = 6

10.5-0.75y + 0.30y = 6

y = 10

x = 14  - y

x = 14 - 10 = 4

Therefore, the number of apples x will be 10 and the number of bananas y will be 4.

To know more about an expression follow

https://brainly.com/question/14989788

#SPJ1

WILL GIVE BRAINLY, BUT WILL REPORT NONSENSE ANSWERS...


Why doesn't the following function have a hole at x=2, the function is 3x(x-2)/(x-2)(x-2)?

Answers

Answer:

This is because the function is an exception - it is a special type of function called a Separatrix Separation Function.

Step-by-step explanation:

The Separatrix Separation Function theorem helps us prove through complex conjugates the reason why there is no hole at x =2.

Work out the area of this triangle.
8 cm
11 cm
13 cm

Answers

Answer:

44

Step-by-step explanation:

BxH/2=Area

8x11=88

88/2=44

area=44

Which relation is a function?

Answers

Answer:

i think A is a function because when you search what it looks like it looks kind of like A so i am sure it is A

Step-by-step explanation:

Mackenzie is trying to find the height of a radio antenna on the roof of a local
building. She stands at a horizontal distance of 29 meters from the building. The
angle of elevation from her eyes to the roof (point A) is 24°, and the angle of
elevation from her eyes to the top of the antenna (point B) is 32°. If her eyes are 1.71
meters from the ground, find the height of the antenna (the distance from point A to
point B). Round your answer to the nearest meter if necessary.

Answers

The antenna's height is determined to be 10 m using right triangle relations.

What are the relations in a right triangle?

Following are the relationships in a right triangle:

The sine of an angle is equal to the length of the hypotenuse divided by the length of the side opposite the angle.

The cosine of an angle is equal to the neighboring side's length divided by the hypotenuse's length.

The tangent of an angle is calculated by dividing the length of the angle's adjacent side by its opposite side.

So, n this case, the side opposite to the 17o angle is the vertical height from her eyes to the top of the antenna, and the next side is the horizontal distance of 29 m, then:

tan 17° = h/29

h = 29 tan 17°

h = 8.87

Including eye height:

h = 8.87 + 1.51 = 10.38 m.

The antenna is 10 meters tall, rounded to the nearest meter.

Therefore, the antenna's height is determined to be 10 m using right triangle relations.

know more about relations in a right triangle here:

brainly.com/question/26396675

#SPJ1

Other Questions
Cara wants to build an 80 foot long rectangular sheep pen in back of her barn. If she bought 180 feet of fencing and used her barn wall as one side of the pen equaling the width, what would be the area of the sheep pen?. Different between serial and reference sources Gary and Florence are hired at the same time for the same position. They are both equally qualified, but Florence, who is blind, is paid less because the company thinks she will not be able to complete as much work as Gary. This is an example of ethnic discrimination disability discrimination racial discrimination religious discriminationplease answer this aspa! Question 12(Multiple Choice Worth 2 points)(01.01 LC)Which type of figurative language is present in the following line of poetry?From the jingling and the tinkling of the bells.O HyperboleO MetaphorO OnomatopoeiaO Simile In a simplified model of a city, the zone where retail and office activities are clustered is the. Fe(OH)3 FeO3 +HO which employee group was not included in the nlrb decision identifying categories of hospital workers permitted to organize in a bargaining unit? Help solve this please:Adam has saved 2 less than Dan. Write and expression for the amount that Dan saved. churchville county is trustee for a multi-government investment pool and has established an investment trust fund. included in the investment trust fund, for management purposes, are investments in the amount of $15 million from the county's general fund, $3 million from the county's special revenue funds, and $112 million from other governments. which of the following would be true? At the July 1980 Olympics, the record for the women's shot put was 22.41 meters, which was 5.09 meters less than double the 1948 Olympic winning distance. What was the women's winning shot put distance in the 1948 Olympics? What game is an ancestor to chess? A. Chaturanga B. Mancala C. Othello D. The Royal Game of Ur On July , the billing date, Marvin Zug had a balance due of $265.72 on his credit card. His card charges an interest rate of 1.25% per month. The transactions he made are to the right.a) Find the finance charge on August , using the previous balance method.b) Find the new balance on August 7.(see photo) Angelina will be traveling worldwide as a goodwill ambassador for a nonprofit organization. She is asked to gather information and suggestions regarding the organizations next humanitarian outreach program. What strategy can best reduce any listening errors caused by cultural differences?. Determining Theme: Tutorial ? Question What statement represents the best theme in the excerpt from Little Women? A Dreams are difficult to accomplish. B Dreams are only fantasies. C Dreams are fulfilled through ambition. D Dreams give us a purpose in life. what we usually think of as government, the set of institutions that set laws and govern life within a set of geographical boundaries, is also known as the . simple q help pls due tomorrow in the early 1900s which of these probably led to the greatest increase in the factory output in the united states A)wireless radio B)mass production C)air transportation D)word-processing equipment I think of a number and add 3. The answer is 18 The diameter of a circle is 18m.Eugene claims that the circumference of the circle is about 113.04m. assume fur color is controlled by one gene with two alleles in squirrels, and gray is dominant to brown. if a population of 360 gray and 640 brown squirrels is in hardy-weinberg equilibrium, what is the frequency of the dominant allele?