A person places $9680 in an investment account earning an annual rate of 5.3%, compounded continuously. Using the formula V = P e r t V=Pe rt , where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 18 years.

Answers

Answer 1

Answer:

[tex]\displaystyle V \approx 25129.99[/tex]

General Formulas and Concepts:

Math

Euler's number e ≈ 2.718

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Continuously Compounded Interest Rate Formula: [tex]\displaystyle V = Pe^{rt}[/tex]

V is value of accountP is principle initially investede is base of lnr is rate of interestt is time in years

Step-by-step explanation:

Step 1: Define

P = $9680

r = 5.3% = 0.053

t = 18 years

Step 2: Solve

Substitute in variables [Continuously Compounded Interest Rate]:            [tex]\displaystyle V = 9680e^{0.053(18)}[/tex]Multiply exponents:                                                                                        [tex]\displaystyle V = 9680e^{0.954}[/tex]Evaluate exponents:                                                                                       [tex]\displaystyle V = 9680(2.59607)[/tex]Multiply:                                                                                                           [tex]\displaystyle V = 25129.988684793[/tex]Round:                                                                                                             [tex]\displaystyle V \approx 25129.99[/tex]

Related Questions

Points (−3, 5) and (3, 5) on the coordinate grid below show the positions of two players on a tennis court:

Which statement best describes the relationship between the positions of the two players? (4 points)

Select one:
a. Player 2's position is Player 1's position reflected across the y-axis; only the signs of the y-coordinates of Player 1 and Player 2 are different.
b. Player 2's position is Player 1's position reflected across the x-axis; only the signs of the x-coordinates of Player 1 and Player 2 are different.
c. Player 2's position is Player 1's position reflected across the x-axis; only the signs of the y-coordinates of Player 1 and Player 2 are different.
d. Player 2's position is Player 1's position reflected across the y-axis; only the signs of the x-coordinates of Player 1 and Player 2 are different.

Answers

Answer:

B

Step-by-step explanation:

1. Plot the points on a graph (reflected across x-axis)

17. The base of a 30-foot ladder is placed 11 feet from the building. How
high up the building does the ladder reach, to the nearest foot? *

Answers

We would use the Pythagorean thrm

a=11 b=height of building c=30

11^2+b^2=30^2
121+b^2=900
b^2=779 *square root both sides*
b=28 feet

. Bree sold 2 paintings for $95 each,
5 stone sculptures for $64 each, and
1 mini-bronze sculpture for $150 in the
month of April. Bree doubled her sales
in May. How much were her total sales in
April and May?

Answers

Her sales in April&May were 1,320.
2x95=190
64x5=320
+150
Add those together and you get 660.
Since it’s doubled, multiply 660 by 2 to get 1,320.
Hope this helps! <3

Find the volume of the figure. Round to the tenths if necessary

Answers

Answer:

308.9 cm³

Step-by-step explanation:

6x3.9x13.2=308.88

A town has a fireworks display, where fireworks are set off from a bridge over a lake. The function h (t) = -16t2 + 150t + 10.5 represents

the approximate height of each firework, in feet, t seconds after it is launched.

Approximately when do the fireworks reach their maximum height?

Answers

Answer:

h(t) = 4.68 seconds

Step-by-step explanation:

The function that represents the height of each firework in feet is :

[tex]h (t) = -16t^2 + 150t + 10.5[/tex] .....(1)

We need to find the time the fireworks take to reach their maximum height. For maximum height,

dh/dt = 0

So,

[tex]\dfrac{d}{dt}(-16t^2 + 150t + 10.5 )=0\\\\-32t+150=0\\\\t=\dfrac{150}{32}\\\\t=4.68\ s[/tex]

Put t = 4.68 in equation (1).

[tex]h (t) = -16(4.68)^2 + 150(4.68)+ 10.5\\\\h(t)=362.06\ text{feet}[/tex]

So, the fireworks will take 4.68 seconds to their maximum height.    

If a=.3 and b=.5, what is the value of a=b ?

Answers

Answer:

5.0/5.

Step-by-step explanation:

Answer:

3A = 5B A/B=5/3 (A + B) / B=(5+3) / 3 (A + B) / B=8/3 इसलिए सही उत्तर विकल्प B है।

Hope this helps

Step-by-step explanation:

someone help me ASAP

Answers

Answer:

there's nothing here at all....

Step-by-step explanation:

I need help ASAP will mark the brainliest

Answers

Answer: 7,3

Step-by-step explanation: do the x line the y line (not the best explanation)

Answer:

16,7

Step-by-step explanation:

The answer is 16,7 because y value will go up 3 since the JKLM is the same and x value will go right 10.

Y+3, x+10

Hope this help!

Can someone please help me it’s very important please ASAP

Answers

The answer to this question is c)

What is the area of the following circle?
Either enter an exact answer in terms of or use 3.14 fort and enter your answer as a decimal.
MA
As
d=8
MY
Co
MY
units

Answers

Answer:

[tex]A=50.24\ \text{unit}^2[/tex]

Step-by-step explanation:

Given that,

The diameter of the circle, d = 8 unit

Radius, r = 4 units

We need to find the area of the circle. The formula for the area of a circle is given by :

[tex]A=\pi r^2\\\\A=3.14\times 4^2\\A=50.24\ \text{unit}^2[/tex]

So, the area of the circle is equal to [tex]50.24\ \text{unit}^2[/tex].

The side lengths of the following right triangle 15,20 and 25, as shown below. The altitude from the right angle splits the hypotenuse into line segments of length x and y. Solve for h,x, and y.

Answers

Answer:

[tex]h = 12[/tex]

[tex]x = 9[/tex]

[tex]y= 16[/tex]

Step-by-step explanation:

Given

The attached triangle

Required

Find h, x and y

Let the base of the triangle be 15.

So, the area is:

[tex]A = \frac{1}{2} * 15 * 20[/tex]

[tex]i.e\ height = 20[/tex]

[tex]A = \frac{1}{2} * 300[/tex]

[tex]A = 150[/tex]

Let the base of the triangle be 25.

So, the area is:

[tex]A = \frac{1}{2} * 25 * h[/tex]

[tex]i.e\ height = h[/tex]

[tex]A = \frac{1}{2} * 25h[/tex]

Substitute [tex]A = 150[/tex]

[tex]\frac{1}{2}*25h = 150[/tex]

Solve for h

[tex]h = \frac{150 *2}{25}[/tex]

[tex]h = 6 *2[/tex]

[tex]h = 12[/tex]

Considering the smallest triangle

[tex]Hypotenuse = 15[/tex]

So:

[tex]15^2 = h^2 + x^2[/tex]

[tex]15^2 = 12^2 + x^2[/tex]

This gives:

[tex]15^2 - 12^2 = x^2[/tex]

[tex]81 = x^2[/tex]

Take square roots

[tex]9 =x[/tex]

[tex]x = 9[/tex]

Solving for y

[tex]x + y = 25[/tex]

[tex]y= 25 - x[/tex]

[tex]y= 25 - 9[/tex]

[tex]y= 16[/tex]

A pyramid has a rectangular base that is 5 cm wide and 9 cm long. The height of the pyramid is 10 cm.
10 cm
5 cm
9 cm
What is the volume of the pyramid?

Answers

Answer:  450 cm

Step-by-step explanation:

10 x 9 = 90 x 5 = 450

find tan C will mark branylis​

Answers

Answer:

i think26 and 10

Step-by-step explanation:

Answer:

c.  12/5

Step-by-step explanation:

With reference angle C

perpendicular (P)= 24

base(b) = 10

Then

Tan < C = p / b

Tan < C = 24/ 10

Tan < C = 12/5

Hope it helps :)

100 POINTS AND BRAINLIEST !!!!! (I need the answer ASAP) A school is planning to construct two rectangular play areas in the playground.

The length of play area A must be 1 foot longer than four times its width. The width of play area B must be 2 feet longer than the width of play area A, and the length must be 2 feet longer than three times its own width. In addition, the areas of the two play areas must be equal.

Write a system of equations to represent this situation, where y is the area of the play areas and x is the width of play area A. Which statement describes the number and viability of the system’s solutions?

A.
The system has two solutions, and both are viable because they result in positive widths.
B.
The system has only one solution, but it is not viable because it results in a negative width.
C.
The system has two solutions, but only one is viable because the other results in a negative width.
D.
The system has only one solution, and it is viable because it results in a positive width.

Answers

Answer:

D.

Step-by-step explanation:

I'ts just reading the question over and over.

Answer:

The Answer is C

Step-by-step explanation:

I blessed you all and just guessed on the test on Plato/Edmentum and this was the right answer.

i need help finding the surface area and the volume

Answers

Answer:

it is 5.6

Step-by-step explanation:

Multiple all the sides

Answer:

Surface area: 24.4

Volume: 5.6

how do i find r in a geometric sequence of (243, 81, 27)? also how do i find the explicit formula for this?

Answers

Answer:

Step-by-step explanation:

The initial term is 243. Since it is a geometric sequence, each term is r times the preceding term.

r = 81/243 = ⅓

nth term = a₁rⁿ⁻¹ = 243(⅓)ⁿ⁻¹

Hard question need help My mom is mad please help Middle school will like and give brainliest

Answers

Isiah, you have been to careless to cut out your tabs on your computer. Now a stranger knows you go to Belmont Ridge Middle School in Loudon Virginia.
Please learn about internet safety with an adult because stuff like this can be dangerous

PLZ HELP
which of the following is true

2 + 21 =27
2 + 21 = 32
2 + 21 = 23

Answers

The third one is correct
The answer is the third one

the net of a retangular prism is shown below. The surface area of each face is labeled. 12 square centimeters, 12 square centimeters, 18 square centimeters, 18 square centimeters, 24 square centimeters, and 24 square centimeters. which values represent the dimentions, in centimeters, of the retangular prism?



HELP QUICKLY PLEASE

Answers

Answer:

76

Step-by-step explanation:

Help im being timed.

Answers

Answer:

the answer is D

Step-by-step explanation:

Answer:

D. 6g

Step-by-step explanation:

Please answer ASAP this is due tomorrow

Answers

I found this answer online for the same question so i suppose this is it

200% of what number is 66?

Answers

Answer:

33

Step-by-step explanation:

Because 66 is 200% just divide that by 2. Then 33 would be 100%

Graph f(x) = 3[x] +9

Answers

Answer:

Step-by-step explanation:

The equation of line is y = 3x + 9 , where the slope is m = 3

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

y = 3x + 9   be equation (1)

The equation is of the form y = mx + b where m is the slope and b is the y-intercept

Substituting the values in the equation , we get

Slope m = 3

The y intercept of the line is ( 0 , 9 )

Now , the equation of line is plotted on the graph below

Hence , the equation of line is y = 3x + 9

To learn more about equation of line click :

https://brainly.com/question/14200719

#SPJ5

A flying disc has a radius of 10 inches. What is the area of one side of the flying disc to the nearest square inch? Use 3.14
as an approximation for .

Answers

The area of the disk is approximately 314 inches

Solve.
10x^2 - 6 = 9x

Answers

Answer:

B

Step-by-step explanation:

use quadratic formula:  (-b ±√b²-4ac) ÷ 2a

a = 10,  b = -9,  c = -6

I need help showing my work for this so and answers help.​

Answers

Answer:

240 yd²

Step-by-step explanation:

I assume you’re looking for area?

24x8=192

1/2x12x8=48

192+48= 240 yd²

PLEASEEEEE I NEED HELPPPPP !!!!!!!

Answers

(Volume for a rectangular shape is length x width x height)

We can split up this 3D composite figure into two main parts (as shown in the picture I attached), and find each part’s volume before adding them together for the total volume.

Cube —> 5x5x5 —> 25x5 = 125 in^3

Rectangular Prism —> 20x5x5 —> 100x5 = 500 in^3

125 + 500 = 625

So the answer is A. 625 in^3

Hope this helped! If I was correct, I’d appreciate it if you marked my answer as Brainliest.

I need help fast I will give brainliest ​

Answers

Answer:

7

Step-by-step explanation:

y

Answer:

I think its 97.51

Step-by-step explanation:

Area of circle is A = [tex]\pi r^{2} = \pi 6^{2}[/tex]

Area of a triangle is [tex]\frac{\sqrt{3} }{4}a^{2}[/tex] = [tex]\frac{\sqrt{3} }{4}6^{2}[/tex]

Area of triangle = 15.59

Area of circle = 113.1

113.1 - 15.59 = 97.51

A swimming pool is 14 yards long and 6 yards wide.Which equation can you use to find the area of the bottom of the pool?

Answers

If it is 14 yards long and 6 yards wide it will be 84 yards

Please confirm my answer

Answers

Yes your answer is correct
the slope would be 0
y-int: (0, -8)
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