5. Sabrina put $3,000 into a Money Market (high-yield savings)
account with an interest rate of 2.6% compounded quarterly.

a. Write an equation to model the amount in the account over
time.

b. Assuming no deposits or withdrawals are made, how much
money would be in the account after 15 years? Show your
calculation.

c. How would this problem be different if it was compounded
"continuously" instead? Calculate the amount after 15 years.

d. Name 2 or more other situations (other than a savings
account) where you might encounter compound interest later in
your life.

Answers

Answer 1

let me answer the last one first

compound interest is just an exponential sequence really, where the next value is some exponential amount of the previous.

hmmm that can happen in say, a bouncing ball, the 1st bounce is high, let it keep on boucing by itself and the next bounce is usually a compounded value of the previous one, since it's smaller it'd be a Decay type of equation.

hmmm it also happens in say population growth, of any organism, humans, bees, amoebas.

now let's do the others

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3000\\ r=rate\to 2.6\%\to \frac{2.6}{100}\dotfill &0.026\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years \end{cases} \\\\\\ A=3000\left(1+\frac{0.026}{4}\right)^{4\cdot t}\implies \boxed{A=3000(1.0065)^t} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{after 15 years}}{t=15}\hspace{5em} A=3000(1.0065)^{15}\implies A\approx 3306.19 \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$3000\\ r=rate\to 2.6\%\to \frac{2.6}{100}\dotfill &0.026\\ t=years\dotfill &15 \end{cases} \\\\\\ A=3000e^{0.026\cdot 15}\implies A=3000e^{0.39}\implies A\approx 4430.94[/tex]

Related Questions

Pls help me with my math

Answers

Answer:a

Step-by-step explanation:Bottom line includes the end point so should be less than or equal. Top line does not so should be greater than

Please Help
Use the probability distribution table to answer the question.

X / P
0 / 0.03
1 / 0.13
2 / 0.70
3 / 0.10
4 / 0.04

What is P(2

Answers

Considering the given discrete probability distribution, it is found that [tex]P(2 < X \leq 4) = 0.14[/tex].

What does the discrete probability distribution gives?

It give the probability of each outcome, and each outcome is represented by a countable number.

The desired probability is:

[tex]P(2 < X \leq 4) = P(X = 3) + P(X = 4)[/tex]

As there is an open interval at X = 2, it does not enter the calculation. The values are:

P(X = 3) = 0.1.P(X = 4) = 0.04.

Hence:

[tex]P(2 < X \leq 4) = P(X = 3) + P(X = 4) = 0.1 + 0.04 = 0.14[/tex]

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1. Sue made a cookie cake for her friend's birthday. The diameter is 8 inches. The area of the cake is
inches² (round to the nearest hundredths place)

Answers

Answer:

50.24 inches^2

Step-by-step explanation:

D=8 inches, r=D/2, r=8/2=4 inches

Area of circle= πr^2

=3.14×4×4

=3.14×16

=50.24

Help PLS ASAP!!!!!!!!!!!!

Answers

Answer:

The answer is

" THe middle triangle is scalene"

and "the right and left triangle are isosceles"

Step-by-step explanation:

This is because B, and D are wrong.

B is wrong because all three sides are different lengths

D is wrong because the right and left triangles are not equalateral

give brainliest please!

hope this helps :)

The middle triangle is scalene

The right and left triangles are isosceles

A multiple-choice examination has 10 questions, each with four possible answers, only one of which is correct. Suppose that one of the students who takes the examination answers each of the questions with an independent random guess. What is the probability that he answers at least six questions correctly?

Answers

Answer:

[tex]0.0197277[/tex]

Step-by-step explanation:

Consider the random variable X

Where X denotes the number of (success/having a correct answer)

in 10 identical and independent trials .

then

X follows the Binomial distribution with parameters

10 and p = p(success) = 1/4

[tex]p\left( X\geq 6\right) =\sum^{10}_{k=6} p\left( X=k\right)[/tex]

[tex]=\sum^{10}_{k=6} C^{k}_{10}\left( \frac{1}{4} \right)^{k} \left( \frac{3}{4} \right)^{10-k}[/tex]

[tex]=\frac{20686}{2^{20}} \\= 0.0197277[/tex]

A car and a motor bike are priced at $33090. If the value of the car is three times the value of the motor bike, how much is the car worth?

Answers

So, you have the price combined for the motorcycle and car, and the car is 3x the amount of the bike. Here, we can separate their prices into fractions/percents (whatever works easiest for you). So, the car is 3/4 (75%) of the price, and the motorcycle is 1/4(25%) of the price.

Therefore, to find the price of the motorcycle, you multiply 33090 x 1/4 or .25 which equals $8272.50

And the car is 33090 x 3/4 or .75 which equals $24817.50.

The car is $24817.50

Kurt and Courtney are playing basketball. Kurt makes 2 baskets in the first game and 4 baskets in each game after that. Courtney makes 4 baskets in the first game and 2 baskets in each game after that. The table below shows the number of baskets each made in the first 4 games. Which graph shows the ordered pairs of the total number of baskets each has made after each game?

Answers

Answer:

Kurt 10 Courtney 10 Mark brainiest

Step-by-step explanation:

I did this too

Answer:

they each have 10 if you count mark me brainiest, please

Step-by-step explanation:

Can someone explain how to get the answer I’m confused on how to solve

Answers

Answer:

x=29

Step-by-step explanation:

The square notation indicates 90 degrees.

90=(x+3)+(x-1)+(x+1)

90=3x+3

87=3x

x=29

Answer:

x = 29

(x + 3)° = 32°

(x - 1)° = 28°

(x + 1)° = 30°

Step-by-step explanation:

(x + 3)° + (x - 1)° + (x + 1)° = 90°

-> (x + x + x +3 -1 + 1)° = 90°

-> (3x + 3)° = 90°

-> 3x + 3= 90

-> 3x = 90 - 3

-> 3x = 87

-> x = 87/3

-> x = 29

-> (x + 3)° = (29 + 3)° = 32°

-> (x - 1)° = (29 - 1)° = 28°

-> (x + 1)° = (29 + 1)° = 30°

This figure represents a small collectible box. Vicki wants to cover 45 of the surface with glitter.

How much of the total surface will be covered with glitter?

Enter your answer as a decimal or mixed number in simplest form in the box.

cm²

Right trapezoidal prism. The height of the trapezoid base is labeled 4 centimeters. The larger base is labeled 6 and 1 half centimeters, and the shorter base is 5 and 1 fourth centimeters. The two legs of the trapezoid are labeled 4 centimeters and 4 and 1 fifth centimeters. The height of the prism is labeled 9 centimeters.

PLease helpppp!! only have 2 minutesd

Answers

Answer:

181.24

Step-by-step explanation:

The total surface area of the Trapezoidal Prism to be covered is: 181.24 cm².

What is the Surface Area of a Trapezoidal Prism?

Surface Area = 2(area of trapezoid) + area of the 4 rectangular faces.

Area of Rectangle 1 = length × width = 9 × 4 = 36 cm²

Area of Rectangle 2 = length × width = 9 × 5 1/4 = 47.25 cm²

Area of Rectangle 3 = length × width = 9 × 4 1/5 = 37.8 cm²

Area of Rectangle 2 = length × width = 9 × 6 1/2 = 58.5 cm²

Area of the two trapezoids = 2[1/2(a + b)h] = 2[1/2(6½ + 5¼)4] = 47 cm²

Surface area = 36 + 47.25 + 37.8 + 58.5 + 47 = 226.55 cm²

Total surface that will be covered = 4/5(226.55) = 181.24 cm²

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If 5 apples cost $1.15, find the cost of 16 apples

Answers

Answer:

3.68$

Step-by-step explanation:

If 5 apples cost $1.15, find the cost of 16 apples

we can solve with an equation

5 : 1.15 = 16 : x

x = 1.15 * 16 : 5

x = 18.04 : 5

x = 3.68

check

5 : 1.15 = 16 : 3.68

4.34 = 4.34

the answer is good

1
Select the correct answer.
Find the quotient.
24-3÷1
7
I
=
1²
7
OA.
1(21 - 3)
OB.
71
21
3
-
O C.
21 3
-
71
OD. (213)
7

Answers

the right answer is D

(2x² - 3x) / 7 is the quotient of the given division.

What is simplification?

Simplifying procedures is one way to achieve uniformity in job efforts, expenses, and time. It reduces diversity and variation that is pointless, harmful, or unneeded. Parenthesis, exponents, multiplication, division, addition, and subtraction are all referred to as PEMDAS. The order of the letters in PEMDAS informs you what to calculate first, second, third, and so on, until the computation is finished, given two or more operations in a single statement.

To divide by a fraction, we can multiply by its reciprocal. So to simplify the expression:

((2x-3)/x ) / (7/x²)

We can multiply the numerator by the reciprocal of the denominator:

((2x-3)/x ) * (x²/7)

Simplifying this expression, we can cancel out the common factor of x in the numerator and denominator:

(2x-3) * (x/7)

Expanding the product:

(2x² - 3x) / 7

Therefore, the quotient of ((2x-3)/x ) / (7/x^2) is (2x² - 3x) / 7.

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if a person paid rs 32 as VAT to buy an article of cost Rs 2750 then how much money he /she pay? find it

Answers

The total amount paid for the article is Rs2782

How to determine the amount paid?

The given parameters are:

Article = Rs 2750

VAT = Rs 32

The amount paid is calculated using:

Amount = Article + VAT

This gives

Amount = 2750 + 32

Evaluate

Amount = 2782

Hence, the total amount paid for the article is Rs2782

Answers

Answer:

1.43

Step-by-step explanation:

12 tenths ⇒ 1.2

23 hundredths ⇒ 0.23

0.23 + 1.2 = 1.43

Jim is designing a seesaw for a children's park. The seesaw should make an angle of 30° with the ground, and the maximum height to which it should rise is 1 meter, as shown below:

A seesaw is shown with one end on the ground and the other in the air. The seesaw makes an angle of 30 degrees with the ground. The height of the seesaw from the ground, at the other end, is labeled 1 meter.

What is the maximum length of the seesaw?

Answers

Using the slope concept, it is found that the maximum length of the seesaw is of 1.73 meters.

What is a slope?

The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.

In this problem:

The vertical change is of 1 m.The horizontal change is the length l.The angle is of 30º.

Hence:

tan(30º) = 1/l

l = 1/tan(30º)

l = 1.73.

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I don’t know how to solve

Answers

Answer:

line it, then try to add each number going from the top, my mother gave me that advice before, it works (:

Step-by-step explanation:

Answer:

X go's first then Y

Step-by-step explanation:

I did this before and got 100% promise and mark me brainiest

7. What are the x- and y-intercepts for -x + 2y = 8?
O
A. x-intercept =-8; y-intercept = 4
O
B. x-intercept = 4; y-intercept = 8
O
C. x-intercept = 4; y-intercept = -8
O D. x-intercept = 8; y-intercept = -4

Answers

Answer:

the answer

Step-by-step explanation:

the answer is A

Find the 9th term of the geometric sequence 8,32,128,

Answers

[tex]\text{First term,}~ a = 8\\\\\text{Common ratio,}~ r= \dfrac{32}8 = 4\\\\\text{nth term} = ar^{n-1} \\\\\text{9th term} = 8\cdot 4^{9-1}\\\\\\~~~~~~~~~~~~~=8 \cdot 4^8\\\\\\~~~~~~~~~~~~~=524288\\\\\text{The 9th of the geometric sequence is 525288.}[/tex]

These equations represent the number of bacteria in four different dishes as a function of time, t, in days. Which equation represents the population with the greatest growth factor (also called common factor)?

SOMEONE ANSWER THIS ANS YOU’LL EARN FREE EASY POINTS FOR GIVING ME THE RIGHT ANSWER!!

Answers

The growth factor:

⇒ is the base in the exponent:

⇒ the larger it is ⇒ the greater the growth factor is!

Let's Analyze our choices:

c(t)'s growth factor: 5/2a(t)'s growth factor: 5/6d(t)'s growth factor: 3b(t)'s growth factor: 1/50

The greatest growth factor is 3

Answer: d(t)

Hope that helps!

Point G is on line segment FH. Given FG = 10 and GH =
10 and GH = 5, determine the
length FH.

Answers

Answer:

FH = 15

Step-by-step explanation:

G is lying between the point F & H on the line FH.

So, the distance of FH will be given by the sum of distance of FG and GH.

FH = FG + GH

= 10 + 5

= 15

5/8 multiple by 4/10

Answers

Answer:

1/4

Step-by-step explanation:

[tex]\frac{5}{8}[/tex]x[tex]\frac{4}{10}[/tex]

multiply the numerators and denominators

[tex]\frac{20}{80}[/tex]

simplify

cancel the zeros and get 2/8

then simplify to 1/4

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to multiply 5/8 times 4/10.

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

How do we multiply fractions? See below! ^-^

///\\\\///\\\\////\\\\///\\\///\\\///\\\////\\\///\\\///\\\///\\\//\\\\////\\\\////\\\\///\\\\///\\\///\\\//\\

Multiplying fractions

Multiply the numerator of one fraction times the numerator of the other fraction:

5×4=20

Same with the denominator:

8×10=80

Put them together:

[tex]\pmb{\cfrac{20}{80}}[/tex]

Divide the numerator and denominator by 20:

[tex]\pmb{\cfrac{1}{4}}[/tex]

Hope it helps you out! :D

Ask in comments if any queries arise.

#StudyWithBrainly

~Just a smiley person helping fellow students :)

[tex]\bf{\overline{\underline{\overline{\underline{Maribel\:Peri}}}}[/tex]

Opinions about a current event issue are recorded through responses given on a website. Opinions gathered in this fashion are an example of a ______________.
A. random sample
B. stratified random sample
C. self-selecting sample
D. systematic sample

Answers

Answer:

this is one of systematic sample and correct option is d

círculo de diámetro de 9 cm calcular radio perímetro y area doy corona

Answers

Answer:

Radio
r=4.5cm

Area
63.62cm2

Perímetro
C≈28.27cm

name the marked angle two different ways

Answers

tbh I have no Idea ask your mother

find the length of the third side round to the nearest tenth if needed . 24 10

Answers

Answer:

the length of the third side is 26

Step-by-step explanation:

By Pythagoras theorem

AC² = AB² + BC²

AC² = 10² + 24²

AC² = 100 + 576

AC² = 676

AC = √676

AC = 26

NEED HELP
(8.02-8.05)

Solve the systems of equations below using the method indicated in each part of the table. Be sure to show ALL your work for each method in order to get full points! (15 points)

Answers

The solutions to the systems of equations are:

1. (2, 3) (see attachment below). [one solution]

2. no solution

3. (3, 13) [one solution]

Solution to a System of Equations?

The solution to a system of equations is the x-value and y-value that will make both equations true. It can be found either using a graph, by elimination method, or substitution method as explained below.

1. Using graph to solve y = 2x - 1 and y = 4x - 5:

The solution is the point where both lines intersect which is: (2, 3) (see attachment below). [one solution]

2. Solving using substitution method:

x = -5y + 4 ---> eqn. 1

3x + 15y = -1 ---> eqn. 2

Substitute x = -5y + 4 into eqn. 2

3(-5y + 4) + 15y = -1

-15y + 12 + 15y = -1

-15y + 15y = -1 - 12

0 = -13 (this shows that there is no solution)

3. Using elimination method:

14x = 2y + 16 ---> eqn. 1

5x = y + 2 ---> eqn. 2

1(14x = 2y + 16)

2(5x = y + 2)

14x = 2y + 16 ----> eqn. 3

10x = 2y + 4 -----> eqn. 4

Subtract

4x = 12

x = 12/4

x = 3

Substitute x = 3 into eqn. 2

5(3) = y + 2

15 = y + 2

15 - 2 = y

13 = y

y = 13

The solution is: (3, 13).

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What do you think are the biggest advantages & disadvantages regarding the kind of technology we have access to in the early 21st century?

Answers

The advantages and disadvantages of the kind of technology we have access to in the early 21st century include:

Advantages:

The improvement of productivity.

Better and easier communication between people.

Disadvantages:

Can be bad for the environment.

Technology might be able to replace humans in jobs.

What is technology?

Technology is the result of accumulated knowledge and the application of skills, and processes used in industrial production and scientific research.

Technology is embedded in the operation of all machines for the intended purpose of an organization.

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To verify the associative property of addition, begin
by finding the sum of the polynomials:
(3x + 4) + ((5x²-1) + (2x + 6))
x² +
X +
DONE

Answers

The sum of the given polynomial is 5x²- 5x +9

Sum of polynomial

Polynomials are expressions with a degree of 3 and above. Given the equation shown;

(3x + 4) + ((5x²-1) + (2x + 6))

Expand

(3x + 4) + ((5x²-1) + (2x + 6))

3x + 4 + 5x²-1 + 2x + 6

Collect the like terms

5x² + 5x + 4 - 1 + 6

5x²- 5x +9

Hence the sum of the given polynomial is 5x²- 5x +9

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Does the equation xy + 6y = 9 define y as a function of x?
O Yes
O No

Answers

Answer:

no. a function doesnt contain an = sign

Step-by-step explanation:

Answer:

Yes, it is a function.

Explanation:

xy + 6y = 9

y(x + 6) = 9

y = 9/(x + 6)

It is a inverse variation function.

Where equation: xy = k ["k" is constant]

Each value of x corresponds to a single value of y.

Simplify the expression (7 + 9i)(8 - 10i)

Answers

The simplified expression of (7 + 9i)(8 - 10i) is 146 + 2i

How to simplify the expression?

The expression is given as:

(7 + 9i)(8 - 10i)

Expand the bracket

7 * 8 + 9i * 8 -7 * 10i - 9i * 10i

Evaluate the products

56 + 72i -70i - 90(i²)

Evaluate the difference

56 + 2i - 90(i²)

In complex numbers;

i² = -1

So, we have:

56 + 2i - 90(-1)

Evaluate

56 + 2i + 90

Add the like terms

146 + 2i

Hence, the simplified expression of (7 + 9i)(8 - 10i) is 146 + 2i

Answers

Answer:

1) 600cm^3 2) 10 glasses

Step-by-step explanation:

x = total amount in ml

(3/10)x = 180ml (MILK)

x = 600ml

(2/10)600 = 120ml (TIA MARIA)

(1/2)600 = 300ml (VODKA)

1) 600cm^3

2) 600ml : 60ml = 10 (GLASSES)

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