1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Natali [406]
3 years ago
8

How much will you spend on an investment if you want to receive $7,000 at an annual rate of 6% compounded weekly in 4 years?

Mathematics
1 answer:
s344n2d4d5 [400]3 years ago
3 0

Answer:

The investment required is: $5687

Step-by-step explanation:

Future Amount A= $7000

Rate r = 6% =0.06

Time t = 4

Compounded Weekly = n= 52

We need to find Principal Amount P

The formula used is: A=P(1+\frac{r}{n})^{n*t}

Putting values and finding P

A=P(1+\frac{r}{n})^{n*t}\\7000=P(1+\frac{0.06}{52})^{4*52}\\7000=P(1.001)^{208}\\7000=P(1.231)\\P=\frac{7000}{1.231}  \\P=5687

So, The investment required is: $5687

You might be interested in
Find the general solution of the given higher-order differential equation. d3u dt3 + d2u dt2 − 2u = 0
STALIN [3.7K]

\dfrac{\mathrm d^3u}{\mathrm dt^3}+\dfrac{\mathrm d^2u}{\mathrm dt^2}-2u=0

This ODE has characteristic equation

r^3+r^2-2=(r^3-r)+(r^2+r-2)=r(r^2-1)+(r+2)(r-1)

=(r(r+1)+(r+2))(r-1)=(r^2+2r+2)(r-1)=0

which has roots at r=1,-1\pm i. Then the characteristic solution to the ODE is

u(t)=C_1e^t+C_2e^{(-1+i)t}+C_3e^{(-1-i)t}

\implies\boxed{u(t)=C_1e^t+C_2e^{-t}\cos t+C_3e^{-t}\sin t}

6 0
3 years ago
Part ion even know of the hardest test
ladessa [460]

Given:

The equation of a line is:

y=-\dfrac{5}{7}x+2

A line passes through the point (-5,-3) and perpendicular to the given line.

To find:

The equation of the line.

Solution:

Slope intercept form of a line is:

y=mx+b                 ...(i)

Where, m is the slope and b is the y-intercept.

We have,

y=-\dfrac{5}{7}x+2          ...(ii)

On comparing (i) and (ii), we get

m=-\dfrac{5}{7}

We know that the product of slopes of two perpendicular lines is always -1.

m_1\times m_2=-1

-\dfrac{5}{7}\times m_2=-1

m_2=\dfrac{7}{5}

Slope of the required line is \dfrac{7}{5} and it passes through the point (-5,-3). So, the equation of the line is:

y-y_1=m_2(x-x_1)

y-(-3)=\dfrac{7}{5}(x-(-5))

y+3=\dfrac{7}{5}(x+5)

Using distributive property, we get

y+3=\dfrac{7}{5}(x)+\dfrac{7}{5}(5)

y+3=\dfrac{7}{5}x+7

y=\dfrac{7}{5}x+7-3

y=\dfrac{7}{5}x+4

Therefore, the equation of the line is y=\dfrac{7}{5}x+4. Hence, option A is correct.

4 0
3 years ago
Gaming a video-game designer is using the expression 6n3 in a program to determine points earned, where n is the game level. sim
charle [14.2K]

Gaming a video-game designer is using the expression 6n3 in a program to determine points earned, where n is the game level.

Given expression is 6n^3. the given expression is for the nth level.

To simplify the expression for the  n^2 level, we plug in n^2  in the place of 'n' in the given expression

6n^3

6(n^2)^3 (multiply the exponents)

6n^6


5 0
3 years ago
Read 2 more answers
I’d appreciate help ASAP please and thank you!
White raven [17]
<h3>Answer:  Choice C) 40 </h3>

==========================================================

Work Shown:

Plug in x = 0

g(x) = 3^{2x}\\\\g(0) = 3^{2*0}\\\\g(0) = 3^{0}\\\\g(0) = 1\\\\

This indicates that (0,1) is on the curve. This is the y intercept.

Do the same for x = 2

g(x) = 3^{2x}\\\\g(2) = 3^{2*2}\\\\g(2) = 3^{4}\\\\g(2) = 81\\\\

So we know that (2,81) is another point on this curve.

We need to find the slope of the line through (0,1) and (2,81) to get the slope of the secant line we want.

m = \text{slope}\\\\m = \frac{\text{rise}}{\text{run}}\\\\m = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{y_2-y_1}{x_2-x_1}\\\\m = \frac{g(2)-g(0)}{2-0}\\\\m = \frac{81-1}{2-0}\\\\m = \frac{80}{2}\\\\m = 40\\\\

The slope of the line through (0,1) and (2,81) is m = 40. This value of m is exactly the slope of the secant line your teacher is asking for. This is why the answer is choice C.

5 0
2 years ago
Coefficiants of (2x+y)^4​
sattari [20]

By the binomial theorem,

(2x+y)^4=\displaystyle\sum_{k=0}^4\binom 4k(2x)^{4-k}y^k=\sum_{k=0}^4\binom 4k2^{4-k}x^{4-k}y^k

where

\dbinom nk=\dfrac{n!}{k!(n-k)!}

Then the coefficients of the x^{4-k}y^k terms in the expansion are, in order from k=0 to k=4,

\dbinom 402^{4-0}=1\cdot2^4=16

\dbinom412^{4-1}=4\cdot2^3=32

\dbinom422^{4-2}=6\cdot2^2=24

\dbinom432^{4-3}=4\cdot2^1=8

\dbinom442^{4-4}=1\cdot2^0=1

3 0
3 years ago
Other questions:
  • *PLEASE ANSWER* (: Find the measure of angle A.
    6·2 answers
  • The list of digits below is from a random number generator using technology. Use the list of numbers to obtain a simple random s
    6·1 answer
  • The Rodriquez family drove 115 miles on 5 gallons of gasoline. Which equation can be used to find how far they can travel on a f
    13·2 answers
  • Which expression is equivalent to 5x + 4 - x - 2<br> a. 4x + 2<br> b. 4 + 4x<br> c. 4x<br> d. 4x + 6
    6·2 answers
  • How can models help you rename a mixed number as an improper fraction of an improper fraction as a mixed mixed number?
    7·1 answer
  • Find the derivative of f(x) = 5 divided by x at x = -1.
    14·2 answers
  • What is the midpoint of (-2,-5) and (-6,3)? What quadrant is it in?
    14·1 answer
  • The Staten Island Skating Pavilion charges a $5 entrance fee and an hourly rate for for ice skating. The total cost for ice skat
    9·1 answer
  • Which is the solution to the equation 2.6 a + 18.4 = 28.8? Round to the nearest tenth if necessary.
    5·2 answers
  • After a heavy snowfall, Joe and Karin made an igloo. The dome of the igloo is in the shape of a parabola and the height of the i
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!