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Vesna [10]
3 years ago
10

Morticia took the money she made working this summer, $3125.00, and placed it in her bank account. Her account makes 6% interest

, and she plans to leave it there for 10 years where it will be compounded annually. How much will she have at the end of 10 years? How do you know?
Mathematics
1 answer:
oee [108]3 years ago
8 0

Answer:

$5,596.40

Step-by-step explanation:

Lets use the compound interest formula to solve:

A=P(1+\frac{r}{n} )^{nt}

<em>P = initial balance</em>

<em>r = interest rate (decimal)</em>

<em>n = number of times compounded annually</em>

<em>t = time</em>

First, change 6% into a decimal:

6% -> \frac{6}{100} -> 0.06

Next, plug the values into the equation:

A=3,125(1+\frac{0.06}{1})^{1(10)}

A=5,596.40

After 10 years, Morticia will have $5,596.40. We know this because by using the compound interest formula and plugging in all the values, you will get the correct answer.

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Find the volume of the figure. Use 3.14 for Pi​
nydimaria [60]

Answer:

The answer would be 17

Step-by-step explanation:

The answer would be 17 because if you add 12 plus 5 That would be your answer

6 0
3 years ago
Need help with AP CAL
anzhelika [568]

Answer: Choice C

\displaystyle \frac{1}{2}\left(1 - \frac{1}{e^2}\right)

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

Explanation:

The graph is shown below. The base of the 3D solid is the blue region. It spans from x = 0 to x = 1. It's also above the x axis, and below the curve y = e^{-x}

Think of the blue region as the floor of this weirdly shaped 3D room.

We're told that the cross sections are perpendicular to the x axis and each cross section is a square. The side length of each square is e^{-x} where 0 < x < 1

Let's compute the area of each general cross section.

\text{area} = (\text{side})^2\\\\\text{area} = (e^{-x})^2\\\\\text{area} = e^{-2x}\\\\

We'll be integrating infinitely many of these infinitely thin square slabs to find the volume of the 3D shape. Think of it like stacking concrete blocks together, except the blocks are side by side (instead of on top of each other). Or you can think of it like a row of square books of varying sizes. The books are very very thin.

This is what we want to compute

\displaystyle \int_{0}^{1}e^{-2x}dx\\\\

Apply a u-substitution

u = -2x

du/dx = -2

du = -2dx

dx = du/(-2)

dx = -0.5du

Also, don't forget to change the limits of integration

  • If x = 0, then u = -2x = -2(0) = 0
  • If x = 1, then u = -2x = -2(1) = -2

This means,

\displaystyle \int_{0}^{1}e^{-2x}dx = \int_{0}^{-2}e^{u}(-0.5du) = 0.5\int_{-2}^{0}e^{u}du\\\\\\

I used the rule that \displaystyle \int_{a}^{b}f(x)dx = -\int_{b}^{a}f(x)dx which says swapping the limits of integration will have us swap the sign out front.

--------

Furthermore,

\displaystyle 0.5\int_{-2}^{0}e^{u}du = \frac{1}{2}\left[e^u+C\right]_{-2}^{0}\\\\\\= \frac{1}{2}\left[(e^0+C)-(e^{-2}+C)\right]\\\\\\= \frac{1}{2}\left[1 - \frac{1}{e^2}\right]

In short,

\displaystyle \int_{0}^{1}e^{-2x}dx = \frac{1}{2}\left[1 - \frac{1}{e^2}\right]

This points us to choice C as the final answer.

5 0
2 years ago
HELP order to find the percentage of households in a town that own more than one vehicle, a survey asks 1000 randomly selected d
alekssr [168]
Answer is D jjkkkkmmm
5 0
3 years ago
HELP!!!!!!!!!!!!!
Misha Larkins [42]

Answer:

P'(7,0)Q'(2,1) R'(12,-6)

Step-by-step explanation:

P(3,5)------>P'(3+4,5-5)

P'(7,0)

Q(-2,6)----->Q'(-2+4,6-5)

Q'(2,1)

R(8,-1)------>R'(8+4,-1-5)

R'(12,-6)

8 0
3 years ago
Mr Turner buys 12 pencils for $0.57 each . He pays with a $10 bill how much change would he revive
Delvig [45]
12(0.57)= 6.84

10-6.84= 3.16

Mr. Turner’s change is $3.16.


Hope this helps!
6 0
3 years ago
Read 2 more answers
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