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inysia [295]
3 years ago
13

Mackenzie put $6,000.00 in a retirement account that offers 11% interest compounded annually. She makes no additional deposits o

r withdrawals. How much interest will she have earned at the end of 6 years? Make sure you round to the nearest hundreth!
Mathematics
1 answer:
Veronika [31]3 years ago
8 0

Answer:

$39,960

Step-by-step explanation:

11% of 6000

= 11/100 × 6000

=$660

Year 1=$6,660.00

Year 6= $6,660.00 × 6 years

=$39, 960.00

You might be interested in
A light bulb is designed by revolving the graph of:
nadya68 [22]

Answer:

\displaystyle 0.251327 \ in. \ of \ glass

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

<u>Algebra I</u>

  • Terms/Coefficients
  • Expand by FOIL (First Outside Inside Last)
  • Factoring

<u>Calculus</u>

Differentiation

Derivative Notation

Basic Power Rule:

  • f(x) = cxⁿ
  • f’(x) = c·nxⁿ⁻¹

Integration

  • Integration Property: \displaystyle \int\limits^a_b {cf(x)} \, dx = c \int\limits^a_b {f(x)} \, dx
  • Fundamental Theorem of Calculus: \displaystyle \int\limits^a_b {f(x)} \, dx = F(b) - F(a)
  • Area between Two Curves
  • Volumes of Revolution
  • Arc Length Formula: \displaystyle AL = \int\limits^a_b {\sqrt{1+ [f'(x)]^2}} \, dx
  • Surface Area Formula: \displaystyle SA = 2\pi \int\limits^a_b {f(x) \sqrt{1+ [f'(x)]^2}} \, dx

Step-by-step explanation:

<u>Step 1: Define</u>

\displaystyle y = \frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}\\Interval: [0, \frac{1}{3}]

<u>Step 2: Differentiate</u>

  1. Basic Power Rule:                    \displaystyle y' = \frac{1}{2} \cdot \frac{1}{3}x^{\frac{1}{2} - 1} - \frac{3}{2} \cdot x^{\frac{3}{2} - 1}
  2. [Derivative] Simplify:                \displaystyle y' = \frac{1}{6}x^{\frac{-1}{2}} - \frac{3}{2}x^{\frac{1}{2}}
  3. [Derivative] Simplify:                \displaystyle y' = \frac{1}{6\sqrt{x}} - \frac{3\sqrt{x}}{2}}

<u>Step 3: Integrate Pt. 1</u>

  1. Substitute [Surface Area]:                                                                             \displaystyle SA = 2\pi \int\limits^{\frac{1}{3}}_0 {(\frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}) \sqrt{1+ [\frac{1}{6\sqrt{x}} - \frac{3\sqrt{x}}{2}}]^2}} \, dx
  2. [Integral - √Radical] Expand/Add:                                                               \displaystyle SA = 2\pi \int\limits^{\frac{1}{3}}_0 {(\frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}) \sqrt{\frac{81x^2+18x+1}{36x}} \, dx
  3. [Integral - √Radical] Factor:                                                                         \displaystyle SA = 2\pi \int\limits^{\frac{1}{3}}_0 {(\frac{1}{3}x^{\frac{1}{2}} - x^{\frac{3}{2}}) \sqrt{\frac{(9x + 1)^2}{36x}} \, dx
  4. [Integral - Simplify]:                                                                                       \displaystyle SA = 2\pi \int\limits^{\frac{1}{3}}_0 {-\frac{|9x + 1|(3x - 1)}{18}} \, dx
  5. [Integral] Integration Property:                                                                     \displaystyle SA = \frac{- \pi}{9} \int\limits^{\frac{1}{3}}_0 {|9x + 1|(3x - 1)} \, dx

<u>Step 4: Integrate Pt. 2</u>

  1. [Integral] Define:                                                                                             \displaystyle \int {|9x + 1|(3x - 1)} \, dx
  2. [Integral] Assumption of Positive/Correction Factors:                                 \displaystyle \frac{9x + 1}{|9x + 1|} \int {(9x + 1)(3x - 1)} \, dx
  3. [Integral] Expand - FOIL:                                                                                 \displaystyle \frac{9x + 1}{|9x + 1|} \int {27x^2 - 6x - 1} \, dx
  4. [Integral] Integrate - Basic Power Rule:                                                         \displaystyle \frac{9x + 1}{|9x + 1|} (9x^3 - 3x^2 - x)
  5. [Expression] Multiply:                                                                                      \displaystyle \frac{(9x + 1)(9x^3 - 3x^2 - x)}{|9x + 1|}

<u>Step 5: Integrate Pt. 3</u>

  1. [Integral] Substitute/Integral - FTC:                                                              \displaystyle SA = \frac{- \pi}{9} (\frac{(9x + 1)(9x^3 - 3x^2 - x)}{|9x + 1|})|\limits_{0}^{\frac{1}{3}}
  2. [Integrate] Evaluate FTC:                                                                                \displaystyle SA = \frac{- \pi}{9} (\frac{-1}{3})
  3. [Expression] Multiply:                                                                                     \displaystyle SA = \frac{\pi}{27} \ ft^2

<em>It is in ft² because it is given that our axis are in ft.</em>

<u>Step 6: Find Amount of Glass</u>

<em>Convert ft² to in² and multiply by 0.015 in (given) to find amount of glass.</em>

  1. Convert ft² to in²:                    \displaystyle \frac{\pi}{27} \ ft^2 \ \div 144 \ in^2/ft^2 = \frac{16 \pi}{3} \ in^2
  2. Multiply:                                   \displaystyle \frac{16 \pi}{3} \ in^2 \cdot 0.015 \ in = 0.251327 \ in. \ of \ glass

And we have our final answer! Hope this helped on your Calc BC journey!

5 0
3 years ago
the population of a colony grows from 250 in the year 2000 to 400 in the year 2004. what is the average rate of change of popula
Ilia_Sergeevich [38]

Given:

Population of a colony in 2000 = 250

Population of a colony in 2004 = 400

To find:

The average rate of change.

Solution:

Let y be the population of the colony at x year.

The population of a colony grows from 250 in the year 2000 to 400 in the year 2004.  So, the two points are (2000,250) and (2004,400).

Formula for slope or average rate of change is

m=\dfrac{y_2-y_1}{x_2-x_1}

m=\dfrac{400-250}{2004-2000}

m=\dfrac{150}{4}

m=37.5

Therefore, the  average rate of change of population is 37.5.

3 0
3 years ago
Y 9 &lt;12x + 141 true?
lesya692 [45]
Yes it is true if you need me to explain lmk
4 0
3 years ago
Please help! Correct answer only!
melisa1 [442]

Answer:

$7.50

Step-by-step explanation:

Since there is a 50% chance that the card is odd, the expected payoffs would be $15 * 50%=0.5*15=7.5. Hope this helps!

5 0
3 years ago
Find the area of the composite figure.
MArishka [77]

2 × 6 = 12

12 ÷ 2 = 6

2 × 14 = 28

10 × 20 = 200

6 + 28 + 200 = 234

7 0
3 years ago
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