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4 years ago

5

Ken started saving for retirement at age 35 with plans to retire at age 70. He invested an average of $600 per month in various

securities, with an average annual return of 5% adjusted for inflation. Assuming monthly compounding, how much has Kent saved at the start of retirement
A: $54,192.18
B: $825,655.45
C: $499,355.18
D: $681,655.46

2 answers:

Irina-Kira [14]4 years ago

8 0

The answer is C $499,355.18

VARVARA [1.3K]4 years ago

7 0

Answer:

<u>D - $681,655.46</u>

Step-by-step explanation:

Just took the test and found out the answer. The other person provided the wrong answer and explanation. What a idiot.

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John’s piggy bank contained 7 dimes and 3 quarters. He pulled out 1 coin without looking. Without replacing the first coin, John

yKpoI14uk [10]

Probability Trees - See linked image

A good visual method for this is a probability tree.

Each set of branches represents the probabilities of on coin being removed, the second set is out of 9 as the first coin is taken and not replaced.
Multiply along the lines to work out the probability of each of the combinations.

*Even though only 'Dime Dime' is needed, it is best to do all of them as this way you are able to get all marks in an exam; you can also add up all the final values as a check to see if you are right.

5 0

3 years ago

Jim sells used drones for 70% of the original manufacturer's purchase price of a new drone. Jim also sells new drones for 15% mo

adell [148]

The function for the amount saved if they purchase a used drone rather than a new drone from Jim's store is f(x) = 0.45x

He sells used drones at 70% of the price (x).

So, the selling price of a used drone is:

$\mathbf{Used = 70\% \times x}$

Express percentage as decimal

$\mathbf{Used = 0.7 \times x}$

$\mathbf{Used = 0.7x}$

Also, he sells new drones at 15% more of the price (x).

So, the selling price of a new drone is:

$\mathbf{New= (1 + 15\%) \times x}$

Express percentage as decimal

$\mathbf{New= (1 + 0.15) \times x}$

$\mathbf{New= 1.15 \times x}$

$\mathbf{New= 1.15x}$

The amount saved is the difference between the prices of the drones.

So, we have:

$\mathbf{Saved =New - Old}$

This gives

$\mathbf{Saved =1.15x- 0.7x}$

Subtract

$\mathbf{Saved =0.45x}$

Express as a function

$\mathbf{f(x) = 0.45x}$

Hence, the function for the amount saved is f(x) = 0.45x

Read more about proportions at:

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7 0

2 years ago

DESPERATE FOR EXPLANATION PLEASE HELP

Hitman42 [59]

This one is the Law of Sines again.

The Law of Sines relies on the standard labeling of triangle ABC with vertices A, B, and C and respective opposite sides of a, b and c. Then

$\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}$

Here we have A=150 degrees (opposite side a), b= 10 cm and B = 12 degrees. We seek a.

So we need the first equation of the Law of Sines:

$\dfrac{a}{\sin A} = \dfrac{b}{\sin B}$

$a = \dfrac{b \sin A }{\sin B}$

$a = \dfrac{10 \sin 150}{\sin 12} \approx 28.0$

7 0

3 years ago

nadya68 [22]

Answer:

C. Determine how many feet −55 feet is below zero feet.

D. Determine how far −55 is from zero on the number line

Step-by-step explanation:

Determine how many feet −55 feet is below zero feet.

This will give us the answer of 55feet , and the absolute value of -55 is 55.

0--55= 0+55 = 55

Determine how far −55 is from zero on the number line

This will also give me us 55 feet because the distance from 0 to -55 is 55

I.e. 0--55= 0+55 = 55

5 0

4 years ago

The displacement of a 500 g mass, undergoing simple harmonic motion, is defined by the function :

Valentin [98]

To solve this problem, we have to write out the simple harmonic motion equation and then use the respective formula to solve. The maximum kinetic energy, maximum potential energy and the maximum mechanical energy is equal to 7.56J.

<h3>Simple Harmonic Motion</h3>

The given equation of the simple harmonic motion is

$x = 3.5sin(\frac{\pi}{2t} + \frac{5\pi}{4})\\$

Data;

ω = π/2
k = 1.254N/m

Solving this

$\frac{dx}{dt} = \theta = -3.5 * \frac{\pi}{2} cos (\frac{\pi }{2}t + \frac{5\pi}{4})\\$

Let's calculate the maximum velocity.

$V_m = \frac{3.5\pi}{2}$

This is only possible when cos θ = -1

The maximum kinetic energy is

$K_m = \frac{1}{2}mv_m^2 = \frac{1}{2}* \frac{500}{1000} * (\frac{7\pi}{4} )^2\\K_m = 7.56J$

The maximum kinetic energy is 7.56J

The maximum potential energy can be calculated as

$\omega^2 = \frac{k}{m} \\k = \omega^2 m \\k = \frac{\pi^2}{4} * \frac{500}{1000}\\ k= 1.254 N/m$

Using the value of spring constant, we can find the maximum potential energy

$P.E = \frac{1}{2}kx^2\\P.E = \frac{1}{2} * 1.234 * 3.5^2\\P.E = 7.56J$

The maximum potential energy is 7.56J

The maximum mechanical energy is equal to the sum of maximum potential energy and the maximum kinetic energy.

$ME = P.E + K.E\\ME = 7.56J$

The reason ME is equal to 7.56J is because when x is at maximum, v = 0 and makes kinetic energy equal to zero.

ME = 7.56J

From the calculations above, the maximum kinetic energy, maximum potential energy and the maximum mechanical energy is equal to 7.56J.

Learn more on simple harmonic motion here;

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3 0

2 years ago