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3 years ago

If $3 000 000 is invested at 6 interest compounded continuously, how much will the investment be worth in 35 years?

1 answer:

3 0

Continuous compounding is computed using the product of interest rate and time as the power of e, the base of natural logarithms. That exponential is the multiplier of the initial amount.

... $3,000,000 × e^(.06×35) ≈ $24,498,509.74 . . . . matches choice A

You might be interested in

Resistors are labeled 100 Ω. In fact, the actual resistances are uniformly distributed on the interval (95, 103). Find the mean

Zinaida [17]

Answer:

$E[R]$ = 99 Ω

$\sigma_R$ = 2.3094 Ω

P(98<R<102) = 0.5696

Step-by-step explanation:

The mean resistance is the average of edge values of interval.

Hence,

The mean resistance, $E[R] = \frac{a+b}{2} = \frac{95+103}{2} = \frac{198}{2}$ = 99 Ω

To find the standard deviation of resistance, we need to find variance first.

$V(R) = \frac{(b-a)^2}{12} =\frac{(103-95)^2}{12} = 5.333$

Hence,

The standard deviation of resistance, $\sigma_R = \sqrt{V(R)} = \sqrt5.333$ = 2.3094 Ω

To calculate the probability that resistance is between 98 Ω and 102 Ω, we need to find Normal Distributions.

$z_1 = \frac{102-99}{2.3094} = 1.299$

$z_2 = \frac{98-99}{2.3094} = -0.433$

From the Z-table, P(98<R<102) = 0.9032 - 0.3336 = 0.5696

5 0

4 years ago

Can someone help me for this?

Ludmilka [50]

Answer:

500000N=2m

x. =6m

cross multiply, it'll be

6×50000÷2

=150,000N

8 0

2 years ago

The length of a rectangle is 3 yd more than twice the width, and the area of the rectangle is 54 yd?. Find the dimensions of the

s344n2d4d5 [400]

Answer:

The length of the rectangle is 37 yards, and the width of the rectangle is 17 yards.

Step-by-step explanation:

Given that the length of a rectangle is 3 yards more than twice the width, and the area of the rectangle is 54 yards, the following calculation must be performed to find the dimensions of the rectangle, knowing that the area of a rectangle arises from multiplying its base by its height:

2X + 3 + X = 54

3X + 3 = 54

3X = 54 - 3

X = 51/3

X = 17

(17 x 2) + 3 = 37

Therefore, the length of the rectangle is 37 yards, and the width of the rectangle is 17 yards.

4 0

3 years ago

Point A is at (-2,-7) and point B is at (7,4).<br> What is the midpoint of line segment AB?

Lyrx [107]

Use the midpoint formula and solve. work pictured below

4 0

3 years ago

15x-7=2+12x I need help with this

Amanda [17]

Answer:

$\huge{ \boxed{ \bold{ \tt{x = 3}}}}$

<h3>♁ Question : Solve for x</h3>

15x - 7 = 2 + 12x

<h3>♁ Step - by - step explanation</h3>

$\text{15x - 7 = 2 + 12x}$

Move 12x to L.H.S ( Left Hand Side ) and change it's sign

➛ $\sf{15x - 12x - 7 = 2}$

Move 7 to R.H.S ( Right Hand Side) and change it's sign

➛ $\sf{15x - 12x = 2 + 7}$

Subtract 12x from 15x

Remember that only coefficients of like terms can be added or subtracted.

➛ $\sf{3x = 2 + 7}$

Add the numbers : 2 and 7

➛ $\sf{3x = 9}$

Divide both sides by 3

➛ $\sf{ \frac{3x}{3} = \frac{9}{3}}$

➛ $\boxed{ \bold{ \sf{x = 3}}}$

The value of x is $\boxed{ \sf{3}}$

✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄

☄ Now, let's check whether the value of x is 3 or not!

<h3>☥ Verification :</h3>

$\sf{15x - 7 = 2 + 12x}$

$\dashrightarrow{ \sf{15 \times 3 - 7 = 2 + 12 \times 3}}$

$\dashrightarrow{ \sf{45 - 7 = 2 + 36}}$

$\dashrightarrow{ \sf{38 = 38}}$

L.H.S = R.H.S ( Hence , the value of x is 3 ).

✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄

<h3>✒ Rules for solving an equation :</h3>

If an equation contains fractions ,multiply each term by the L.C.M of denominators.
Remove the brackets , if any.
Collect the terms with the variable to the left hand side and constant terms to the right hand side by changing their sign ' + ' into ' - ' and ' - ' into ' + ' .
Simplify and get the single term on each side.
Divide each side by the coefficient of variable and then get the value of variable.

Hope I helped!

Have a wonderful time ! ツ

~TheAnimeGirl

5 0

3 years ago