Will give 100 pointsss!!
Find the time required for the
amount to double. (Approximate the result to two decimal places.)

Will Give 100 Pointsss!!Find The Time Required For Theamount To Double. (Approximate The Result To Two

Answers

Answer 1

Answer:

12.16 years

Step-by-step explanation:

Continuous Compounding Formula

[tex]\large \text{$ \sf A=Pe^{rt} $}[/tex]

where:

A = Final amountP = Principal amounte = Euler's number (constant)r = annual interest rate (in decimal form)t = time (in years)

Given:

A = $5,000 (double the initial investment)P = $2,500r = 0.0570

Substitute the given values into the formula and solve for t:

[tex]\sf \implies 5000=2500e^{0.0570t}[/tex]

[tex]\sf \implies \dfrac{5000}{2500}=\dfrac{2500e^{0.0570t}}{2500}[/tex]

[tex]\sf \implies 2=e^{0.0570t}[/tex]

Take natural logs of both sides:

[tex]\sf \implies \ln 2=\ln e^{0.0570t}[/tex]

[tex]\textsf{Apply the power law}: \quad \ln x^n=n \ln x[/tex]

[tex]\sf \implies \ln 2=0.0570t\ln e[/tex]

As ln e = 1:

[tex]\sf \implies \ln 2=0.0570t[/tex]

[tex]\sf \implies \dfrac{\ln 2}{0.0570}=\dfrac{0.0570t}{0.0570}[/tex]

[tex]\sf \implies t=\dfrac{ \ln 2}{0.0570}[/tex]

[tex]\implies \sf t=12.16047685...[/tex]

Therefore, the time required for the amount to double is 12.16 years (2 d.p.).

Learn more about continuous compounding interest here:

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Related Questions

Please help me with this one??

Answers

Answer:

Y =-25x +225

Step-by-step explanation:

First you can count the gradient first. Use then you can count y intercept

Question 16 of 20
To the nearest hundredth, what is the circumference of a circle with a radius
of 7 units?
A. 43.98 units
B. 21.99 units
C. 35.75 units
D. 153.94 units

Answers

Answer:

43.98

Step-by-step explanation:

The circumference of a circle with a radius of 7 units is approximately 43.98 units, which corresponds to option A.

What is the Circumference of a circle?

The Circumference of a circle is defined as the product of the diameter of the circle and pi.

Given that the radius of the circle is 7 units, we can substitute this value into the formula:

To find the circumference of a circle, we can use the formula C = 2πr, where C represents the circumference and r represents the radius.

C = 2π(7) = 14π

Use the approximation π ≈ 3.14:

C ≈ 14(3.14) = 43.96

Rounding this value to the nearest hundredth, we get approximately 43.98 units.

Therefore, the circumference of a circle with a radius of 7 units is approximately 43.98 units.

Learn more about the Circumference of the circle here:

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solve this system of equations
y=x-4
y=6x-10

Answers

Step-by-step explanation:

put 6x-10 in y=x-4

so

y = (6x-10) - 4

y = 6x-14

point form: (6/5, -14/5)

equation form: x=6/5 y= -14/5

to solve, set the equations equal to each other so it’s x-4=6x-10 which gives you x

then plug x into one of the equations so y=6/5-4 which gives you y=-14/5

hope this helps!

Fine the area of a triangle with :base=7ft and height =5ft

Answers

Answer:

Step-by-step explanation:

7 x 5 = 35

35/2 = 17.5

[tex]17.5ft^{2}[/tex]

The area of the given triangle is 17.5 ft²

What is area?

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

Given a triangle with base=7ft and height =5ft

We know that area of a triangle = 1/2 × base × height

Therefore, the area of a triangle = 1/2 (7)(5) = 17.5 ft²

Hence, the area of the given triangle is 17.5 ft²

For more references on area, click;

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find all the possible of x for which of the below is true:

[tex] \frac{2x}{x + 3} + \frac{3}{x - 3} = \frac{8}{x^{2} - 9 } [/tex]

Answers

Answer:

x = [tex]\frac{1}{2}[/tex] , x = 1

Step-by-step explanation:

Given

[tex]\frac{2x}{x+3}[/tex] + [tex]\frac{3}{x-3}[/tex] = [tex]\frac{8}{x^2-9}[/tex] ← denominator is a difference of squares

[tex]\frac{2x}{x+3}[/tex] + [tex]\frac{3}{x-3}[/tex] = [tex]\frac{8}{(x+3)(x-3)}[/tex]

Multiply through by (x + 3)(x - 3) to clear the fractions

2x(x - 3) + 3(x + 3) = 8 ← distribute left side and simplify

2x² - 6x + 3x + 9 = 8

2x² - 3x + 9 = 8 ( subtract 8 from both sides )

2x² - 3x + 1 = 0 ← in standard form

(2x - 1)(x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

2x - 1 = 0 ⇒ 2x = 1 ⇒ x = [tex]\frac{1}{2}[/tex]

x - 1 = 0 ⇒ x = 1

During which time interval is the squirrel traveling at the fastest speed?


1–2 min

2–3 min

5–6 min

8–9 min

Answers

I think that the answer is 8-9min

Which linear function has a y-intercept of -5?

Answers

Answer: Upper right corner (northeast corner)

x-3y = 15

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

Explanation:

The y intercept always occurs when x = 0.

If we plug x = 0 into 2x+y = -10 (northwest corner), then we solve for y to get...

2x+y = -10

2(0)+y = -10

0+y = -10

y = -10

We see that the y intercept here is -10, but we want -5 instead. So we can rule this out.

In the northeast corner, plugging x = 0 leads to,

x-3y = 15

0-3y = 15

-3y = 15

y = 15/(-3)

y = -5

We get the correct y intercept we're after. So we can stop here.

If you plugged x = 0 into the equation of the southwest corner, you'll get y =  5 which is fairly close but not quite what we want. The southeast corner equation leads to a y intercept of y = 5 as well.

Answer:

x - 3y = 15

Step-by-step explanation:

x - 3y = 15

-3y = -x + 15

y = 1/3x - 5

-5 is the y-intercept.

Ted left at 8:00 a.m to walk to the dog park. It took him 30 minutes to get there.

what time did ted get to the dog park?

Answers

Answer:

8:30 am

Step-by-step explanation:

Answer:

8:30 a.m

Step-by-step explanation:

8:00

+ 30

_____

8:30 a.m

HELPPPPPP!!! pls pls

Answers

Answer:

12 inches

Step-by-step explanation:

hope this helps

Answer:

720

Step-by-step explanation:

20 yards = 720 inches

Fast problem! Please help

Answers

Answer:

D. 122 degrees

Step-by-step explanation:

The angle next to the 133 degree angle is equal to 47 degrees because they are linear pairs. (Linear pairs will always add up to 180 degrees).

The angle below the 75 degree angle is equal to 75 degrees because they are vertical angles. (Vertical angles will always be equal to each other).

Then by using the Triangle Exterior Angle Theorem. Your missing angle is equal to 47 degrees + 75 degrees = 122 degrees.

5 pleaseeee help me out ill mark you brainlist
I'm on the verge of failing smh

Answers

Answer:

D) y = -4/3x + 5

Step-by-step explanation:

Can be checked with a calculator or by replacing the variables into the equation.

My number 4752512944

Answers

Answer:

no thanks for your number

Step-by-step explanation:

Have a great day

write three rational numbers between 1. -1 and 1 2. -4 and-3​

Answers

Answer:

1. -1/2 1/2 1/4

2. -3.5 -3.6 -3.7

3. -1/10 -1/11 -1/12

hope this helps

have a good day :)

Step-by-step explanation:

NEED HELP RIGHT NOW PLZ!!!!!!!!!!!!Two candidates, Joe Smith and Maria Jones run for office in a local election. In all, 12,402 votes are cast and the ratio of votes for Joe Smith to Maria Jones was 4:5. How many votes did they each get?

Answers

Answer:

Joe 5512

Maria 6890

Step-by-step explanation:

Joe  : Maria  : total

4           5         9

We have a total of 12402

Divide this by 9

12402/9 =1378

Multiply each number by 1378

Joe  :          Maria             : total

4*1378           5*1378         9*1378

5512                6890              12402

What number is 48 out of 250%

Answers

Answer:

120

Step-by-step explanation:

reduce the fraction from

[tex]48 \times \frac{250}{100 } [/tex]

to

[tex]48 \times \frac{5}{2} [/tex]

then multiply and you get 24 × 5 which is 120

Rommel has 3 kilograms of potatoes and 4 kilogramsof onions. He plans to use 1.5 kilograms of potatoes and 880 grams of onions fora recipe. How many total kilograms of the produce will not be used?

Answers

Answer:

4.62 KG

Step-by-step explanation:

1000 grams = 1kg

3kg = 3000g

4 kg = 4000g

1.5 = 1500g

left over potatoes = 3000 - 1500 = 1500 g or 1.5kg

left over onions = 4000 - 880 = 3120 = 3.12kg

total kilos not used = 1.5 + 3.12 = 4.62

Please help I’ll make you Brainiest (please no link people)

Answers

the answer is c, I could explain if you would like.

Please help!!!!!!
if

Answers

Answer:

if what

Step-by-step explanation:

if we dare or if we must

Answer:

If what?

Step-by-step explanokation:

So, I don't understand what the question is here. Please elaborate.

A mechanic began pouring a full can of motor oil into a funnel. The can of motor oil has a radius of 2.5 inches and a
height of 6 inches. The funnel has a radius of 3 inches and a height of 5.5 inches. If the hole on the bottom of the
funnel is plugged so that the funnel is not able to drain, what percentage of the oil would remain in the can after the
funnel is completely filled?

Answers

ANSWER =56%

HOPE IT HELPED

Does the following statement refer to a growth or fixed mindset? "I dont know how to do this yet."

Answers

GROWTH

growth because the statement is showing potential for improvement with a “yet” word
It’s a growth mindset because it’s says yet in the end. Hope this helped!

Help help legit answers only

Answers

Answer:

x ≈ 46.7°

Step-by-step explanation:

Using the sine ratio in the right triangle

sin x = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{OP}{NP}[/tex] = [tex]\frac{4}{5.5}[/tex] , then

x = [tex]sin^{-1}[/tex] ([tex]\frac{4}{5.5}[/tex] ) ≈ 46.7° ( to the nearest tenth )

Here’s the answer and explanation

2a + 3b = 5
b= a - 5

Answers

Answer:

I'm not sure but I thing the answer is 10

Step-by-step explanation:


Find the circumference of the given circle.
Use 3.14 as an approximation of Pi.

Answers

Answer:

Step-by-step explanation:

circumference=2*pie*r

=2*3.14*7

=43.96 in.

Answer:  43.96 inches (choice B)

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

Work Shown:

C = 2*pi*r

C = 2*3.14*7

C = 43.96 inches is the approximate circumference, aka the distance around the circle.

Use more decimal digits in pi to get a more accurate circumference.

A bag contains 3 yellow marbles and 6 blue marbles. You randomly select two marbles from the bag. What is the probability that both marbles are
yellow when you do not replace each marble before selecting the next marble? Write your answer as a decimal rounded to three decimal places.

Answers

1/12

explanation- the first draw the probability is 3/9 or 1/3 and the second draw would be either 2/8 or 3/8 depending on the first marble color. but the likely hood of two yellow marbles in a row would be 6/72 chances or 1/12.

A recipe for fruit punch is 3 parts orange juice to 2 parts apple juice. Jim mixes 180 ml of orange juice with 120 ml of apple juice.
Has Jim made the fruit punch correctly? Explain your answer.
PLEASE HELP ASAP

Answers

There you go. I explained in the picture hope it helps

Solve for x. Round to the nearest thousandth (0.001) if necessary.
11^x = 22

Answers

Answer:

x = 1.289

Step-by-step explanation:

11^x = 22

Take the log of both sides

xlog11 = log22

Divide both sides by log11

x = log22 / log11

Use calculator

x = 1.289

HALP TELLL ME HOW!!!!!!!!!!!!

Answers

Answer:

V=82944

Step-by-step explanation:

FORMULA (Im guessing u just wanted answer but if u want formula there u go.

V= 1/3(a^2h)

Answer:

[tex]576 ~cubic ~centimeters[/tex]

Step-by-step explanation:

[tex]B=144cm^2[/tex]

[tex]h=12cm[/tex]

[tex]V=1/3~B*h[/tex]

[tex]=1/3(144)(12)[/tex]

[tex]=576 cm[/tex]

--------------------

hope it helps...

have a great day!!

Simplify the following polynomial and write the answer in standard form

Answers

Answer:

D

Step-by-step explanation:

We have to added up the like therms (the therms with the same literal parts)

x^2 + 2x^2 = 3x^2

3x - 4x = -x

2 + 1 = 3

3x^2 - x + 3

Answer:

D

Step-by-step explanation:

Edge 2022

hey! pls help i’ll give brainliest

Answers

Answer:

landslide

Step-by-step explanation:

Answer:

I believe that the answer might be the second one

Volcanic Eruption

How many solutions does the system of equations below have?
y=3x+4
y+6x=3x

Answers

Answer:

x = -[tex]\frac{2}{3}[/tex]

y = 2

Step-by-step explanation:

The process of elimination is a method of solving a system of equations. One must first manipulate one of the equations such that one of the variables shared between the two equations has the inverse coefficient of the same variable in the other equation. Therefore, when one adds the equations, the variable cancels. One can solve for the variable using inverse operations, and then backsolve to find the value of the first variable.

When given the following system:

y = 3x + 4

y + 6x = 3x

Use inverse operations so that both equations are solve for one variable,

y = 3x + 4

y = -3x

Add the systems so that one of the variables (x) cancels, this process is called the process of elimination;

y = 3x + 4

y = -3x

_________

2y = 4

Inverse operations,

2y = 4

y = 2

Now backsolve, find the value of (x) by substituting the value of (y) into the equation:

y = -3x

2 = -3x

x = -[tex]\frac{2}{3}[/tex]

Answer: No solution.

Step-by-step explanation:

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