Will give 100 pointsss!!
Find the time required for the
amount to double. (Approximate the result to two decimal places.)
Answers
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 = 0.0570Substitute 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
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
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
HOPE IT HELPED
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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Does the following statement refer to a growth or fixed mindset? "I dont know how to do this yet."
Answers
growth because the statement is showing potential for improvement with a “yet” word
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
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
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.
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
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!!
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 )
Please help I’ll make you Brainiest (please no link people)
Answers
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.
========================================================
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.
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
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:
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.
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
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:
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
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.
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.
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
My number 4752512944
Answers
Answer:
no thanks for your number
Step-by-step explanation:
Have a great day
HELPPPPPP!!! pls pls
Answers
Answer:
12 inches
Step-by-step explanation:
hope this helps
Answer:
720
Step-by-step explanation:
20 yards = 720 inches
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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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.
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
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
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!
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
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
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
2a + 3b = 5
b= a - 5
Answers
Answer:
I'm not sure but I thing the answer is 10
Step-by-step explanation: