How many years will it take $2,000 to grow to $3,300 if it is invested at 4.75% compounded continuously?
Answer:
10.54263764
Step-by-step explanation:
[tex]3300=2000e^{.0475t}\\\\1.65=e^{.0475t}\\\ln(1.65)=.0475t\\.500775288=.0475t\\t=10.54263764[/tex]
Answer:
It will take about 10.5 years for the investment to reach $3,300.
Step-by-step explanation:
Continuous compound is given by:
[tex]\displaystyle A=Pe^{rt}[/tex]
Where P is the principal, e is Euler's number, r is the rate, and t is the time (in this case in years).
Since our principal is $2,000 at a rate of 4.75% or 0.0475, our equation is:
[tex]\displaystyle A=2000e^{0.0475t}[/tex]
We want to find the number of years it will take for our investment to reach $3,300. So, substitute 3300 for A and solve for t:
[tex]3300=2000e^{0.0475t}[/tex]
Divide both sides by 2000:
[tex]\displaystyle e^{0.0475t}=\frac{33}{20}[/tex]
We can take the natural log of both sides:
[tex]\displaystyle 0.0475t=\ln\left(\frac{33}{20}\right)[/tex]
Therefore:
[tex]\displaystyle t=\frac{1}{0.0475}\ln\left(\frac{33}{20}\right)\approx 10.54\text{ years}[/tex]
It will take about 10.5 years for the investment to reach $3,300.
Marcel and Floyd are playing games at an arcade. Marcel has $8.25 and is only playing $0.25 games. Floyd has $9.75 and is only playing $0.75 games. Jorge wants to find the number of games after which Marcel and Floyd will have the same amount of money remaining. Jorge’s work is shown below.
Answer:
3 games
Step-by-step explanation:
25. Kendra owns a toy store. She charges $8.00 for two puzzles and a piece of candy. She charges (1 poi
$4.50 for one puzzle and a piece of candy. How much does each puzzle cost?
O $3.50
O $4.50
O $1.00
$2.25
Given:
Kendra charges $8.00 for two puzzles and a piece of candy.
She charges $4.50 for one puzzle and a piece of candy.
To find:
The cost of each puzzle.
Solution:
Let x be the cost of a puzzle and y be the cost of piece of candy.
Kendra charges $8.00 for two puzzles and a piece of candy.
[tex]2x+y=8[/tex] ...(i)
She charges $4.50 for one puzzle and a piece of candy.
[tex]x+y=4.50[/tex] ...(ii)
Subtracting (ii) from (i), we get
[tex]2x+y-(x+y)=8-4.50[/tex]
[tex]2x+y-x-y=3.50[/tex]
[tex]x=3.50[/tex]
The cost of puzzle is $3.50. Therefore, the correct option is A.
PLEASE HELP ITS EASY BUT LIKE yh
Answer:
40 I told u
Step-by-step explanation:
right angles are 90 degrees
Answer :
x +25 +25 =90 degrees
x +50 =90 degrees
x = 90 -50
x = 40 degrees
Which expression has a solution of 11, if m = 1?
m - 11
11 + m
14 - m
m + 10
Answer:
m+10 has the solution of 11
(-6)^-1 multiply by x = 27^-1. find x
A farmer wants to fence in a rectangular plot in a large field, using a rock wall which is already there as the north boundary. The fencing for the east and west sides of the plot will cost $4 a yard, but the farmer needs to use special fencing which cost $5 a yard on the south side of a plot. If the area of the plot is to be 600 square yards, find the dimensions for the plot which will minimize the cost of the fencing.
Hello,
Let's assume x the length of the north's wall
and y the length of west side .
Area:x*y=600 ==> y=600/x
Cost: 2*y*4+5*x=8y+5x= 4800/x+5x
Minimize cost: (4800/x+5x)'=0
-4800/x²+5=0
x²=4800/5
x²=960
[tex]x=8\sqrt{15} \\\\y=5\sqrt{15} \\[/tex]
8.
Out of total population of 50,000, only 28,000 read Newspaper and 23,000 read
magazines while 4,000 read both. How many of them do not read any paper ?
the answer is in the picture
Multiply the following rational expressions and simplify the result
Answer:
Step-by-step explanation:
We have to solve the given expression,
[tex]\frac{9y-33y^2-3y^4}{100-49y^2}.\frac{7y^2+17y+10}{14y^2+28y}[/tex]
[tex]\frac{9y-33y^2-3y^4}{100-49y^2}.\frac{7y^2+17y+10}{14y^2+28y}[/tex] = [tex]\frac{-y(-9+33y+3y^3)}{100-49y^2}.\frac{7y^2+17y+10}{14y(y+2)}[/tex]
= [tex]\frac{-y(-9+33y+3y^3)}{(10-7y)(10+7y)}.\frac{7y^2+10y+7y+10}{14y(y+2)}[/tex]
= [tex]\frac{-y(-9+33y+3y^3)}{(10-7y)(10+7y)}.\frac{y(7y+10)+1(7y+10)}{14y(y+2)}[/tex]
= [tex]\frac{-y(-9+33y+3y^3)}{(10-7y)(10+7y)}.\frac{(y+1)(7y+10)}{14y(y+2)}[/tex]
= [tex]\frac{-3y(-3+11y+y^3)}{(10-7y)}.\frac{(y+1)}{14y(y+2)}[/tex]
= [tex]\frac{-3(-3+11y+y^3)}{(10-7y)}.\frac{(y+1)}{14(y+2)}[/tex]
= [tex]\frac{3(3-11y-y^3)(y+1)}{(10-7y)(14(y+2)}[/tex]
At the beginning of the chemistry experiment, Lisa measured the temperature of a liquid to be -5°C. During the experiment, she measured the liquid 3 times and the results showed, its dropped 9°C, rose 25°C, and drop 15°C. What was the liquid temperature at the end of the experiment?
Answer:
-4°C
Step-by-step explanation:
At the beginning of the chemistry experiment the temperature of the liquid was -5°C and it dropped 9°C so you do:
-5°C - 9°C = -14°C
The answer is -14°C for the first part of the question because when you are subtracting a positive number from a negative number you have to add the two numbers together but your answer will always be a negative number.
Then you add 25°C to -14°C:
-14°C + 25°C = 11
Because when adding a negative number to a positive number that is bigger than the negative number you have to subtract but your answer will always be a positive number, however if the positive number is smaller than the negative number your answer will be a negative number.
Then you subtract 11°C from 15°C:
11°C - 15°C = -4°C
Because when you subtract a number that is bigger than the first number you get a negative number.
When the angle of elevation of the sun is
42°, fnd the length of the shadow, to the
nearest foot, cast by a tree 60 feet tall.
Answer:
The shadow length is 67
Step-by-step explanation:
solution shown in the picture
PLS HELP SOON WILL MARK BRAINLYEST
A railroad tunnel is shaped like a semi-ellipse, as shown below. A semiellipse is shown on the coordinate plane with vertices on the x axis and one point of intersection with the positive y axis. The height of the tunnel at the center is 35 ft, and the vertical clearance must be 21 ft at a point 8 ft from the center. Find an equation for the ellipse.
According to the question
b= 35 and (8,21) lies on the ellipse
After calculation we get a= 10
equation for the ellipse.
[tex] \frac{ {x}^{2} }{100} + \frac{ {y}^{2} }{1225} = 1[/tex]
the LCM of 16 and 18 is
the lcm of 16 and 18 is 144 !
Which equation is equivalent to (x^2-5)^2-3x^2+15=-2 in terms of m?
Answer:
x = 67/x^4
Step-by-step explanation:
I did step by step on the whiteboard. I hope it helps!
Find the H.C.F. of the following numbers using division method
(a) 24, 40
Answer:
Ok
Thank you for
your time
I don't get this can somone help me please
Answer:
f = m+h
Step-by-step explanation:
just add h to both sides of the equation to isolate f.
Hope this helps!
Which is the ratio of triangles and to hearts
there is 22 hearts and
11 triangles
Answer:
triangles : hearts = 11 : 22 = = 11 : 2(11) = 1 : 2
If you put it in fraction form it's [tex]\frac{triangles}{hearts} =\frac{11}{22} =\frac{11}{2(11)}=\frac{1}{2}[/tex].
After substituting, what is the first step when evaluating vegy 4 2 when x 6?
O Multiply 3 by 5
O Add 5 and 3
Subtract 4.2 from 5
Add 3 and 4.2 hurry I'm being timedd!!!
Answer:
Multiply 3 by 5
Step-by-step explanation:
After substituting, what is the first step when evaluating x+3x-4.2 when x=5
Given:
x + 3x - 4.2
when x = 5
Substitute x = 5 into the expression
x + 3x - 4.2
= 5 + 3(5) - 4.2
= 5 + 15 - 4.2
= 20 - 4.2
= 16.8
x + 3x - 4.2, when x = 5 is 16.8
After substituting, the first step when evaluating x + 3x - 4.2 when x = 5 is Multiply 3 by 5
I need help ASAP!
List the fractions and decimals in order least to greatest.
Question1. 2.3 , 2 4/5 , 2.6
Question 2. 0.5 , 3/16 , 0.75 , 5/48
Who ever helped me thank you :D
Answer:
Q1: 2.3, 2.6, 2 4/5
Q2: 5/48, 3/16, 0.5, 0.75
Step-by-step explanation:
that should be correct sorry if im wrong
Answer: The answer is already completed
Step-by-step explanation:
What is the midpoint of the segment with endpoints(-4, -
2) and (2, 6)?
Answer:
(-1,2)
Step-by-step explanation:
hope you find this useful!
https://ncalculators.com/geometry/mid-points-calculator.htm
a man invested 800.00in a bank at a simple interest rate of 5% per annum .Find his total amou year
Answer:
£840
Step-by-step explanation:
800 × 1.05 = 840
(1.05 Is the decimal multiplier = (100% + 5%)/100)
is Catholic Schools bad?
Answer:
Not really。。
Step-by-step explanation:
this school had remained excellent。students grduating from these school have higher ACT scores
Freebie!! Enjoy! Have a good day!
“Never follow anyone else’s path. Unless you’re in the woods and you’re lost and you see a path. Then by all means follow that path.”
—Ellen DeGeneres
Answer:
You as well!
Step-by-step explanation:
Find the first five terms of the sequence described.
Answer:
I dont think i dont know this but its 10?
An article in Human Factors (June 1989) presented data on visual accommodation (a function of eye movement) when recognizing a speckle pattern on a high-resolution CRT screen. The data are as follows: 36.45, 67.90, 38.77, 42.18, 26.72, 50.77, 38.9, and 50.06. Calculate the sample mean and sample standard deviation.
Answer:
Mean = 43.969
Standard deviation = 12.341
Step-by-step explanation:
Given the data :
36.45, 67.90, 38.77, 42.18, 26.72, 50.77, 38.9, 50.06
The sample mean :
Σx / n = 351.75 / 8 = 43.969
Sample standard deviation :
√Σ(x - mean)²/n-1
√[(36.45-43.969)² + (67.90-43.969)² + (38.77-43.969)² + (42.18-43.969)² + (26.72-43.969)² + (50.77-43.969)² + (38.9-43.969)² + (50.06-43.969)² ] / ((8 - 1)
Standard deviation = 12.341
Find the exterior angle.
50°
70°
60
X = [?]
Answer:
110
Step-by-step explanation:
180-70=110
the full line is 180 so subtract the angle, 70.
the area of a rectangular bathroom mirror is 20 square feet. it is 2 feet tall. how wide is it?
Area = length x width
Fill in the given information
20 = 2 x width
Solve for width by dividing both sides by 2
Width =20/2
Width = 10 feet
Answer:
It is 10 feet wide
Step-by-step explanation:
The area of a rectangle is:
A = Length x width
So if we have the area, finding the width means diving the area by the given length.
In this case, the area of the rectangle is 20 square feet and the length is 2 feet:
20/2 = 10
Therefore the missing width is 10 feet
Find the TWO integers whos product is -12 and whose sum is 1
Answer:
[tex] \rm Numbers = 4 \ and \ -3.[/tex]
Step-by-step explanation:
Given :-
The sum of two numbers is 1 .
The product of the nos . is 12 .
And we need to find out the numbers. So let us take ,
First number be x
Second number be 1-x .
According to first condition :-
[tex]\rm\implies 1st \ number * 2nd \ number= -12\\\\\rm\implies x(1-x)=-12\\\\\rm\implies x - x^2=-12\\\\\rm\implies x^2-x-12=0\\\\\rm\implies x^2-4x+3x-12=0\\\\\rm\implies x(x-4)+3(x-4)=0\\\\\rm\implies (x-4)(x+3)=0\\\\\rm\implies\boxed{\red{\rm x = 4 , -3 }}[/tex]
Hence the numbers are 4 and -3
Answer:
Step-by-step explanation:
If the product of 2 integers is -12, then that equation looks like this:
xy = -12
If the sum of those same 2 integers in 1, then that equation looks like this:
x + y = 1
Let's solve the second equation for x and plug it into the first equation. Solving the second equation for x gives us
x = 1 - y and plug that into the first equation in place of x to get:
(1 - y)y = -12 and
[tex]y-y^2=-12[/tex] Now move everything over to one side and factor to find y:
[tex]-y^2+y+12=0[/tex] and the 2 values for y are
y = -3 and y = 4. Let's see what happens when we solve for x.
If xy = -12 and y is -3:
x(-3) = -12 so
x = 4
If xy = -12 and y is4:
x(4) = -12 so
x = -3
So it looks like the 2 integers are -3 and 4
Write in the form a to the power of k, where a is a prime number and k is rational
[tex]\sqrt[4]{27}[/tex]
The answer is 3 to the 3/4 power.
A metal smith is mixing two molten metals
Answer:
I think the answer is going to be A (15)(0.75) and 0.7(15 – x) + 0.9x, I hope this helps!! :)
Step-by-step explanation:
