Answers
A)
Replace the letters in the given equation with the corresponding values given in the problem:
A = 10,000 x 2.718^(0.05 x 2)
A = 11,051.59 , rounded to nearest dollar = $11,052
B)20,000 = 10000 x 2.718^(0.05 x t)
Divide both sides by 10,000:
2 = 2.718^(0.05 x t)
Apply exponent rules:
0.05tln(2.718) = 2
Solve for t:
t = ln(2) / 0.05ln(2.718)
t = 13.86 years, rounded to nearest year = 14 years.
Answer:
Step-by-step explanation:
Using [tex]A=Pe^{rt[/tex] as instructed, our equation looks like this:
[tex]A=10,000e^{(.05)(2)}[/tex] which simplifies a bit to
[tex]A=10,000e^{.1[/tex] which simplifies a bit more to
A = 10,000(1.10517) so
A = 11,051.71 Easy. Now onto the second part: solving for the number of years it takes for the investment to double. Setting A equal to 20,000 since 20,000 is 10,000 doubled:
[tex]20,000=10,000e^{.05t[/tex] Begin by dividing both sides by 10,000 to get
[tex]2=e^{.05t[/tex] and take the natural log of both sides to get that exponent down out front, keeping in mind that the natural log will "undo" the e, leaving us with:
ln(2) = .05t and
t = 14 years (that's 13.8 rounded up to the nearest year)
Related Questions
What is the slope of the line whose equation is y-4=5/2(x-2)?
Answers
Answer:
5/2
Step-by-step explanation:
We know,
Equation of the slope is, y = mx + c. Where m is the slope.
y - 4 = 5/2*(x-2)
y = 5/2*(x-2) + 4
y = (5/2)x - 5 + 4
y = (5/2)x - 1
y = (5/2)x + (-1) [y = mx + c form]
Slope, m = 5/2
Hope this will help. Please mark me brainliest.
Simplify 52⋅(x−2)52⋅(x-2). Apply the distributive property. y−4=5/2x+5/2⋅−2 Combine 5252 and x
y−4=5x2+5/2⋅−2 Cancel the common factor of 2.Factor 2 out of −2
y−4=5x2+52⋅(2(−1))y-4=5x2+52⋅(2(-1))
Cancel the common factor.
y−4=5x2+52⋅(2⋅−1)y-4=5x2+52⋅(2⋅-1)
Rewrite the expression.
y−4=5x2+5⋅−1y-4=5x2+5⋅-1
Multiply 55 by −1-1.
y−4=5x2−5
Add 44 to both sides of the equation.
y=5x2−5+4y=5x2-5+4
Add −5-5 and 44.
y=5x2−1
Reorder terms.
y=52x−1
THE ANSWER IS M = 5/2
Simplify (5np3)3
Question shown as picture
Answers
Answer:
[tex]125 {n}^{3} {p}^{9} [/tex]
In order for the parallelogram to be a rhombus x = ?
Answers
The value of the x is 27.
We have given that the diagram of a rhombus
We have to determine the value of the x
What is the angle of the rhombus?The angle is sitting on a right angle because rhombuses have 4 right angles
90 = 4x-18
108 = 4x
x = 27
Therefore the value of the x is 27.
To learn more about the rhombus visit:
https://brainly.com/question/20627264
#SPJ1
Answer: It's 14, not 27.
Step-by-step explanation:
Sally plots (−4,π)on the polar plane.
How does she proceed?
Drag a phrase to each box to correctly complete the statements.
Answers
Solution :
As Sally determines the angle of rotation, since it is π, she lies on the negative x-axis. The first block then should be negative x-axis if r is positive and in the positive x-axis if r is negative.
My other reason for changing the dragged phase would be as they used the word, therefore, in the last sentence, which would mean an interference from the above statements, from the drag phase you have given the interference would be positive x-axis.
An indoor track is made up of a rectangular region with two semi-circles at the ends. The distance
around the track is 400 meters. Determine the radius of the semicircular ends of the track in terms of y.
Answers
Answer:
r = (200 - y)/π
Step-by-step explanation:
The question details includes;
The shape of the indoor track = Two semi-circular ends and a mid rectangular region
The distance around the indoor track = 400 meters
The radius, r, of the semicircular ends in terms of y = Required
Let y represent the length of the rectangular middle area of the track, we have;
The perimeter of the indoor track = The distance around the track = 400 m
The perimeter of the indoor track = 2 × π·r + 2 × y = 400
2 × (π·r + y) = 400
∴ π·r + y = 400/2 = 200
r = (200 - y)/π
The cuboid and the triangular prism have the same volume. Find the value of x.
Answers
Answer:
x = 25
Step-by-step explanation:
The volume (V) of the triangular prism is calculated as
V = Al ( A is the area of the triangular face and l is its length )
A = [tex]\frac{1}{2}[/tex] bh = 0.5 × 5 × 8 = 20 cm² , then
V = 20 × 20 = 400 cm³
The volume of the cuboid is calculated as
V = lbh = 3.2 × 5 × x = 16x
Given V = 400 cm³ , then
16x = 400 ( divide both sides by 16 )
x = 25
Which of these expressions is equivalent to log (9.4)?
O A. log (9) + log (4)
O B. log (9) - log (4)
O c. 9. log (4)
O D. log (9) • log (4)
Answers
Answer:
log (9) + log(4)
Step-by-step explanation:
log (9.4)
Log (ab) = log (a) + log (b)
log (9) + log(4)
Answer:
A. log ( 9 ) + log ( 4)
Step-by-step explanation:
log( 9.4)
use log (a*b) = log (a) + log (b) to expand expression
log (9) + log (4)
Marcos decide abrir una cuenta de ahorro para financiar en el futuro los estudios de su hijo recien nacido. Por suerte, el banco le ofrecio la tasa de interes anual de 4,8%. El monto que deposito Marcos en la cuenta fue de $1000 000.Si no retira el dinero ni los intereses, ¿que capital tendra a los 5 años? ¿que capital tendra cuando su hijo cumpla 18 años?
Answers
Answer:
Resultados debajo
Step-by-step explanation:
Dada la siguiente información:
Tasa de interes anual (i)= 4,8%
Inversión inicial (VP)= $1.000.000
Para calcular el valor final (VF), debemos usar la siguiente formula:
VF= VP*(1 + i)^n
Para 5 años:
VF= 1.000.000*(1,048^5)
VF= $1.264.172,72
Para 18 años:
VF= 1.000.000*(1,048^18)
VF= $2.325.429,02
I kinda need help
What is the fraction 1/4 in decimal form?
I need help with this one to
Solve 3^3
Answers
Answer: easy
Step-by-step explanation: 0.25 there
The list shows the number of points Emma scored in eight basketball games.
5, 11, 9, 9, 4, 5, 6, 7
Find the mean.
Answers
Answer:
Mean = 7
Step-by-step explanation:
Given the following data;
Number of games = 8
Scores = 5, 11, 9, 9, 4, 5, 6, 7
We would sum all the scores together to get a total score.
Total scores = 5 + 11 + 9 + 9 + 4 + 5 + 6 + 7 = 56
Now, to find the mean;
[tex] Mean = \frac {total \; scores}{number \; of \; games} [/tex]
Mean = 56/8
Mean = 7
Answer:
7 is the mean score.
Step-by-step explanation:
Now we have to,
→ find the required mean score.
The given scores are,
→ 5, 11, 9, 9, 4, 5, 6, 7
→ Numbers = 8
Then the mean score will be,
→ (5 + 11 + 9 + 9 + 4 + 5 + 6 + 7)/8
→ 56/8 = 7
Hence, the mean score is 7.
Given m||n, find the value of x and y
Answers
Answer:
x=20,y=34
Step-by-step explanation:
x+14=2x-6 (vertically opposite angles)
x-2x = -6-14
-x = -20
x=20
x+14=y (corresponding angles)
20+14=y
y=34
Answer:
x = 20, y = 34
Step-by-step explanation:
(2x - 6) and (x + 14) are vertical angles and are congruent, then
2x - 6 = x + 14 ( subtract x from both sides )
x - 6 = 14 ( add 6 to both sides )
x = 20
Then
2x - 6 = 2(20) - 6 = 40 - 6 = 34
y and (2x - 6) are alternate angles and are congruent , so
y = 34
5.
The cube root for three hundred and forty three is
Punca kuasa tiga bagi tiga ratus empat puluh tiga adalah
A. 343
B. 73
C. 3433
D. 7
Answers
D. 7
Hope this helps! :)
______________
Answer:
The cube root of 343 is 7.
The graph below shows the solution to which system of inequalities?
Answers
Answer:
A
Step-by-step explanation:
gregory wants to buy a new video game system priced at $179.00. if the sales tax is 6%, what is the total amount he will pay for the video game system
Answers
Answer:
$189.74
Step-by-step explanation:
Since the sales tax is 6%,
179x0.06=10.74
Add to the starting price, 179.00+10.74=189.74!
I hope this helped!
On the coordinate plane, MNO has vertices M(4,4), N(5,-7) and O(-6,-6). What is the perimeter of MNO? If necessary, round your answer to the nearest tenth
Answers
Answer:
The perimeter is 36.2 units.
Step-by-step explanation:
M (4,4), N (5,-7) and O (-6,-6)
The distance formula is
[tex]d =\sqrt{(x''-x')^2 + (y''-y')^2}\\\\MN =\sqrt{(5 -4)^2 + (- 7 - 4)^2}\\\\MN = 11.05 \\\\MO =\sqrt{(-6 -4)^2 + (- 6 - 4)^2}\\\\MO = 14.14\\\\ON =\sqrt{(-6-5)^2 + (- 6 + 7)^2}\\\\ON = 11.05[/tex]
The perimeter is given by
P = MN + NO + MO
P = 11.05 + 14.14 + 11.05 = 36.24 units
Write an equation in
slope-intercept form that
passes through (-6, -2)
and has a y-intercept
located at y= -5
Answers
Answer:
y = -1/2 x -5
Step-by-step explanation:
The slope intercept form of an equation is
y = mx+b where m is the slope and b is the y intercept
We know b
y = mx-5
Substitute the values of x and y into the equation to determine the slope
-2 = m(-6) -5
Add 5 to each side
-2+5 =-6m
3 = -6m
Divide by -6
3/-6 = m
The slope is -1/2
y = -1/2 x -5
An electric blender has a price of $240 after import duty is added to the cost price.What is the cost price of the blender if import duty is 20%?
Answers
Answer:
$200
Step-by-step explanation:
Given :
Cost of blender + import duty = $240
Import duty = 20% of cost price
Let :
Cost of blender = x
Import duty = 20% of x = 0.2x
Therefore,
x + 0.2x = $240
1.2x = 240
x = 240 / 1.2
x = $200
Cost of blender = $200
Which formula gives the coordinates of the midpoint of the segment connecting points (a, b) and (c, d)?
attached below is the options
this is worth 100 points
Answers
Step-by-step explanation:
the correct answer is
a. { ½(c-a), ½(d-b) }
________________
General formula
((x_1+x_2)/2,(y1+y2)/2)So
Here
for (a,b) and (c,d)
Midpoint
((a+c)/2,(b+d)/2)Option A
If k is a non-zero constant, determine the vertex of the function y = x2 - 2kx + 3 in terms of k.
Answers
Answer:
Set y = 0, evaluate the quadratic at h=−b2a and solve for k.
k=9 I think..... I'm not completely sure but I think that's how it is
Answer:
[tex]\displaystyle \text{Vertex} = \left(k, 3-k^2\right)[/tex]
Step-by-step explanation:
We are given the quadratic equation:
[tex]y=x^2-2kx+3[/tex]
Where k is a non-zero constant.
And we want to determine the vertex of the parabola in terms of k.
The vertex of a parabola is given by the formulas:
[tex]\displaystyle \text{Vertex}=\left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]
In this case, a = 1, b = -2k, and c = 3.
Find the x-coorinate of the vertex:
[tex]\displaystyle x=-\frac{(-2k)}{2(1)}=\frac{2k}{2}=k[/tex]
To find the y-coordinate, we substitute the value we acquired back into the equation. So:
[tex]\displaystyle \begin{aligned} y(k)&=(k)^2-2k(k)+3\\&=k^2-2k^2+3\\&=3-k^2\end{aligned}[/tex]
Therefore, our vertex in terms of k is:
[tex]\displaystyle \text{Vertex} = \left(k,3-k^2\right)[/tex]
(4/5 - 1/10) + 2/3
PLSS URGENT
Answers
Answer:
41/30
Step-by-step explanation:
4/5 ---> 24/30
1/10 ---> 3/30
2/3 ---> 20/30
(24/30 - 3/30) + 20/30 =
21/30 + 20/30 =
41/30
Evaluate 13 - 0.75w+8x when w=12 and x= 1 over 2
Answers
Answer:
8
Step-by-step explanation:
Given:
13 - 0.75w + 8x
where,
w = 12
x = 1/2
13 - 0.75w + 8x
Substitute the value of w and x into the equation
= 13 - 0.75(12) + 8(1/2)
= 13 - 9 + 8/2
= 13 - 9 + 4
= 8
Therefore,
13 - 0.75w + 8x = 8
For homework, Anya had to find the width of a bedroom after the scale changed from 1 inch : 4 feet to 1 inch : 7 feet. Her work is shown below.
1 inch = 4 feet. 1 inches = 7 feet. A rectangle with length of 4 inches and width of 2 inches. StartFraction 1 over 7 EndFraction = StartFraction x over 2 EndFraction. 7 x = 2. x = StartFraction 2 over 7 EndFraction feet.
1
7
= x
2
7x = 2x = 2
7
feet
What error did Anya make?
Answers
Answer:
she set up the proportion incorrectly; the second ratio should be 2/x
Step-by-step explanation:
To obtain the width :
Scale drawing :
Initial = 1 inch = 4 feet
New = 1 inch = 7 feet
Width of rectangle = 2 inches
New width should be in the form :
new scale = width of rectangle / width of drawing
If width of drawing = x
1 / 7 = 2 / x
Cross multiply
x = 7*2
x = 14
Answer:
its A
Step-by-step explanation:
harlie is a hotel manager. Their responsibilities include renting rooms for conferences. The hotel charges $250 per day plus $15 per person for the grand ballroom.
Create a formula for the cost, C, in dollars, to rent the ballroom for any number of people for 1 day.
Hint: Use C for cost and n for the number of people. C = ________
How much should Charlie charge to rent the hall for 50 people? What about 100 people?
Rearrange your formula to express n in terms of C (rewrite your formula to solve for n)
How many people could attend a wedding reception if the planners have a budget of:
$4000
$2000
Answers
Answer:
Formula: C= $15n + $250
50 People: $1000
100 People: $1750
Formula: n= (C- $250)/ 15
$4000 Budget: 250 Guests
$2000 Budget: 116.67 Guests
Step-by-step explanation:
Since the rental is $250 with an additional charge of $15 per person, we write this as C = $250 + $15n.
With the given equation, simply substitute n for the amount of guests.
C = $250 + $15(50) = $1000
C = $250 + $15(100) = $1750
To solve for n, everything would need to be moved to isolate n. This can be achieved by first subtracting $250 from each side: C- 250= 15n
Then divide both sides by 15, making the new equation: (C-250)/15 = n
Again, substitute C with allowed cost to find the amount of guests allowed.
n = ($4000- 250)/ 15 = 250 People
n = ($2000-250)/15 = 116.67 People
Which equation is a function of x?
Answers
Answer:
X=5
x=y2+9
x2=y
x2=y2+16
Step-by-step explanation:
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
draw a graph for the equation above
Answers
Answer:
look at image given
Step-by-step explanation:
im assuming the -3 is seperate :p
Anyone know the answer?
Answers
Answer:
565.6854249 without rounds
Answer:
Step-by-step explanation:
Well, the area is 400m^2 so we know each side is 20 feet long. Then with that we can make a 40deg 40deg 90deg triangle with the side lengths 20, 20, and x. So, the proportion would be 20/1=x/rad2. This gives us x=28.28, so the fence is 28.28m long. Hope this helps :))
through: (4,4), slope
9/4
Answers
Answer:
y - 4 = (9/4)(x - 4)
Step-by-step explanation:
Here we're given the slope (9/4) of a line and one point (4, 4) on the line. The easiest form of the equation of a straight line to use here is the point-slope form:
y - k = m(x - h).
Here h = 4 and k = 4; the slope is m = 9/4.
Thus, the desired equation is
y - 4 = (9/4)(x - 4)
Line l has a slope of −3. The line through which of the following pair of points is perpendicular to l?
Answers
Answer:
The slope of the perpendicular line will 1/3.
Step-by-step explanation:
20% of 2kg ( in g).
Please help
Answers
Answer:
[tex]{ \tt{ = 20\% \times 2}} \\ = 0.4 \: kg \\ { \tt{ = 400 \: grams}}[/tex]
Answer:
400 g
Step-by-step explanation:
0.20 x 2 kg = 0.4 kg
0.4 kg x (1000g / 1kg) = 400 g
What is the slope of the line with equation y−3=(x−2)?
A coordinate plane with a line passing through the points at (2, 3) and (4, 2).
–2
–negative StartFraction one-half EndFraction.
StartFraction one-half EndFraction
2
Answers
Explanation:
Answer:
B on edge 2021
Step-by-step explanation:
