Find the time required for $5000 to be equal to $14,000 when deposited at 7% compounded monthly
Answers
[tex]\bf \cfrac{14}{5}=\left( 1+\frac{7}{1200} \right)^{12t}\implies \cfrac{14}{5}=\left(\cfrac{1207}{1200} \right)^{12t} \\\\\\ log\left(\frac{14}{5} \right)=log\left[ \left(\frac{1207}{1200} \right)^{12t} \right]\implies log\left(\frac{14}{5} \right)=12t\cdot log\left[ \left(\frac{1207}{1200} \right) \right] \\\\\\ \cfrac{log\left(\frac{14}{5} \right)}{12\cdot log\left[ \left(\frac{1207}{1200} \right) \right]}=t\implies 14.75\approx t[/tex]
so, about 14 years and 9 months.
See the attached formula.
Related Questions
there are seven days how many days are there in 16 weeks
Answers
16 x 7 = 112
6.14 x 10 to the power of negative 9 in standard form
Answers
Prove that if b is a square matrix then b+b^t is symmetric
Answers
[tex](\mathbf B+\mathbf B^\top)^\top=\mathbf B^\top+(\mathbf B^\top)^\top=\mathbf B^\top+\mathbf B=\mathbf B+\mathbf B^\top[/tex]
and so [tex]\mathbf B+\mathbf B^\top[/tex] is indeed symmetric.
What is the domain of the function f(x)= 1/3x+2
Answers
if it is 1/(3x)+2, 3x≠0, x≠0, the domain is all real number except 0
It is hard to tell from your equation what the demonstrator is.
The answer is the last one
x≥-6
I hope this helps, and God bless <3
Line M passes through the points (–5, 9) and (–1, 9).
Answers
Let me tell you why, first the y intercepts are not changing, the x intercepts are just changing which means that the line will be horizontal. You can also prove this by actually graphing the points and connecting the dots.
Two, a horizontal line always has a slope of zero, slope is rise over run, when rise = 0, no matter what the run is the slope will be zero.
For example 0/9 = 0, 0/1 = 0.
Jack is mowing a lawn that has a shed. Jack wants to know the area of the lawn he has to mow. here are the dimensions of the yard and the shed. 13x-4 length 5x withd shed is 2x+4length withd is 2x
find a polynomial that describes the area of the lawn he has to mow. i.e. find the area of the area of the shed.
Answers
We know that the formula for area is simply:
area = l w
where l is length and w is width
yard dimensions: l = 13x – 4, w = 5x
Ayard = (13x – 4) 5x = 65x^2 – 20x
shed dimensions: l = 2x + 4, w = 2x
Ashed = (2x + 4) 2x = 4x^2 + 8x
Therefore the area to mow is:
Amow = Ayard – Ashed
Amow = 65x^2 – 20x – (4x^2 + 8x)
Amow = 65x^2 – 20x – 4x^2 – 8x
Amow = 61x^2 – 28x
Last year Mr. Henderson paid a total of $98.40 for phone service and $79.20 for garbage pick up what was his average cost per month for phone service and garbage pick up?
Answers
So 98.4 / 12 = 8.2 and next part 79.2 / 12 = 6.6
Mr. Henderson spent $8.2 a month for phone service and $6.6 for garbage pick up.
A = (97.40 + 79.20)/2
You finish.
Find 14/15−1/3 . Write your answer as a fraction in simplest form.
Answers
~PutarPotato
Officer Brimberry wrote 8 tickets for traffic violations last week, but only 5 tickets this week. What is the percent decrease? Give your answer to the nearest tenth of a percent.
Answers
(8-5)/(8)
3/8=0.375
*100 to get percentage
0.375*100=37.5% decrease
Answer:
The percent decrease is [tex]37.5\%[/tex]
Step-by-step explanation:
we know that
[tex]8\ tickets[/tex] ------> represent the [tex]100\%[/tex]
so
by proportion
Find the percent decrease
[tex]\frac{100}{8}\frac{\%}{tickets} =\frac{x}{(8-5)}\frac{\%}{tickets} \\ \\x=100*(8-5)/8\\ \\x=100*3/8\\ \\x=37.5\%[/tex]
which of the following steps were applied to abc obtain a'b'c'
Answers
Answer:
Shifted 2 units left and 4 units up
Step-by-step explanation:
Given are two triangles
ABC is having vertices as (4,6) (7,6) and (5,9)
The transformed image A'B'C' has vertices as
(2,10) (5,10) (3,13)
On comparing the vertices corresponding we find a certain pattern.
X coordinate is reduced by 2 and y coordinate is increased by 4.
This implies the transformation is
Shifted 2 units left and 4 units up
Marika Perez’s gross biweekly pay is $2,768. Her earnings to date for the year total $80,272. What amount is deducted from her pay for Social Security taxes if the rate is 6.2%? What amount is deducted for Medicare, which is taxed at 1.45%?
Answers
Answer:
The deduction for social Security tax is $4976.86 and the deduction for Medicare tax is $1163.94 .
Step-by-step explanation:
Marika Perez’s gross biweekly pay is $2,768. Her earnings to date for the year total $80,272.
What amount is deducted from her pay for Social Security taxes if the rate is 6.2%?
[tex]0.062\times80272=4976.86[/tex] dollars
What amount is deducted for Medicare, which is taxed at 1.45%?
[tex]0.0145\times80272=1163.94[/tex] dollars
what is a decimal number which never ends, but whose digits after the decimal point come in a predictable pattern called? it starts with the letters re.
Answers
if it takes Joan one and a half hours to watch a movie, how many films can he watch in ten and a half hours
Answers
steps:
10 1/2 divided by 1 1/2
Which product represents the fraction of the circle that is shaded?
A. 3/4 x 1/2
B. 2/3 x 3/4
C. 1/4 x 3/4
D 3/4 x 3/4
Answers
Answer:
D 3/4 × 3/4
Step-by-step explanation:
The part of the circle that is black is 1/4 of the circle. The remaining 3/4 is divided by the dashed lines into 4 equal parts, so each of those parts is 1/4 of 3/4 of the circle. 3 of the parts are shaded blue, so those represent ...
... 3/4 × 3/4 . . . of the circle
The correct product that represents the fraction of the shaded circle is D. 3/4 x 3/4.
Explanation:The correct answer is D. 3/4 x 3/4.
The fraction represents the shaded part of the circle. We can determine the shaded area of the circle by multiplying the fraction of the radius by the fraction of the circumference that is shaded. In this case, 3/4 x 3/4 would yield a product that represents the fraction of the circle that is shaded.
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What is the distance between S and T? If necessary, round to the nearest tenth.
Answers
36/81=48/ST
ST=108
The length of a rectangle is given by 5t+4sqrt(t), and its height is sqrt(t), where t is time in seconds and the dimensions are in centimeters. Fine the rate of change of the area of the rectangle with respect to time when the length of the rectangle is 9 centimeters.
Answers
Answer:
11.5 cm²/s
Step-by-step explanation:
We must solve two problems to answer this question:
find the time at which the length is 9 cmfind the rate of change of area with respect to time (at that time)For the first problem, we have ...
... 9 = 5t +4√t
... 9 -5t = 4√t . . . . . subtract 5t
... 81 -90t +25t² = 16t . . . . square both sides
... 25t² -106t +81 = 0 . . . subtract 16t
... (t -1)(25t -81) = 0 . . . . factor
... t = 1 or 3.24 . . . . . . t=3.24 is an extraneous solution
_____
For the second problem, we have area (a(t)) is ...
... a(t) = length×height = (5t +4√t)(√t) = 5t^(3/2) +4t
Then the derivative is ...
... a'(t) = (3/2)(5√t) +4
and
... a'(1) = (3/2)(5√1) +4 = 11.5 . . . . . cm²/s
_____
Comment on the attachment
A graphing calculator can help solve both problems. It can help find the time at which length is 9 cm by solving ... length-9 = 0. (The nice thing here is that there is no extraneous solution.) It can compute the derivative of a function, too.
Every 3 days Marco fills up his car with gas. Every 8 days he washes his car. On what day will Marco fill his car with gas and wash it?
Answers
Tina has put 15 of her old CDs in a storage crate. How many more CDs can she store in the crate if it can hold no more than 23 CDs
Answers
23 - 15 = 8
She can only fit 8 more CDs.
Hope this helps!
Which graph represents the function y=2/3x-2
Answers
We know one point, which is the y-intercept. The y-intercept is (0,-2) so that is our first point. Plot that point on the chart. Now to find another point, we can just insert a number for x and solve for y. I am going to use the number 3.
y = 2x/3 - 2
y = 2(3)/3 - 2
y = 6/3 - 2
y = 2 - 2
y = 0
So when x = 3 y = 0. We have another point,which is (3,0) Plot the points (0, -2) (3, 0) and draw a line between the points and that is your graph. It will look the image I attached.
Answer:
Here you go! used a graphing calculator for accuracy.
Step-by-step explanation:
if 2 out of every 20 ducks were banded, What percent were not banded?
Answers
if 2 were banded that means 18 out of 20 were not banded
18 divided by 20 = 0.9
so 90% were not banded
Write an equation for "eight less than a number is seventy-five". What is the number? n - 8 < 75; -67 n - 8 = 75; 67 n - 8 = 75; 83 n - 8 < 75; 67
Answers
n is the number
so number minus 8 equals 75
n-8=75
n is the number
so number minus 8 equals 75
A six-sided rectangular box is to hold 1/2 cubic meter; what shape should the box be to minimize surface area?
Answers
A circle is an object which has the lowest surface area to volume ratio. So in this case, the shape should be like that of a circle but we cannot have a circle here because we want to form a 6 sided box. So the next thing closer to circle is a square. Hence the shape should be a square:
Answer:
square
To minimize surface area for a given volume of 1/2 cubic meter, the box should be shaped as a cube with each side measuring approximately 0.7937 meters. This cube shape offers the smallest surface area for the given volume.
Explanation:To minimize the surface area of a six-sided rectangular box with a volume of 1/2 cubic meter, it is best to make the box in the shape of a cube. This shape has the smallest surface area for a given volume. To find the dimensions of the box, let's denote the side of the cube as 's'. We know that volume V of a cube is given by V = s³. So, if the volume is 1/2 cubic meter, we have:
s³ = 1/2
s = ∛(1/2) ≈ 0.7937 meters
Each side of the cube should be approximately 0.7937 meters to achieve the minimal surface area. The surface area SA of the cube can be calculated as:
SA = 6s²
SA = 6 × (0.7937)² ≈ 3.770 meters²
Thus, a cube with sides of about 0.7937 meters will have the minimal surface area for a volume of 1/2 cubic meter.
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what is the value of this expression when x = -1 and y = 2?
4x³y²
Answers
A rectangular room is 22 meters longer than it is wide, and its perimeter is 1616 meters. find the dimension of the room.
Answers
1616 meters= 2 (L+w) substitute for L
1616m+ 2(w+22m+w) divide each side by 2
808m= 2w+22m subtract 22m from each side
786m=2w divide each side by 2
393m=w Anwer: The width is 393 meters
L=w+22m=393m+22m=415m Answer: The length is 415 meters
Which statement proves that PQRS is a parallelogram? The slopes of SP and RQ are both –2 and SP = RQ = . The slopes of RS and QP are both 3 and SP = RQ = . The midpoint of RP is and the slope of RP is . The midpoint of SQ is and SQ = 5
Answers
Answer:
The correct option is 1. The figure PQRS is a parallelogram, if slope of SP and RQ are both –2 and SP = RQ.
Step-by-step explanation:
The opposite sides of a parallelogram are parallel are equal.
In the quadrilateral PQRS,
PQ and RS are opposite sides.
SP and RQ are opposite sides.
The slope of two parallel lines are same.
If the slopes of SP and RQ are both –2. It means SP and RQ are parallel. It is also given that
SP = RQ
Since one pair of opposite sides are equal and parallel, therefore the another set of opposite sides is also parallel and equal.
The opposite sides are prallel and equation, so the quadrilateral PQRS is a parallelogram.
Thus correct option is 1.
The statement that proves that quadrilateral PQRS is a parallelogram is: A. The slopes of SP and RQ are both –2 and SP║RQ.
Properties of the Sides of a Parallelogram
A parallelogram is a quadrilateral having two pairs of opposite sides that are equal and parallel to each other, and also, the slopes of opposite sides of a parallelogram are the same.
Therefore, the statement that proves that quadrilateral PQRS is a parallelogram is: A. The slopes of SP and RQ are both –2 and SP║RQ.
Learn more about parallelogram on:
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the sum of the measures of the three of a angles of triangle is 180. In a triangle, the measures of three angles are x,x-5 and x+23. What is the measure of each angle
Answers
x + x-5 + x +23 = 180
combine like terms:
3x +18 = 180
subtract 18 from each side:
3x = 162
divide both sides by 3
x = 162 / 3 = 54
Angle x = 54 degrees
Angle x-5 = 54-5 = 49 degrees
Angle x +23 = 54 +23 = 77 degrees
after 9 months, the simple interest earned on an investment of $1200 is $72. find the interest rate.
Answers
Here i = $72 = $1200 r (9/12) (9 months is 9/12, or 3/4, of 1 year)
Reducing,
$72 = $900r
Solving for r, r=0.08, or 8 percent per year.
Barbara D’Angelo’s bank granted her a single-payment loan of $1,000 for 100 days at 12% ordinary interest. What is the amount of ordinary interest owed?
Answers
I=prt
I interest owed?
P principle 1000
R interest rate 0.12
T time 100days/360days
360 days in a year which ordinary interest means
I=1,000×0.12×(100÷360)
I=33.33. ..Answer
Hope it helps!
A cube has a volume of 512 mm^3. If all sides of the cube are divided by 4, what will the resulting volume be?
A) 8 mm^3
B) 27 mm^3
C) 7.2 mm^3
D) 12 mm^3
Answers
after taking 1/4 pound of flour from a canister to make muffins, maria has 7/8 of the flour left. If each batch of muffins requires 2/5 pound of flour, find the greatest number of batches of muffins that Maria can make using the remaining flour/