If $900 is invested at 3%, compounded monthly, the future value S at any time t (in years) is given by the following.S = 900(1.0025)^12tHow long (in years) will it take for the amount to double? (Round your answer to one decimal place.)
Answers
Number of years it will take for the amount to double is 23 years
The principal amount = $900
The interest rate = 3%
The interest is compounded monthly
The given equation is
S = 900(1.0025)^12t
Where S is the final amount
t is the time period in years
The final amount is the double of principal amount
Final amount = 2 × 900
= $1800
Substitute the values in the equation
1800 = 900(1.0025)^12t
1.0025^12t = 1800/900
1.0025^12t = 2
Then value of t = ln(2) / 12ln (1.0025)
Divide the numbers
= 23.13b years
Therefore, the time period is 23 years
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Related Questions
the product of two consecutive even integers is 224. find the integers
Answers
Answer:
• 14 and 16
,• -16 and -14.
Explanation:
Let the smaller of the two consecutive even integers = x
The larger of the two consecutive even integers = x+2
We are told that their product is 224, therefore:
\(\begin{gathered} x(x+2)=224 \\ x^2+2x=224 \end{gathered}\)We solve the resulting quadratic equation for x.
\(\begin{gathered} x^2+2x-224=0 \\ x^2+16x-14x-224=0 \\ x(x+16)-14(x+16)=0 \\ (x-14)(x+16)=0 \\ x-14=0\text{ or }x+16=0 \\ x=14\text{ or x=-16} \end{gathered}\)Therefore, the two consecutive even integers are:
• 14 and 16
,• -16 and -14.
,•
I need help :( Pleaseeeeeee
Answers
Answer:
-5
Step-by-step explanation:
-15/-3
-5
If im wrong sorry :(
Step-by-step explanation:
the answer is -63 lol for some reason it said i need 20 letters to answer your question but there you go -63
When Tyrone fell asleep one night, the temperature
was 24°F. When Tyrone awoke the next morning, the
temperature was -12°F. Letting + denote a rise in
temperature and - denote a drop in temperature, what
was the change in temperature from the time Tyrone
fell asleep until the time he awoke?
F. -36°F
G. -12°F
H. +6°F
J. +12°F
K. +36°F
Answers
24 - x = -12 so what do is just add the two together so 24 + 12 = 36 and since it ended on a negative number, the temperature change is -36!!
a) State and explain the two main classes of vitamins
Answers
Answer:
Step-by-step explanation:
Vitamin A is important for normal vision, the immune system, reproduction, and growth and development. Vitamin A also helps your heart, lungs, and other organs work properly. Carotenoids are pigments that give yellow, orange, and red fruits and vegetables their color.
Vitamin D helps regulate the amount of calcium and phosphate in the body. These nutrients are needed to keep bones, teeth and muscles healthy. A lack of vitamin D can lead to bone deformities such as rickets in children, and bone pain caused by a condition called osteomalacia in adults.
Consider the following data representing the price of plasma televisions (in dollars).
1325, 1266, 1123, 1233, 1387, 1249, 1120, 1140, 1347, 1337, 1402, 1259, 1421, 1351, 1452, 1277, 1309, 1232, 1112, 1243, 1429
Copy Data Price of Plasma Televisions (in Dollars) Class Frequency Class Boundaries Midpoint Relative Frequency Cumulative Frequency
1067–1126 1127–1186 1187–1246 1247–1306 1307–1366 1367–1426
Determine the class width of the classes listed in the frequency table.
Answers
Answer:
\(Width = 59\)
Step-by-step explanation:
Given
The above data
Required
The class width
To do this, we simply calculate the difference between the class limits of any one of the classes.
Taking 1187–1246 as a point of reference, the class width is:
\(Width = 1246 - 1187\)
\(Width = 59\)
MATH WEEK 5 HOMEWORK
Answers
Answer:
y=3/5x-1 or y=0.6x-1
Step-by-step explanation:
Answer:
y=3/5x-1 or y=0.6x-1
Step-by-step explanation:
Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval. If the answer is an interval, enter your answer using interval notation. If the answer is a finite set of values, enter your answers as a comma separated list of values.)
Answers
Answer:
(0, 16]
Step-by-step explanation:
∑ₙ₌₁°° (-1)ⁿ⁺¹ (x−8)ⁿ / (n 8ⁿ)
According to the ratio test, if we define L such that:
L = lim(n→∞) |aₙ₊₁ / aₙ|
then the series will converge if L < 1.
aₙ = (-1)ⁿ⁺¹ (x−8)ⁿ / (n 8ⁿ)
aₙ₊₁ = (-1)ⁿ⁺² (x−8)ⁿ⁺¹ / ((n+1) 8ⁿ⁺¹)
Plugging into the ratio test:
L = lim(n→∞) | (-1)ⁿ⁺² (x−8)ⁿ⁺¹ / ((n+1) 8ⁿ⁺¹) × n 8ⁿ / ((-1)ⁿ⁺¹ (x−8)ⁿ) |
L = lim(n→∞) | -n (x−8) / (8 (n+1)) |
L = (|x−8| / 8) lim(n→∞) | n / (n+1) |
L = |x−8| / 8
For the series to converge:
L < 1
|x−8| / 8 < 1
|x−8| < 8
-8 < x−8 < 8
0 < x < 16
Now we check the endpoints. If x = 0:
∑ₙ₌₁°° (-1)ⁿ⁺¹ (0−8)ⁿ / (n 8ⁿ)
∑ₙ₌₁°° -(-1)ⁿ (-8)ⁿ / (n 8ⁿ)
∑ₙ₌₁°° -(8)ⁿ / (n 8ⁿ)
∑ₙ₌₁°° -1 / n
This is a harmonic series, and diverges.
If x = 16:
∑ₙ₌₁°° (-1)ⁿ⁺¹ (16−8)ⁿ / (n 8ⁿ)
∑ₙ₌₁°° (-1)ⁿ⁺¹ (8)ⁿ / (n 8ⁿ)
∑ₙ₌₁°° (-1)ⁿ⁺¹ / n
This is an alternating series, and converges.
Therefore, the interval of convergence is:
0 < x ≤ 16
Or, in interval notation, (0, 16].
For the triangle shown in the picture two angles are given find the third angle without using a protractor.
Answers
Let's use x for the missing angle. The sum of the internal angles of a triangle is equal to 180°. Then we have:
\(\begin{gathered} 180^{\circ}=x+29^{\circ}+109^{\circ}=x+138^{\circ} \\ 180^{\circ}=x+138^{\circ} \end{gathered}\)Then if we substract 138° from both sides we get:
\(\begin{gathered} 180^{\circ}-138^{\circ}^{}=x+138^{\circ}-138^{\circ} \\ x=42^{\circ} \end{gathered}\)Then the answer is 42°.
The product of 46 and a number added to the reciprocal of a number squared.
Answers
The expression for the given word phrase is
46M + M² + 2 + 1/M²
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Number = M
Reciprocal of M = 1/M
Now,
46 x (M + 1/M)²
Step 1:
46M + M² + 2 + 1/M²
Thus,
The expression is 46M + M² + 2 + 1/M²
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A number x increased by 7 is no more than 40
Answers
Answer:
X+7 < 40 is the answer
x can equal anything less than 33
Step-by-step explanation:
The average monthly income of three persons is rs. 3,600. If the income of the first is 1/5 of the combined income of the other two then his monthly income is
Answers
The monthly income of the first person is $600.
Given that, the average monthly income of three persons is RS 3,600.
The income of the first is 1/5 of the combined income of the other two.
Here, Let income of the first be A, let income of the second be B and let Income of the third be C.
A+B+C=3600 -----(i)
Income for the first person = 1/5(B+C) -----(ii)
Substitute equation (ii) in equation (i), we get
(B+C)/5 +B+C =3600
B+C+5B+5C=3600×5
6B+6C=18000
6(B+C)=18000
B+C=3000 ------(iii)
Substitute (iii) in equation (i), we get
A=$600
Therefore, the monthly income of the first person is $600.
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On the surface, it seems easy. Can you think of the integers for x, y, and z so that x³+y³+z³=8? Sure. One answer is x = 1, y = -1, and z = 2. But what about the integers for x, y, and z so that x³+y³+z³=42?
Answers
Answer:
(-80538738812075974)^3 + 80435758145817515^3 + 12602123297335631^3 = 42
Step-by-step explanation:
This is obviously a bait question.
How many to digit numbers are there that have six and eight as factors
Answers
Answer:36 i think
Step-by-step explanation:
What are the cordinates of the image of the point (11,1)after a translation 10 units down followed by a reflection over the y-axis
Answers
Answer:
(-11,-9)
Step-by-step explanation:
translate 10 units down: y value: 1-10=-9
reflect over y-axis: x-value becomes opposite: 11 becomes -11
Find the side length, b.
Round to the nearest tenth.
C
a
BL
b
A
C
b = [?]
B = 90°
a = 6
C=7
![Find the side length, b.Round to the nearest tenth.CaBLbACb = [?]B = 90a = 6C=7](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/aNYVDg7ey4EH5J1dBnGf9645QlVlYe91.png)
Answers
Answer:
b = 9.2 (Rounded to the nearest tenth)
Step-by-step explanation:
ABC is a right-angled triangle at B.
Then ,according to the Pythagorean theorem:
\(b = \sqrt{a^2 + c^2}\)
\(= \sqrt{6^2 + 7^2}\)
\(= \sqrt{36 + 49}\)
\(= \sqrt{85}\)
\(=9.219544457293\)
(a) Show that if λ is an eigenvalue of A, then λ is an eigenvalue of \(A^{T}\). Show with an example that the eigenvectors of A and \(A^{T}\) are not the same.
(b) Show that if λ is an eigenvalue of A, and A is invertible, then λ^-1 is an eigenvalue of A^-1.
Answers
If λ is an eigenvalue of A, then λ is an eigenvalue of \(A^T\). Show with an example that the eigenvectors of A and \(A^T\) are not the same.
What are eigenvalues and eigenvectors?The equation Av = λv, where v is a non-zero vector, is satisfied by an eigenvector v and an eigenvalue given a square matrix A. In other words, the eigenvector v is multiplied by the matrix A to produce a scalar multiple of v. Due to their role in illuminating the behaviour of linear transformations and differential equation systems, eigenvectors play a crucial role in many branches of mathematics and science. When the eigenvector v is multiplied by A, the eigenvalue indicates how much it is scaled.
The eigenvalue and eigenvector states that, let v be a non-zero eigenvector of A corresponding to the eigenvalue λ.
Then, we have:
Av = λv
Taking transpose on both sides we have:
\(v^T A^T = \lambda v^T\)
The above equations thus relates transpose of vector and transpose of A to λ.
Now, consider a matrix:
\(\left[\begin{array}{cc}1&2\\3&4\\\end{array}\right]\)
Now, the eigen values of this matrix are λ1 = -0.37 and λ2 = 5.37.
The eigenvectors are:
\(v1 = [-0.8246, 0.5658]^T\\v2 = [-0.4159, -0.9094]^T\)
Now, for transpose of A:
\(A^T=\left[\begin{array}{cc}1&3\\2&4\\\end{array}\right]\)
The eigen vectors are:
\(u1 = [-0.7071, -0.7071]^T\\u2 = [0.8944, -0.4472]^T\)
Hence, we see that, if λ is an eigenvalue of A, then λ is an eigenvalue of \(A^T\). Show with an example that the eigenvectors of A and \(A^T\) are not the same.
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Given n(A) = 288, n(B) = 183, and n(AU B) = 434, find n(A∩ B).a) 37b) None of thesec) 539d) 329
Answers
We have to find n(A∩B), which is the number of elements that belong both to A and B.
We can use the following relation:
\(n(A\cup B)=n(A)+n(B)-n(A\cap B)\)We can then calculate n(A∩B) as:
\(\begin{gathered} n(A\cup B)=n(A)+n(B)-n(A\cap B) \\ n(A\cap B)=n(A)+n(B)-n(A\cup B) \\ n(A\cap B)=288+183-434 \\ n(A\cap B)=37 \end{gathered}\)Answer: 37 [Option a]
Write an equation in point-slope form of the line that passes through (1,0) and (4,4).
y- __= __(x - 1)
Answers
We want this in the form
y
=
m
x
+
c
, where
m
is the gradient, and
c
is the y-intercept.
Gradient is the change in y over the change in x, or the rise over run; however you like to think about it.
m
=
y
2
−
y
1
x
2
−
x
1
So for our points
(
1
,
4
)
and
(
4
,
9
)
m
=
9
−
4
4
−
1
=
5
3
Now, by rearranging our equation for gradient, we can show that:
y
−
y
1
=
m
(
x
−
x
1
)
Here,
x
and
y
are general points on the line - we've just replaced
(
x
2
,
y
2
)
with
(
x
,
y
)
Since we know
m
, and have a set of co-ordinates to sub in as
(
x
1
,
y
1
)
, we can sub values in, then re-arrange to get to the
y
=
m
x
+
c
form.
y
−
4
=
5
3
(
x
−
1
)
y
−
4
=
5
3
x
−
5
3
y
=
5
3
x
−
5
3
+
4
y
=
5
3
x
+
7
3
as required.
6. The fixed costs of producing a Wild Widget are $34,000. The variable costs are $5.00 per widget. What is the average cost per widget of producing 7,000 Wild Widgets? Round to the nearest cent. :))))
Answers
Answer: To calculate the average cost per widget, we need to consider both the fixed costs and the variable costs.
Fixed costs: $34,000
Variable costs per widget: $5.00
Total costs = Fixed costs + (Variable costs per widget × Number of widgets)
Total costs = $34,000 + ($5.00 × 7,000)
Total costs = $34,000 + $35,000
Total costs = $69,000
Average cost per widget = Total costs / Number of widgets
Average cost per widget = $69,000 / 7,000
Average cost per widget ≈ $9.86
Therefore, the average cost per widget of producing 7,000 Wild Widgets is approximately $9.86.
Step-by-step explanation: :)
Is an estimate of 28,000 over under the actual peoduct of 360 68? How can you tell
Answers
Answer:
Over Estimate of the actual product.
Step-by-step explanation:
360*68= 24,480
The estimate of 28,000 is larger than the actual product 360 and 68 which is 24480, which means that the estimate is an over estimate (an over estimate means that the number you estimated is bigger than the actual number, and an under estimate is when the estimate is smaller than the actual number, Just FYI)
A. 3(x+2)=18 B. 3x+6=18
Answers
Answer:
B
Step-by-step explanation:
3x6 is 18 so therefore its B
A tech company is curious about marketing their new drones for home security. Let the proportion of houses that have home security be p. If the tech company would like to know if the proportion of houses that have home security is different than 45%, what are the null and alternative hypotheses
Answers
Answer:
Step-by-step explanation:
The null hypothesis is described as the default hypothesis while the alternative hypothesis us always tested against this null ie the opposite of the null hypothesis.
In this case study, Let the proportion of houses that have home security be p
Thus, the null hypothesis is proportion of houses that have home security is 45% : p = 45%
The alternative hypothesis is proportion of houses that have home security is different than 45%: p =/ 45%
Linkin Corporation is considering purchasing a new delivery truck. The truck has many advantages over the company’s current truck (not the least of which is that it runs). The new truck would cost $55,440. Because of the increased capacity, reduced maintenance costs, and increased fuel economy, the new truck is expected to generate cost savings of $8,400. At the end of 8 years, the company will sell the truck for an estimated $27,700. Traditionally the company has used a rule of thumb that a proposal should not be accepted unless it has a payback period that is less than 50% of the asset’s estimated useful life. Larry Newton, a new manager, has suggested that the company should not rely solely on the payback approach, but should also employ the net present value method when evaluating new projects. The company’s cost of capital is 8%.
Answers
The payback period of the investment is 6.6 years.
The net present value is $7,797.22.
The payback period calculates the amount of time it takes to recover the amount invested from the cumulative cashflows.
Payback period = Amount invested / cost saving
$55,440 / $8,400 = 6.6 years
Net present value is the present value of after-tax cash flows from an investment less the amount invested.
NPV can be determined using a financial calculator
Cash flow in year 0 = $-55440
Cash flow in year 1 to 7 = $8,400
Cash flow in year 8 = $8400 + $27,700
I = 8%
NPV = $7,797.22
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Use the formula for present value of money to calculate the amount you need to invest now in one lump sum in order to have $25,000 after 10 years with an APR of 11% compounded monthly.
Answers
The amount will be $8805.
The Present value formula is PV = FV x 1/\((1+r)^{n}\)
where,
PV = present value.
FV = future value.
r = annual percentage rate.
n = number of periods.
we have to put given values in the formula for Present value-
FV = $25,000
r = 11%
n = 10 year
PV = $25,000 x 1/\((1+11/100)^{10}\)
PV = $8805.
Hence, Present value of money will be $8805.
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The sum of three numbers is 11. The sum of twice the first number, 5 times the second
number, and 6 times the third number is 57. The difference between 3 times the first
number and the second number is 5. Find the three number
Answers
Answer:
the three number : 2 , 1 , 8
Step-by-step explanation:
hello : here is an solution
Statesville's population in 2010 was about 24,500, and was growing by about 1% each year. If this continues, what will Statesville's population be in 2016?
Answers
Answer:
26,003 people in 2016
Step-by-step explanation:
If the population is growing by one percent each year, you take the 2010 population and divide by 100 (which is 1%) and add it with the population. That is 2011 population. Take this population, divide it by 100, and add to 2011 population. Do this 4 more times and 26,003 is your answer.
which statement best describes the difference between the formula for population and sample variance?
Answers
The formula for population variance uses the division of (sum of squared deviations) by the total number of elements in the population, while the formula for sample variance uses the division of (sum of squared deviations) by the sample size minus one.
Difference between the formula for population and sample variance?The formula for population variance uses the division of (sum of squared deviations) by the total number of elements in the population, while the formula for sample variance uses the division of (sum of squared deviations) by the sample size minus one.
The formula for population variance is given by:
σ² = (1/N) * ∑(X - μ)²,
where N is the total number of elements in the population, X is an individual value in the population, and μ is the mean of the population.
s²= (1/(n-1)) * ∑(X - m)²,
where n is the sample size and m is the mean of the sample.
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please help me im on a timer
Answers
Answer:
11/8
Step-by-step explanation:
Airiona pays a finance charge on her average daily balance of $1565.00. Her APR is 18%. What is her finance charge for this billing cycle?
Answers
her daily balance is $1565.00
Her APR is 18%
her finance charge is APR X Daily balance
Her finance charge = 18 / 100 x $1565
= 0.18 x $1565
= $281.7
Her finance charge is $281.7$
please explain
without using tables or a calculator evaluate
Answers
Answer:
49.2
9
Step-by-step explanation:
7.46² - 2.54² = (7.46 - 2.54)(7.46 + 2.54)
= (4.92)(10)
= 49.2
(1 x 4) x 3 = [1² + √(1 x 4)] x 3 = [1 + √4] x 3 = [1 + 2] x 3 = 3 x 3 = 9