Suppose $40,000 is deposited into an account paying 2. 5% interest, compounded continuously.
How much money is in the account after eight years if no withdrawals or additional deposits are made?
Answers
The formula for calculating the amount of money in an account with continuous compounding is:
\(A = Pe^{(rt)}\)
where A is the amount of money in the account, P is the principal (initial deposit), e is the mathematical constant e (approximately equal to 2.71828), r is the interest rate (expressed as a decimal), and t is the time (in years).
Plugging in the given values, we get:
A =\(40000 * e^{(0.025 * 8)\)
Using a calculator, we find that \(e^{(0.025 * 8)\) is approximately 1.2214, so:
A = 40000 * 1.2214 = $48,856.12
Therefore, the amount of money in the account after eight years with continuous compounding is $48,856.12.
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Related Questions
Find the missing length indicated. Pls show ur work.
Answers
33-9=24
\(\\ \sf\longmapsto \dfrac{24}{9}=\dfrac{40}{-x+30}\)
\(\\ \sf\longmapsto 24(-x+30)=320\)
\(\\ \sf\longmapsto -24x+720=320\)
\(\\ \sf\longmapsto -24x=320-720=-400\)
\(\\ \sf\longmapsto x=\dfrac{-400}{-24}\)
\(\\ \sf\longmapsto x=16.6\)
_________
\( \: \)
Answer in the picture.
Which equation represents the graph below?
-10
Oy = ²r + 10
Oy - 2x + 5
O y = 5x + 2
O y
=
-5
=
x+5
-10
0
-5-
5
Answers
y = -1/3 x + 5 this equation represents the given graph.
How do you plot points on graph ?
The horizontal axis is called the x-axis. And the vertical one is the y-axis. Points are written as xy pairs in parentheses, like so: (x, y).Now, just locate the position on x-axis as well as in y-axis and finally plot where these points meet.Proof :
(0, 5) and ( 15, 0) these are the points where the graph is plotted.
y = -1/3 x + 5
put x= 0 and find y
y = 0 + 5
y = 5
put y = 0 and find x
0 = -1/3 x + 5
-5 = -1/3 x
x = 15
So, now we get the same points i.e, (0, 5) and ( 15, 0) as plotted in the given graph.
Hence, we can say that y = -1/3 x + 5 this equation represents the given graph.
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1x+11y=55 substitution
Answers
Answer:
y = -1/11 + 5
Step-by-step explanation:
1x + 11y = 55
-1x -1x
11y = -1x + 55
/11 /11
y = -1/11 + 5
Hope this helps!
A law firm is going to designate associates and partners to a big new case. The
daily rate charged to the client for each associate is $400 and the daily rate
for each partner is $900. How much would the law firm charge the client
daily if 9 associates and 5 partners were assigned to the case? How much
would the law firm charge the client daily if a associates and p partners were
assigned to the case?
Answers
Answer:
The system 800x+1300y=12300 and y = x+3 can be used to determine the number of associate assigned to the case and the number of partners assigned to the case where x represent the number of associates and y represent the number of partner
Step-by-step explanation:
Per day charge of each associate = $800
Per day charge of each partner = $1300
Total charged per day = $12300
Let,
x be the number of associates
y be the number of partners
According to given statement;
800x+1300y=12300 Eqn 1
y = x+3 Eqn 2
The system 800x+1300y=12300 and y = x+3 can be used to determine the number of associate assigned to the case and the number of partners assigned to the case where x represent the number of associates and y represent the number of partners
Divide R4 625 amongst Andrew, Brendan, and Clair so that for every R4 that
Andrew gets, Brendan gets R3 and for every R4 that Brendan gets, Clair gets
R3.
Answers
Using proportions, it is found that:
Andrew gets R 1850.Each of Brendan and Clair get R 1387.5.What is a proportion?A proportion is a fraction of total amount.
In this problem, the total amount divided is R 4625.
For every R4 Andrew gets, both Brendan and Clair gets R3, hence the ratio is 4:3:3, which means that:
Andrew gets \(\frac{4}{4 + 3 + 3} = \frac{4}{10} = 0.4\) of the total amount.Brendan gets \(\frac{3}{4 + 3 + 3} = \frac{3}{10} = 0.3\) of the total amount.Clair gets \(\frac{3}{4 + 3 + 3} = \frac{3}{10} = 0.3\) of the total amount.Then:
\(A = 0.4(4625) = 1850\)
\(B = C = 0.3(4625) = 1387.5\)
Hence:
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solution for the inequality 6x +9 ≤ 27
Answers
Answer:
6x + 9 = 27
-9 -9
6x = 18 Now divide both sides by 6
/6 /6 so the answer is 3
Step-by-step explanation:
what are the answers for these and the coordinates
Answers
Measurement Error on y i
( 1 point) Imagine the following model: y ∗
=Xβ+ε where X is n×k and β is k×1 (and k>2 ). Assume E[ε∣X]=0 and var[ε∣X]= σ ε
2
I n
. Unfortunately, you do not observe y ∗
. You observe y=y ∗
+η and estimate y=Xβ+ν by OLS. i) Write down the least squares problem for equation (3), obtain the first-order conditions, and isolate b (the resulting OLS estimator) (0.25 points). ii) Compute E(b) and describe in details the conditions under which b will be unbiased. Simply stating A3:E[ν∣X]=0 is not an acceptable answer (0.25 points). iii) Now, assuming that E[η∣X]=0 and var[η∣X]=σ η
2
I n
, compute var[b∣X] and explain how this variance will compare it to var[b ∗
∣X], where b ∗
is the OLS estimator for β in equation (1). That is, b ∗
is the OLS estimator that you would get if you could observe y ∗
and estimate equation (1)
Answers
The OLS estimator b in the presence of measurement error will be unbiased if certain conditions are met. The variance of b|X is larger than the variance of b*|X due to the additional measurement error.
i) The least squares problem for equation (3) is formulated as follows: minimize the sum of squared residuals, SSR(b) = (y - Xb)'(y - Xb). The first-order conditions give ∂SSR(b)/∂b = -2X'y + 2X'Xb = 0. Solving for b, we get b = (X'X)^(-1)X'y, which is the OLS estimator.
ii) The OLS estimator b will be unbiased if E(ν|X) = 0 and X is of full rank. Additionally, the error term ε should satisfy the classical linear model assumptions, including E(ε|X) = 0, var(ε|X) = σε^2In, and ε being uncorrelated with X.
iii) The variance of b|X is given by var(b|X) = σε^2(X'X)^(-1). Comparing it to var(b*|X), we find that var(b|X) is larger due to the presence of measurement error. The additional error term η introduces more variability into the estimated coefficients, leading to a larger variance compared to the scenario where y* is observed directly.
Therefore, The OLS estimator b in the presence of measurement error will be unbiased if certain conditions are met. The variance of b|X is larger than the variance of b*|X due to the additional measurement error.
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what is the answer to this 8a-12b+28
Answers
Answer:
4(2a−3b+7)
Step-by-step explanation:
I hope it helps.
Answer:4(2a-3b+7)
Step-by-step explanation:
take the numbers given:
8a, 12b, 28
⬇️. ⬇️. ⬇️
4x2a/4x3b/7x4
4(2a-3b+7)
So we factored the 4, or dived all the numbers by four, because four is the divisible number.
Use the figure to solve for the missing angles
Answers
m<1:51, m<2:39, m<3:90
solve the equation. (find only the real solutions. enter your answers as a comma-separated list.) 2x x 7
Answers
Answer:
14x
Step-by-step explanation:
2x*7=
2*7=14x
find an equation of the curve that passes through the point (0, 1) and whose slope at (x, y) is 5xy. (note: start your answer with y
Answers
The equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is y = (5/2) * x^2y + 1. This equation represents a curve where the y-coordinate is a function of the x-coordinate, satisfying the conditions.
To determine an equation of the curve that satisfies the conditions, we can integrate the slope function with respect to x to obtain the equation of the curve. Let's proceed with the calculations:
We have:
Point: (0, 1)
Slope: 5xy
We can start by integrating the slope function to find the equation of the curve:
∫(dy/dx) dx = ∫(5xy) dx
Integrating both sides:
∫dy = ∫(5xy) dx
Integrating with respect to y on the left side gives us:
y = ∫(5xy) dx
To solve this integral, we treat y as a constant and integrate with respect to x:
y = 5∫(xy) dx
Using the power rule of integration, where the integral of x^n dx is (1/(n+1)) * x^(n+1), we integrate x with respect to x and get:
y = 5 * (1/2) * x^2y + C
Applying the initial condition (0, 1), we substitute x = 0 and y = 1 into the equation to find the value of the constant C:
1 = 5 * (1/2) * (0)^2 * 1 + C
1 = C
Therefore, the equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is:
y = 5 * (1/2) * x^2y + 1
Simplifying further, we have:
y = (5/2) * x^2y + 1
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If hector is 8 years old and Marry is 3 years old, how old will marry be when hector is 16.
Answers
Marry will be 11 when hector is 16
Find a sinusoidal function with the following four attributes: (1) amplitude is 10, (2) period is 5, (3) midline is y = 31, and (4) ƒ(3) = 41. f(x) = =
Answers
The sinusoidal function that satisfies the given attributes is f(x) = 10 * sin(2π/5 * x - π/5) + 31.
To find a sinusoidal function with the given attributes, we can use the general form of a sinusoidal function:
f(x) = A * sin(Bx + C) + D
where A represents the amplitude, B represents the frequency (related to the period), C represents the phase shift, and D represents the vertical shift.
Amplitude: The given amplitude is 10. So, A = 10.
Period: The given period is 5. The formula for period is P = 2π/B, where P is the period and B is the coefficient of x in the argument of sin. By rearranging the equation, we have B = 2π/P = 2π/5.
Midline: The given midline is y = 31, which represents the vertical shift. So, D = 31.
f(3) = 41: We are given that the function evaluated at x = 3 is 41. Substituting these values into the general form, we have:
41 = 10 * sin(2π/5 * 3 + C) + 31
10 * sin(2π/5 * 3 + C) = 41 - 31
10 * sin(2π/5 * 3 + C) = 10
sin(2π/5 * 3 + C) = 1
To solve for C, we need to find the angle whose sine value is 1. This angle is π/2. So, 2π/5 * 3 + C = π/2.
2π/5 * 3 = π/2 - C
6π/5 = π/2 - C
C = π/2 - 6π/5
Now we have all the values to construct the sinusoidal function:
f(x) = 10 * sin(2π/5 * x + (π/2 - 6π/5)) + 31
Simplifying further:
f(x) = 10 * sin(2π/5 * x - 2π/10) + 31
f(x) = 10 * sin(2π/5 * x - π/5) + 31
Therefore, the sinusoidal function that satisfies the given attributes is f(x) = 10 * sin(2π/5 * x - π/5) + 31.
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There are two mystery numbers. The sum of 2 times the first number and 5 times the second number is -5. The sum of 3 times the first number and 10 times the second number is -5. What are the two numbers?
Answers
Answer:
the two numbers are -5 and 1
Step-by-step explanation:
Let x and y be the first number and second number respectively.
According to the question, we can find 2 equations:
2x + 5y = -5
3x + 10y = -5
On solving,
x = -5
y = 1
Answer:
X=-5,Y=1
Step-by-step explanation:
First equation: 2X+5Y=-5
Second equation:3X+10Y=-5
If we subtract the first from the second equation
(3X+10Y)-(2X+5Y)= 0 so, X+5Y= 0
So X= -5Y .then substitute in the second equation
So ,3(-5Y)+10Y= -5 , therefore -15Y + 10Y=-5 so, -5Y=-5 which means that Y=1
Then substitute with that in the first equation so 2X+5= -5
2X= -10 therefore X=-5
Choose the answer. The rate of change of y with respect to tis 3 times the value of the quantity 2 less than y. Find an equation for y given that y 212 when t=0
You get: y = 212e^3t + 2 y = 210e^3t - 2 y = 210e^3t+2
y = 212e^3t-2 y=214e^3t-2
Answers
If the rate of change of y with respect to t is 3 times the value of the quantity 2 less than y, then the equation for y is y = 210e^(3t) + 2.
Explanation:
Let's work on this problem step by step:
Step 1: The problem states that the rate of change of y with respect to t is 3 times the value of the quantity 2 less than y. This can be represented as:
dy/dt = 3(y - 2)
Step 2: We are also given that y = 212 when t = 0. This will be used later to find the constant of integration.
Step 3: Now, we need to solve the differential equation. To do this, first, separate the variables:
dy/(y - 2) = 3 dt
Step 4: Integrate both sides with respect to their respective variables:
∫(1/(y - 2)) dy = ∫(3) dt
Step 5: This gives:
ln|y - 2| = 3t + C
Step 6: To find the constant of integration C, use the given condition that y = 212 when t = 0:
ln|212 - 2| = 3(0) + C
ln|210| = C
Step 7: Substitute C back into the equation:
ln|y - 2| = 3t + ln|210|
Step 8: To remove the natural logarithm, use the exponential function:
y - 2 = 210 * e^(3t)
Step 9: Add 2 to both sides of the equation to isolate y:
y = 210 * e^(3t) + 2
So, the equation for y is y = 210e^(3t) + 2.
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An empty 16 gallon tank is being filled with gasoline at a rate of 2 gallons per minute. State the Domain and Range using interval notation or set notation
Answers
The volume of gasoline in the tank as a function of time can be determined as,
\(V=2t\)The time taken to fill the tank can be determined as,
\(\begin{gathered} 16=2t \\ t=8 \end{gathered}\)Thus, the requried domain is,
\(t\in\lbrack0,8\rbrack\)The range of the function can be determined as,
\(V\in\lbrack0,16\rbrack\)Thus, the above expressions gives the required domain and range of the function.
A hamburger and soda cost $7.50. The hamburger cost $7 more than the soda. How much does the soda cost? $7.25 $0.50 $0.25 $29 $6.50
Answers
The correct choice is $0.25. The soda costs $0.25. The total cost of the hamburger and soda is $7.50. x + (x + $7) = $7.50.
Let's denote the cost of the soda as "x" (in dollars).
According to the given information, the hamburger costs $7 more than the soda, so the cost of the hamburger can be expressed as "x + $7".
The total cost of the hamburger and soda is $7.50. We can set up the equation:
x + (x + $7) = $7.50
Simplifying the equation, we combine like terms:
2x + $7 = $7.50
Next, we isolate the variable "x" by subtracting $7 from both sides of the equation:
2x = $7.50 - $7
2x = $0.50
Finally, we solve for "x" by dividing both sides of the equation by 2:
x = $0.50 / 2
x = $0.25
Therefore, the soda costs $0.25.
So, the correct choice is $0.25.
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need help! h(x) = square root of x-10 what is the domain of h?
Answers
What are all values of x that make the equation true?
Answers
you are skiing down a mountain with a vertical height of 1290 feet. the distance from the top of the mountain to the base of the mountain is 2580 feet. what is the angle of elevation from the base to the top of the mountain?express your answer as a whole angle.
Answers
30° is the angle of elevation from the base to the top of the mountain.
Trigonometric ratios are the ratios of the length of sides of a triangle.
These ratios in trigonometry state the relation between the ratio of sides of a right triangle to the respective angle.
The basic trigonometric ratios are sin, cos, and tan, namely sine, cosine, and tangent ratios.
The other important trig ratios, cosec, sec, and cot, can be derived using the sin, cos, and tan respectively.
Sin θ = Perpendicular / Hypotenuse
According to the question,
Perpendicular = Vertical height of Mountain. = 1290 m
Hypotenuse = The distance from the top of the mountain to the base of the Mountain. = 2580 m
⇒ Sin θ = 1290/ 2580
⇒ Sin θ = 1/2⇒ θ = Sin⁻¹(1/2)
⇒ θ = 30°
Hence, 30° is the angle of elevation from the base to the top of the mountain.
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Find the slope between the two given points (-9, 5) and (-6, 2)
Answers
The slope of the line passing through the points (-9, 5) and (-6, 2) will be [m] = - 1
What is the slope intercept form of a straight line?The slope intercept of a straight line is -
y = mx + c
Where -
[m] is the slope of the line.
[c] is the y - intercept.
Given is a straight line passing through the points (-9, 5) and (-6, 2)
Given is a straight line that passes through the coordinates as follows -
(-9, 5)
(-6, 2)
The slope of the line can be calculated using the formula -
m = (y₂ - y₁)/(x₂ - x₁)
m = (2 - 5)/(- 6 + 9)
m = -3/3
m = - 1
Therefore, the slope of the line passing through the points (-9, 5) and (-6, 2) be [m] = - 1.
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Strawberries are on sale for $1.60 per pound.how much would 0.75 pounds of strawberries cost
Answers
Hi!
To solve this, we just multiply 1.6 by .75
Using a handy-dandy calculator, that is $1.20
Hope this helps! :D
Find the diameter of a cone that has a volume of 83.74 cubic inches and a height of 5 inches
Answers
Answer:
V = πr²(h/3)
Step-by-step explanation:
83.74 = πr²(5/3)
R = 4.00 in
Diamater = 2r = 2 x 4.00 = 8 inches
Consider the following program, x 2 REPEAT 4 TIMES XX * 3 Which of the following expressions represents the value stored in the variable x as a result of executing the program? a. 2*3*3*3 b. 2.4.44 c. 2'3'3'33 d. 24*4*4*4
Answers
The correct expression representing the value stored in the variable x after executing the given program is: a. 2*3*3*3 This is because the program starts with x having a value of 2 and then multiplies x by 3 four times in a row.
The expression that represents the value stored in the variable x as a result of executing the program is option D: 24*4*4*4. This is because the program starts with the x being assigned the value 2, and then the instruction "XX * 3" is executed 4 times.
This means that the value of x is multiplied by 3, four times in a row. So, the final value of x will be 2 * 3 * 3 * 3 * 3, which simplifies to 24 * 4 * 4 * 4.
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Tickets for a concert are sold at a rate of 370 tickets per hour. At this rate, how long will it take to sell all the tickets for a 2100-seat auditorium?
Answers
Answer:
5 hours and 42 mins
Step-by-step explanation:
10) Each year, in the NFL, there are 256 national football games played. You want to select a sample
of games from the past 3 years (768 games) to run some statistics for your new fantasy team. Which of the
following is the range of sample sizes you could take from this population without violating conditions required
for preforming Normal calculations with the sampling distribution of r?
(A)0 ≤ n ≤ 30
(B) 30 < n < 256
(C)30 < n< 77
(D) 30 ≤ n < 768
(E) 77 S n≤ 768
Answers
To determine the range of sample sizes that can be taken from a population of 768 games without violating the conditions required for performing normal calculations with the sampling distribution of r, we need to consider the guidelines for the Central Limit Theorem.
The Central Limit Theorem states that the sampling distribution of a statistic (such as the correlation coefficient r) approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution, under certain conditions.
One of the conditions for the Central Limit Theorem to hold is that the sample size should be sufficiently large. While there is no exact cutoff for the sample size, a general guideline is that the sample size should be at least 30.
Given this information, the correct answer choice is (C) 30 < n < 77. This range ensures that the sample size is greater than 30 and less than the total population size of 768, satisfying the conditions required for performing normal calculations with the sampling distribution of r.
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Company A has a risk percentage of 55% and a return of 14%. Company B has a risk percentage of 3% and a return of 14%. Compute the Coefficient of Variation for each company. Which company is riskier? Why?
Answers
Company A is riskier than Company B. The reason for this is that Company A has a higher risk percentage, meaning that there is a greater chance of experiencing losses, and its Coefficient of Variation is also higher.
The Coefficient of Variation (CV) is used to measure the level of risk in investment portfolios. The formula for CV is given as follows:CV = (Standard Deviation / Expected Return) × 100In this context, we can find out the Coefficient of Variation for Company A as follows:
CV for Company A = (55% / 14%) × 100%
= 392.86
Similarly, we can find out the Coefficient of Variation for Company B as follows:
CV for Company B = (3% / 14%) × 100%
= 21.43
As we can see, the CV for Company A is significantly higher than that for Company B, indicating that Company A is riskier than Company B. The reason for this is that Company A has a higher risk percentage, meaning that there is a greater chance of experiencing losses, and its Coefficient of Variation is also higher.
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Help me please this is due tommorow
Answers
Hopefully someone can see this time, please help
Answers
Answer:
m = -1
Step-by-step explanation:
The slope of the line is -1
Answer:
the slope is -1