If you deposit 4,500 at the end of each of the next 20 years into an account that is paying 9.7% interest, you will have 347,401.59 in the account in 20 years. You will have 2,545,025.81 if you make deposits for 40 years.
Given that you deposited 4,500 at the end of each of the next 20 years into an account that is paying 9.7% interest. Now you have to find out how much money you will have in the account in 20 years and how much will you have if you make deposits for 40 years.
The formula to calculate the future value of an annuity due is:
[tex]FV = PMT \times [(1 + r)^{(n - 1)} / r] \times(1 + r)[/tex]
Where,
FV = Future Value
PMT = Payment (amount) each period
r = Interest Rate per period
n = Number of periods
To find the future value of an annuity due for 20 years:
[tex]FV = 4500 \times [(1 + 0.097)^{(20 - 1)} / 0.097] \times (1 + 0.097)\\FV = 4500 \times [(1.097)^{19} / 0.097] \times (1.097)\\FV = 4500 \times [(6.226)] \times (1.097)\\FV = 347,401.59[/tex]
To find the future value of an annuity due for 40 years:
[tex]FV = 4500 \times [(1 + 0.097)^{(40 - 1)} / 0.097] \times (1 + 0.097)\\FV = 4500 \times [(1.097)^{39} / 0.097] \times (1.097)\\FV = 4500 \times [(38.84)] \times (1.097)\\FV = 2,545,025.81[/tex]
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an apple falls from a tree 100 km to the ground. if the acceleration due to gravity is 9,8 m/s² and the mass of the apple is 0,2 gram. what is the potential energy of the apple?
Answer: 196 Joules (J)
Step-by-step explanation:
To calculate the potential energy of the apple, we can use the formula:
Potential Energy = Mass x Gravity x Height
First, let's convert the height from kilometers to meters:
100 km = 100,000 meters
Now, let's convert the mass of the apple from grams to kilograms:
0.2 gram = 0.0002 kilograms
Using these values, we can calculate the potential energy:
Potential Energy = 0.0002 kg x 9.8 m/s^2 x 100,000 m
Potential Energy = 196 Joules (J)
Therefore, the potential energy of the apple is 196 Joules (J).
Whic expression is not equivalent to 3x-(4-×)
The expression 3x-(4-x) is equivalent to 4x-4
The distributive property is a mathematical property that describes the relationship between multiplication and addition or subtraction. It states that when a number is multiplied by a sum or difference of two or more numbers, the result is the same as if we multiplied the number by each of the individual terms inside the parentheses and then added or subtracted the products.
To simplify the expression 3x-(4-x), we can distribute the negative sign to the second term inside the parentheses, which gives:
3x - (4 - x) = 3x - 4 + x
Now we can combine the like terms (3x and x) to get:
3x - 4 + x = 4x - 4
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The given question is incomplete, the complete question is:
Which expression is equivalent to 3x-(4-x)?
Solve for x 5x
-2(x+1)=10
Step-by-step explanation:
5x-2(x+1)=10
5x-2x+2=10
3x+2=10
3x=10-2
3x=8
8/3
2.7 if you do round it
2.666666667 before you do
x=2.7
(I think it's right Because I've already been taught this if not just tell me.)
50 POINTS PLEASE HELP
IN YOUR OWN WORDS PLEASE:)
The purpose of filling out a W-4 is to make it easier for individuals to meet their tax liability by
paying income taxes as they earn income. Paying anticipated taxes from each paycheck
reduces the amount an individual owes when filing taxes and can even result in a tax refund.
To guarantee or increase the refund, individuals sometimes claim fewer allowances (to have
more income tax withheld) or request a specific additional amount to be withheld from each
paycheck.
Daniel's employer will automatically deduct taxes from Daniel's pay using the information on
the W-4 form that Daniel completed on his first day. From his W-4 form, Daniel's employer
determined that $75 needs to be withheld from each of Daniel's weekly paychecks, totaling
$3,900 for the year.
Compare Daniel's tax liability from part B, question 3, with the total amount withheld from his
check: $3,900 for the year. If Daniel wants a refund when he files his taxes, should he have
filled out his W-4 differently? Explain your reasoning.
Answer:
To determine if Daniel should have filled out his W-4 form differently to receive a refund, we need to compare his tax liability with the total amount withheld from his paychecks for the year.
If Daniel's tax liability for the year is less than $3,900, he will receive a refund when he files his taxes. If his tax liability is more than $3,900, he will owe additional taxes when he files his taxes.
If Daniel's tax liability is exactly $3,900, he will neither owe additional taxes nor receive a refund when he files his taxes.
Therefore, to determine if Daniel should have filled out his W-4 form differently, we need to compare his tax liability with $3,900.
If Daniel's tax liability from part B, question 3, is less than $3,900, he will receive a refund when he files his taxes, as the total amount withheld from his paychecks is more than his tax liability. In this case, Daniel may want to consider filling out his W-4 form differently to reduce the amount withheld from his paychecks and increase his take-home pay.
On the other hand, if Daniel's tax liability from part B, question 3, is more than $3,900, he will owe additional taxes when he files his taxes, as the total amount withheld from his paychecks is less than his tax liability. In this case, Daniel may want to consider filling out his W-4 form differently to increase the amount withheld from his paychecks and reduce the amount he will owe when he files his taxes.
If Daniel's tax liability from part B, question 3, is exactly $3,900, he will neither owe additional taxes nor receive a refund when he files his taxes, and his W-4 form is correctly filled out for his tax situation.
In summary, whether or not Daniel should have filled out his W-4 form differently to receive a refund depends on his tax liability compared to the total amount withheld from his paychecks. If his tax liability is less than the total amount withheld, he may want to reduce the amount withheld to increase his take-home pay. If his tax liability is more than the total amount withheld, he may want to increase the amount withheld to reduce the amount he will owe when he files his taxes. If his tax liability is exactly equal to the total amount withheld, his W-4 form is correctly filled out for his tax situation.
Mary bought 8 blouses and 3 skirts for a total of $120.00. Kristy bought 5 blouses and 5 skirts at the same prices for a total of $112.50. What is the cost of each blouse and each skirt?
After solving the equations we know that the price of each blouse and each skirt is $25 and $30 respectively.
What are equations?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation.
As in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others.
The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.
So, the cost of each blouse and skirt:
x be the price of one blouse and y is the price of one skirt.
For a total of $215, Carol purchased 3 skirts and 5 blouses.
5x + 3y = 215
For a total of $135, Ellen purchased 2 skirts and 3 blouses.
3x + 2y = 135
By resolving the equations in the system:
5x + 3y = 215
3x + 2y = 135
We will obtain:
x = $25
y = $30
Therefore, after solving the equations we know that the price of each blouse and each skirt is $25 and $30 respectively.
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Correct question:
Carol bought 5 blouses and 3 skirts for a total of $215. At the same time, her sister Ellen bought 3 blouses and 2 skirts for a total of $135. What was the price of each blouse and each skirt?
PLEASE HELP FAST (giving brainliest)
First one is 6
second one is 12
third one is -8
hope this helps
Answer:
Step-by-step explanation:
x=6
x=12
x=-8
the adaptive-response-rate single exponential smoothing model is best applied to time series data that are multiple choice non stationary. stationary and non seasonal. seasonal. stationary and seasonal. seasonal and nonstationary.
The adaptive-response-rate single exponential smoothing model is best applied to time series data that are non stationary and seasonal which means option D is the right answer.
The adaptive response rate single exponential smoothing model is used to demonstrate the changes in the forecasting data and the fluctuation in data values with respect to time which are smoothened by a coefficient. The larger the coefficient, the greater the smoothing effect.
This kind of model is ineffective for stationary time series as it takes into account the smoothing of the information. Adaptive smoothing is computationally difficult. Exponential smoothing produces accurate forecasts. The forecast shows projected demand and actual demand.
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(04.03 MC)
Find the area of the polygon.
A 41 square units
B 44 square units
C 52 square units
D 56 square units
The area of given polygon is 44 square units from the given graph.
What is Polygon ?
A polygon is a 2-dimensional geometric shape that is formed by joining a finite number of straight line segments to form a closed shape.
The area of each triangle can be found by using the formula:
Area = (base * height)/2
Triangle 1: Base = 4 units, Height = 5 units
Area of Triangle 1 = (4*5)/2 = 10 square units
Triangle 2: Base = 8 units, Height = 3 units
Area of Triangle 2 = (8*3)/2 = 12 square units
The area of the trapezoid can be found by using the formula:
Area = (Sum of parallel sides * Height)/2
Trapezoid: Height = 4 units, Parallel side 1 = 3 units, Parallel side 2 = 7 units
Area of Trapezoid = ((3+7)*4)/2 = 20 square units
Therefore, the total area of the polygon is:
Total Area = Area of Triangle 1 + Area of Triangle 2 + Area of Trapezoid
Total Area = 10 + 14 + 20 = 44 square units
Hence, The area of given polygon is 44 square units from the given graph.
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if 10 friends are going to occupy 10 seats in shuttle on the way to the airport, how many different ways can they arrange themselves in the shuttle? provide your answer below:
If 10 friends are going to occupy 10 seats in a shuttle on the way to the airport, then they can arrange themselves in the shuttle in 10! or 3,628,800 ways.
Step-by-step explanation: There are 10 friends and 10 seats to be occupied in a shuttle.
Therefore, the number of ways to arrange the 10 friends in 10 seats is given by 10! (10 factorial), which is calculated as follows: 10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1= 3,628,800
Therefore, 10 friends can arrange themselves in the shuttle in 3,628,800 ways.
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2x + y = -7
3x = 6 + 4y
x = ?
y = ?
2x + y = -7
y= -7-2x
put this value in 2nd equation
3x=6+4(-7-2x)
3x=6-28-8x
11x= -22
x= -2
y= -7-2(-2)
y= -7+4
y= -3
Please help and please hurry
i need help ASAP
Calculate the amount of interest on $2,000.00 for 4 years, compounding daily at 2.25 % APR.
From the Monthly Interest Table use $1.094171 in interest for each $1.00 invested
A $2,088.34
B $2188.34
C $2,288.34
D $2,388.34
Answer:
Step-by-step explanation:
First, we need to calculate the annual interest rate from the given APR.
APR = 2.25%
Daily interest rate = 2.25% / 365 = 0.00616438
Now, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the final amount
P = the principal (initial amount)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = time in years
In this case, P = $2,000, r = 0.00616438, n = 365 (daily compounding), and t = 4.
A = 2000(1 + 0.00616438/365)^(365*4)
A = 2000(1.00616438)^1460
A = $2,388.34 (rounded to the nearest cent)
Therefore, the answer is option D) $2,388.34.
15 - (p + 1) where p = 3 and 4 = 10 calculate
Answer:
11
Step-by-step explanation:
15 - (p + 1)
Let p=3
15 - (3 + 1)
Parentheses first
15 - (4)
11
Answer:
11
Step-by-step explanation:
Given that,
p = 3
So, to find the value of the expression you have to solve it by replacing p with 3.
15 - ( p + 1 )
15 - ( 3 + 1 )
15 - 4
11
Evaluate. 547+233×5−142 whats this answer
The answer to the expression 547 + 233 × 5 - 142 is 1752. To solve the expression, we must follow the order of operations, which is PEMDAS: Parentheses, Exponents, Multiplication, and Division (performed left to right), and Addition and Subtraction (performed left to right).
Since there are no parentheses or exponents in this expression, we start with multiplication and division. In this case, we have to multiply 233 by 5, which gives us 1165. Then, we add 547 to 1165, which gives us 1712. Finally, we subtract 142 from 1712, which gives us the final answer of 1752. Therefore, the result of the expression 547 + 233 × 5 - 142 is 1752, which can be obtained by following the order of operations and performing the arithmetic operations in the correct order.
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If f(1) = 10, and f(n) = f(n-1) + 4, then find the value of
ƒ (4).
The value of f(4) using recursive formula f(1) = 10 and f(n) = f(n-1) + 4 for n ≥ 2 is 22
Finding the Value of f(4) Using Recursive FormulaGiven that f(1) = 10 and f(n) = f(n-1) + 4 for n ≥ 2.
To find the value of f(4), we can use the recursive formula to work our way up from f(1) to f(4):
Using the above as a guide, we have the following:
f(2) = f(1) + 4 = 10 + 4 = 14
Next, we have
f(3) = f(2) + 4 = 14 + 4 = 18
Next, we have
f(4) = f(3) + 4 = 18 + 4 = 22
Therefore, the value of f(4) is 22.
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If you add two positive numbers together, which of the following is true about the result?
Answer:
If you add two positive numbers together you will get a positive.
Step-by-step explanation:
what moves beyond excel graphs and charts into sophisticated analysis techniques such as controls, instruments, maps, time-series graphs, and more?
Answer:
Data Visualization Tools
Step-by-step explanation:
Pls help answer with good detailed explanation
Jacqui wants to prove that figures abc and def are similar. Which series of transformations would prove that these two figures are similar
One figure should be rotated to match the other's alignment. Expand one figure till it is the same size as another.
what is transformations ?A figure or object in a coordinate plane can be transformed to create a new figure or object that has been relocated, flipped, or altered in some other way. Translations, rotations, and reflections are the three primary forms of transformations. Moving a figure horizontally or vertically without altering its size or shape is known as translation. Rotation entails angling a figure around a fixed point, often known as the rotational center.
given
The subsequent transformations must be used in order to demonstrate similarity between two figures:
Translation (moving the figures to the same spot) (moving the figures to the same position)
Rotation (rotation one figure to fit the other) (rotating one figure to match the other)
Dilation (resizing the figures such that they have the same shape, but maybe different sizes) (resizing the figures so that they have the same shape, but possibly different sizes)
Consequently, the following set of transformations should be used to demonstrate that the figures abc and def are similar.
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what is an equivalent expression to 4x(2x-3)-5(3x-4)
Answer:4x + 3x + 2x - 4 - 3
Step-by-step explanation:Hope this helps
solve for x, using a tangent and secant line
Check the picture below.
[tex]x^2=(8+2)(2)\implies x^2=20\implies x=\sqrt{20}\implies x\approx 4.5[/tex]
The value of x is 4.5 rounded to the nearest tenth.
What is Tangent and Secant of a Circle?Tangent of a circle is defined as the line which passes through exactly one point on the circle.
Secant of a circle is the line which passes through two points on the circle.
Secant-Tangent Rule states that if a tangent and a secant are drawn to a circle from the same point outside the circle, then the square of the length of the tangent segment is equal to the product of the lengths of secant and the segment of secant outside the circle.
Using the theorem, we can say here that,
(8 + 2) 2 = x²
x² = 10 × 2
x² = 20
x = √20
x = 4.472 ≈ 4.5
Hence the value of x is 4.5.
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Are the ratios 4:3 and 5:4 equivalent?
Answer:
They're not promise
Step-by-step explanation:
I did it on the calculator
I hope this helps youuu
Have a good day <3
Solve for x. Round to the nearest tenth of a degree, if necessary.
please help me I will give brainliest to whoever helps me
Answer: x= 71
Step-by-step explanation:
Since each triangle has a sun of all the angles to equal 180, we can figure what is X.
in a survey, 69% of americans said they own an answering machine. if 15 americans are selected at random, find the probability that exactly 7 own an answering machine. round your answer to three decimal places.
Rounding to three decimal places, the probability that exactly 7 Americans out of a sample of 15 own an answering machine is approximately 0.170.
To find the probability that exactly 7 of the 15 Americans selected at random own an answering machine, we can use the binomial distribution formula:
P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)
where P(X = k) is the probability of getting exactly k successes, n is the sample size, p is the probability of success, and (n choose k) is the binomial coefficient which represents the number of ways to choose k successes out of n trials.
In this case, n = 15, p = 0.69 (the proportion of Americans who own an answering machine), and k = 7. Thus, the probability of getting exactly 7 Americans who own an answering machine out of a sample of 15 is:
P(X = 7) = (15 choose 7) * 0.69^7 * (1 - 0.69)^(15 - 7)
Using a calculator or statistical software, we can evaluate this expression to find:
P(X = 7) ≈ 0.170
This means that if we were to repeat this survey many times with samples of size 15, we would expect approximately 17% of the samples to have exactly 7 Americans who own an answering machine.
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the population of a community is known to increase at a rate proportional to the number of people present at time t. if an initial population p0 has doubled in 5 years, how long will it take to triple? to quadruple?
It will take 7.5 years for the population to triple, and 10 years for the population to quadruple.
The population of a community is known to increase at a rate proportional to the number of people present at time t. This means that the rate of increase is directly proportional to the population.
If an initial population of p0 has doubled in 5 years, we can calculate how long it will take to triple or quadruple the population.
To triple the population, we use the equation: t = (5 years x 3) / 2, where t is the amount of time it takes for the population to triple. This gives us t = 7.5 years.
To quadruple the population, we use the equation: t = (5 years x 4) / 2, giving us t = 10 years.
In summary, it will take 7.5 years for the population to triple, and 10 years for the population to quadruple.
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At rolling hills middle school the ratio of the total number of students to the number of students with pets is 3 to 1 if there are 243 students at the school how many students have pets
If there are 243 students at the school, then there are 81 students at Rolling Hills Middle School who have pets.
If the ratio of the total number of students to the number of students with pets at Rolling Hills Middle School is 3 to 1, this means that for every 3 students at the school, there is 1 student with a pet.
Let's represent the total number of students at the school as "3x" (since the ratio is 3 to 1, we can use any multiple of 3 as a placeholder for the total number of students), and the number of students with pets as "x". Therefore, we can write the following equation:
3x : x = 3 : 1
To solve for x, we can cross-multiply:
3x * 1 = x * 3
3x = 3x
We can see that the equation is true for any value of x, which means that there are many possible solutions. However, since we know that the total number of students at the school is 243, we can use this information to solve for x:
3x = 243
x = 81
Therefore, there are 81 students at Rolling Hills Middle School who have pets.
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Find the slope of the line that passes through the points A( 2, -4 ) and B( 3, 4 ).
The slope of AB =
Answer: slope=4
Step-by-step explanation:
[tex]Slope=\frac{y2-y1}{x2-x1}[/tex]
[tex]Slope=\frac{4- - 4}{3-2}[/tex]
[tex]Slope=\frac{4+4}{3-2}[/tex]
[tex]Slope=4[/tex]
Find one solution for the equation, (2x-3)(3x+5)=0.
The two solutions to the equation (2x - 3)(3x + 5) = 0 when solved are x = 3/2 and x = -5/3
How to determine the solution to the equationGiven that, we have the following equation
(2x - 3)(3x + 5) = 0
The above equation means that
2x - 3 = 0 and 3x + 5 = 0
When the equations are evaluated, the equations becoms
2x = 3 and 3x = -5
Lastly, we divide both sides of the equation by the coefficent of x i.e 2 and 3
So, we have
x = 3/2 and x = -5/3
So, the values of the solutions to the equation are x = 3/2 and x = -5/3
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assume that you want to construct a 95% ci for the mean of a normal distribution with population variance 30. the sample average is 10 and the sample size is 20. what is the lower limit of the ci? approximate your answer using only one decimal.
By using the formula for the confidence interval and the standard error, we were able to calculate the lower limit of the interval as 7.59.
To construct a 95% CI for the population mean of a normal distribution, we can use the formula:
CI = sample mean ± z* (standard error)
Where z* is the critical value from the standard normal distribution that corresponds to a 95% confidence level (i.e., 1.96), and the standard error is calculated as:
standard error = population standard deviation / √sample size
In this case, we are given that the population variance is 30, so the population standard deviation is √30 = 5.48 (rounded to two decimal places). The sample size is 20, so the standard error is:
standard error = 5.48 / √20 = 1.226
Now, we can use the formula for the CI:
CI = 10 ± 1.96 x 1.22
Simplifying this expression gives us:
CI = (7.59, 12.41)
This means that we are 95% confident that the true population mean lies within the interval from 7.59 to 12.41. The lower limit of the CI is 7.59, rounded to one decimal place.
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Rewrite the following equation in slope-intercept form. Y + 5 = 1 7 ( x + 7 )
Answer: y = 17x + 114
Step-by-step explanation:
The equation for the slope-intercept form is y = mx + b.
Arrange the equation so that it resembles y = mx + b.
You will do this by multiplying and subtracting so y is on the left side of the equation and mx + b is on the right side of the equation.
y + 5 = 17(x + 7)
y + 5 = 17x + 119
y + 5 - 5 = 17x + 119 - 5
y = 17x + 114
Answer:
Y = 17x + 114
Step-by-step explanation:
1. Y + 5 = 17 (x+7)
2. Y + 5 = 17x + 119 [Multiply the numbers in parenthesis by 17.]
3. Y = 17x + 114. [To keep the balance and move the 5 over, subtract it from 119.]