In response to stated question, we may state that You will need to stitch about 5.0089 metres of piping around the outside border of the area tablecloth, rounded to the closest 0.1 m, for a total length of 5.0 m.
What is area?The size of just an area on either a surface can be represented as an area. The area of an open surface or the border of a two half object is called to as the surface area, meanwhile the area of a horizontal region or planar region pertains to the area of a shape or planar layer. The entire amount of space occupied by a horizontal (2-D) surface or form of an item is referred as its area. With a pencil, draw an square on a sheet of paper. A two-dimensional character. The area of a form on paper is the quantity of area it takes up. Consider the square to be made up of smaller unit squares.
Begin by calculating the radius of the circular tablecloth. We know that the formula A = r2 gives the area of a circle, where A is the area and r is the radius. Hence we may rearrange this formula to find r:
r = √(A/π) = √(2/π) ≈ 0.7979 m (rounded to four decimal places) (rounded to four decimal places)
Now we must determine the circumference of the circle, which is the distance around the tablecloth's outside border. The circumference is calculated using the formula C = 2r.
C = 2π(0.7979) ≈ 5.0089 m
You will need to stitch about 5.0089 metres of piping around the outside border of the tablecloth, rounded to the closest 0.1 m, for a total length of 5.0 m.
To know more about area visit:
https://brainly.com/question/13194650
#SPJ1
Which values from the given replacement set make up the solution set of the inequality?
2b−4≥3 ; {2,3,4,5}
A. {2,3}
B. {3,4,5}
C. {4,5}
D. {2,3,4}
Answer:
We can solve the inequality by adding 4 to both sides:
2b - 4 + 4 ≥ 3 + 4
2b ≥ 7
b ≥ 7/2
The values in the replacement set that are greater than or equal to 7/2 are {3, 4, 5}. Therefore, the solution set is:
{3, 4, 5}
So the answer is B. {3, 4, 5}.
Evaluate. Write your answer as a fraction or whole number without exponents.
6^–3 =
Answer:
i'm pretty sure it's 33
Step-by-step explanation:
6^= 36
36-3= 33
Factor
[tex]64h^3+216k^9[/tex]
Answer:
Factor 64h^3+216k^9
Step-by-step explanation:
The given expression is a sum of two terms:
[64h^3+216k^9
Notice that each term has a common factor. For the first term, the greatest common factor (GCF) is 64h^3, and for the second term, the GCF is 216k^9. So we can factor out these GCFs to get:
64h^3+216k^9 = 64h^3(1 + 3k^6)
This expression cannot be factored any further, so the final answer is:
64h^3+216k^9 = 64h^3(1 + 3k^6)
If you can, give me brainliest please!
find the general solutions to the following inhomogeneous first-order linear differential equations using the particular solution method: i. y 0 3y
The general solution to the given differential equation is y(t) = C * e^(3t).
To find the general solution to the inhomogeneous first-order linear differential equation y'(t) - 3y(t) = 0, follow these steps:
Step 1: Identify the homogeneous equation, which is y'(t) - 3y(t) = 0.
Step 2: Solve the homogeneous equation by finding the general solution. In this case, it is y_h(t) = C * e^(3t), where C is a constant.
Step 3: Identify the inhomogeneous part of the equation, which is missing in this case. Since the given equation is already homogeneous, there is no need to find a particular solution.
Step 4: Combine the homogeneous solution and the particular solution (if present) to form the general solution. In this case, the general solution is y(t) = y_h(t) = C * e^(3t).
So, the general solution to the given differential equation is y(t) = C * e^(3t).
Learn more about Equation
brainly.com/question/24169758
#SPJ11
The equivalent ratios are 2:5 , _ : _ , and _ : _ .
Answer:
The equivalent ratios are 2:5, 4:10, and 10:25
Step-by-step explanation:
2:5 * 2 = 4:10 and 2:5 * 5 = 10:25
the population of chicago is about 3 million. how does that compare to the total number of dead and wounded in world war i? (give your answer as a fraction)
if a sample of 5 lightbulbs is selected, find the probability that none in the sample are defective.
The probability of selecting a sample of 5 lightbulbs without any defective bulbs is then given by p^5, where p is the probability of not having a defective bulb.
In this situation, the probability of selecting a sample of 5 lightbulbs without any defective bulbs is calculated using the binomial distribution. The probability of success, p, is the probability that a single lightbulb is not defective, and the probability of failure, q, is the probability that a single lightbulb is defective. The probability of selecting 5 lightbulbs with no defective bulbs is then given by the equation:
P(x=0) = (p^5)*(q^0) = p^5
In this case, p is the probability of not having a defective bulb, and q is the probability of having a defective bulb. The probability of selecting 5 lightbulbs without any defective bulbs is then given by p^5.
For example, if the probability of not having a defective bulb is 0.95 and the probability of having a defective bulb is 0.05, then the probability of selecting a sample of 5 lightbulbs without any defective bulbs is 0.95^5 = 0.7737. This means that there is a 77.37% chance of selecting a sample of 5 lightbulbs without any defective bulbs.
To sum up, the probability of selecting a sample of 5 lightbulbs without any defective bulbs is calculated using the binomial distribution. The probability of success is the probability of not having a defective bulb, and the probability of failure is the probability of having a defective bulb. The probability of selecting a sample of 5 lightbulbs without any defective bulbs is then given by p^5, where p is the probability of not having a defective bulb.
The correct question is:
A box contains 100 bulbs, out of which 10 are defective. If a sample of 5 lightbulbs is selected, find the probability that none in the sample are defective
To know more about probability refer here:
https://brainly.com/question/30034780
#SPJ11
Neal buys a board game. He pays for the board game and pays
$
1.54
$1.54dollar sign, 1, point, 54 in sales tax. The sales tax rate is
5.5
%
5.5
Proportionately, the cost of the board game without the sales tax is $28.00.
What is the sales tax?The sales tax is the levy imposed by the government on the consumption and production of certain goods and services.
The purposes of imposing sales taxes are to discourage consumption and to increase governmental revenue.
Proportion refers to the equation of two ratios.
In this situation, we can equate the value of the sales tax with its percentage to determine the cost of the board game.
The sales tax in dollars = $1.54
The sales tax rate = 5.5%
Proportionately, the value of the board game without the sales tax = $28.00 ($1.54/5.5%).
Learn more about the sales tax at https://brainly.com/question/30109497
#SPJ1
Question Completion:How how is the cost?
what is the problem with this question item that appeared in a survey? was your phone purchased in the last two years and have you recently updated it?
Option B, The fact that this survey question is a double-barreled question makes it problematic.
A survey question known as a double-barreled question has two questions inside one, making it challenging for respondents to give truthful and insightful responses.
The offered inquiry, in this instance, combines two distinct inquiries: if the phone was acquired within the last two years and whether it has recently had an upgrade.
Inconsistent answers might result from a person who bought their phone more than two years ago but only recently upgraded it, or vice versa. In order to prevent double-barreled questions and guarantee that responders can give precise and complete replies, each question should be isolated and posed independently.
Learn more about the survey at
https://brainly.com/question/17373064
#SPJ4
The question is -
What is the problem with this question item that appeared in a survey? was your phone purchased in the last two years and have you recently updated it?
a. It is a leading question
b. It involves negative wording
c. It is a double-barreled question
d. It is not on a Likert Scale
You wish to compute the 90% confidence interval for the population proportion. How large a sample should you draw to ensure that the sample proportion does not deviate from the population proportion by more than 0. 08? No prior estimate for the population proportion is available
To compute a 90% confidence interval for the population proportion with a margin of error of 0.08 and no prior estimate for the population proportion, a sample size of 181 is needed.
To determine the sample size needed to compute the 90% confidence interval for the population proportion with a margin of error of 0.08, we can use the formula:
n = (z^2 * p * (1 - p)) / E^2
where n is the sample size needed, z is the z-score for the desired confidence level (90% confidence level has a z-score of 1.645), p is the estimated proportion (since no prior estimate is available, we use 0.5 as a conservative estimate), E is the margin of error (0.08)
Substituting the given values, we get:
n = (1.645^2 * 0.5 * (1 - 0.5)) / 0.08^2
n = 180.99
Rounding up to the nearest whole number, we get:
n = 181
Therefore, a sample size of 181 is needed to compute the 90% confidence interval for the population proportion with a margin of error of 0.08, when no prior estimate for the population proportion is available.
To know more about confidence interval:
https://brainly.com/question/30979600
#SPJ4
3. if you measure an interval of 5 seconds between seeing a lighting flash and hearing the thunder, how far away was the lighting? assume the temperature of the air was 20 degree celsius.
It took 5 seconds for the thunder to be heard, the lightning was 343 * 5 = 1715 meters away.
The distance between the lightning flash and hearing the thunder can be calculated using the speed of sound. The speed of sound in air at 20°C is 343 meters/second.
Explanation: When lightning strikes, the initial flash travels at the speed of light, which is 299,792,458 meters per second. The sound wave created by the flash, however, travels at a much slower speed.
The speed of sound in air at 20°C is 343 meters per second.
To calculate the distance of the lightning, we multiply the speed of sound by the amount of time it took to hear the thunder. In this case, the amount of time was 5 seconds, so the lightning was 1715 meters away (343 * 5 = 1715).
To know more about lightning flash click on below link:
https://brainly.com/question/1045095#
#SPJ11
exploraton in math suppose a principal amount of $15,400 is borrowed at a simple interest rate 15% for a period of 13 years. determine the amount of simple interest owed for the use of this loan. round the solution to the nearest cent, if necessary. the amount of simple interest owed is
The amount of simple interest owed for the loan is $30,010.00.
A method for determining the proportion of interest paid on a sum over a predetermined period of time at a predetermined rate is called simple interest. In simple interest, the principal amount remains unchanged. A straightforward and simple method for calculating money interest is simple interest.
To calculate the simple interest, we use the formula:
Simple Interest = P * r * t
where P is the principal amount, r is the interest rate as a decimal, and t is the time period in years.
Substituting the given values, we get:
Simple Interest = $15,400 * 0.15 * 13
= $30,010.00
Therefore, the amount of simple interest owed for the use of the loan is $30,010.00.
Learn more about Simple Interest:
https://brainly.com/question/25793394
#SPJ4
the pharmacy sends the nurse the following coreg tablets. the order is to administer 9.375 mg po daily. how many tablets will the nurse administer? enter only the numeral (not the unit of measurement) in your answer.
The nurse will administer 3 tablets of Coreg to meet the prescribed dosage of 9.375 mg PO daily.
The prescription order is for the nurse to administer 9.375mg of Coreg tablets orally each day. The Coreg tablets have a dosage strength of 3.125mg per tablet. To calculate the number of tablets the nurse needs to administer, we can divide the total dosage needed (9.375mg) by the dosage strength per tablet (3.125mg per tablet).
This results in the nurse administering 3 tablets to meet the prescribed dosage. Therefore, the nurse should give 3 tablets of Coreg to the patient each day to ensure they receive the correct amount of medication.
Learn more about division here
brainly.com/question/4933139
#SPJ4
The given question is incomplete, the complete question is:
the pharmacy sends the nurse the following coreg tablets. the order is to administer 9.375 mg po daily. how many tablets will the nurse administer? enter only the numeral (not the unit of measurement) in your answer.
A line passes through the point (2, 3) and has a slope of 5.
Write an equation in slope-intercept form for this line.
Answer:
y=5x-7
Step-by-step explanation:
Perform the indicated operation.
f(x) = −3x² + 3x; _g(x) = 2x+5
(ƒ + g)(3)
The composite function (f + g)(3) when evaluated from f(x) = −3x² + 3x and g(x) = 2x+5 is -7
Calculating the composite functionGiven that
f(x) = −3x² + 3x and
g(x) = 2x+5
To perform the operation (ƒ + g)(3), we need to add the functions ƒ(x) and g(x) first, and then evaluate the sum at x = 3.
ƒ(x) = −3x² + 3x
g(x) = 2x + 5
To add the functions, we simply add their corresponding terms:
(ƒ + g)(x) = ƒ(x) + g(x) = (−3x² + 3x) + (2x + 5)
When the like terms are evaluated, we have
(ƒ + g)(3) = −3x² + 5x + 5
Now, we can evaluate the sum at x = 3:
(ƒ + g)(3) = −3(3)² + 5(3) + 5
So, we have
(ƒ + g)(3) = −27 + 15 + 5
Lastly, we have
(ƒ + g)(3) = -7
Therefore, (ƒ + g)(3) = -7.
Read more about composite function at
https://brainly.com/question/10687170
#SPJ1
when a person standing in neutral flexes their right shoulder so that their arm is horizontal with the ground, the center of gravity (mass) will
When a person standing in neutral flexes their right shoulder so that their arm is horizontal with the ground, the center of gravity (mass) will shift towards the left side of the body.
Explanation:
What is center of gravity?The point at which the weight of a body or an object is concentrated, that is, the point at which the mass of the body or the object is focused is known as the center of gravity. The center of gravity (CG) is the point where the weight of the body is supposed to act, which is the point about which the body remains in balance. The body's center of gravity is important because it affects its balance and stability
.When a person is standing in a neutral position, the center of gravity is in the midline of the body. When the person flexes their right shoulder and holds their arm horizontally, the center of gravity will shift towards the left side of the body. This is because the weight of the arm is now being supported by the left side of the body. The shift in the center of gravity will cause the person to adjust their posture to maintain balance and stability.
To know more about center of gravity:
https://brainly.com/question/17409320
#SPJ11
suppose that x is the number of cars per minute that pass through a certain intersection, and that x has the poisson distribution. what can be the smallest value of x? enter your answer in accordance to the question statemententer your answer in accordance to the question statement
The smallest value of x in the Poisson distribution is 0, which means that no cars can pass through the intersection in a given minute.
For explain further, a Poisson distribution is a statistical model that describes the probability of a given number of events occurring in a fixed period of time, such as cars passing through an intersection in a minute.
In a Poisson distribution, the probability of x events occurring in a given minute is given by the equation P(x) = e-λλx/x!, where λ is the average number of events in a given minute. In this case, λ would be the average number of cars that pass through the intersection per minute.
The probability of 0 cars passing through the intersection in a given minute is e-λλ0/0! = 1, which is the highest probability in the distribution. Therefore, the smallest value of x in a Poisson distribution is 0.
To learn more about Poisson distribution here:
https://brainly.com/question/7283210#
#SPJ11
a 336-m long fence is to be cut into pieces to make three enclosures, each of which is square. how should the fence be cut up in order to minimize the total area enclosed by the fence?
The fence ought to be cut into 12 pieces, every one of length 28 m, to make three squares, each with a side length of 28 m. This will limit the total area encased by the fence.
To limit the total area encased by the fence, the three squares ought to have equivalent areas. Let x be the length of each side of the squares. Then the perimeter of each square is 4x, and the total length of the fence is 3(4x) = 12x. Since the total length of the fence is given to be 336 m, we have:
12x = 336
Addressing for x, we get:
x = 28
Find out more about fence
brainly.com/question/14785438
#SPJ4
The rate of the jetstream is 300 mph traveling with the jetstream an airplane can fly 3000 miles in the same amount of time as it takes to fly 1000 miles against the jetstream. What is the airplanes, average rate in calm air?
The airplane's average rate in calm air is 600 mph.
What is an average?
In mathematics, the average is a measure of the central tendency of a set of numerical values, which is computed by adding all the values in the set and dividing them by the total number of values. The average is also known as the mean, and it is one of the most commonly used measures of central tendency in statistics
Let's denote the airplane's average rate in calm air by x mph.
When the airplane is flying with the jetstream, its ground speed (speed relative to the ground) is x + 300 mph. We know that it can fly 3000 miles in the same amount of time it takes to fly 1000 miles against the jetstream, so we can set up the following equation:
3000 / (x + 300) = 1000 / (x - 300)
We can cross-multiply to simplify:
3000(x - 300) = 1000(x + 300)
Expanding the brackets gives:
3000x - 900000 = 1000x + 300000
Simplifying and rearranging terms gives:
2000x = 1200000
x = 600
Therefore, the airplane's average rate in calm air is 600 mph.
To learn more about averagevisit the link:
https://brainly.com/question/130657
#SPJ9
Disha states that the circumference and the area of the larger circle are both double the
circumference and the area of the smaller circle. Is she correct? Explain why or why not.
D
10
10
answer two questions about the following rational division.
1. The quotient in lowest terms of the given rational division is (x+2)/(3x-9).
2. The values of r is A. x=-2 and B. x=0.
What is factor?Factor is a quantity which when multiplied by another quantity, produces a given product. Factors are used to simplify and solve equations, as well as in other areas of mathematics. Factors can be numbers, variables, and expressions.
To find the lowest terms, we must divide the numerator and denominator by the same number. The largest common factor of the numerator and denominator is 3. Dividing both the numerator and denominator by 3, we get (x+2)/(3x-9) = (x+2)/(x-3).
The values of r that must be excluded from the domains of the expressions are x=0 and x=3. x=0 must be excluded because it will create a zero in the denominator which is not allowed. x=3 must also be excluded because it will create a zero in the numerator, and thus make the entire expression equal to 0. Thus, the correct answer is A. x=-2 and B. x=0.
For more questions related to division
https://brainly.com/question/25289437
#SPJ1
what happens to the sector area of a circle if you double its radius? what happens to the arc length of a circle if you double its radius? why do you think that happens?
The sector area of a circle is quadrupled when the radius is doubled. When the radius is doubled, the arc length of a circle is also doubled. This happens because the sector area and arc length are both dependent on the radius of a circle. Therefore, any change in the radius of a circle affects both its sector area and arc length.
Let us understand both these concepts in detail:
Sector area of a circle: A sector is a region of a circle, and the area enclosed by two radii and an arc is known as a sector area. The formula for the sector area of a circle is given by:
Sector Area = (θ/360)πr²
where θ is the central angle in degrees,
r is the radius of the circle,
and is a constant value.
If we double the radius of a circle, the sector area increases by a factor of 4. This is because the sector area is directly proportional to the square of the radius.
Hence, doubling the radius of a circle results in an increase in the sector area by a factor of 22 (four).
Arc length of a circle: The length of an arc is the distance between two points on a circle. The formula for the arc length of a circle is given:
Arc Length = (θ/360)2πr
where θ is the central angle in degrees,
r is the radius of the circle,
and 2pie is a constant value.
If we double the radius of a circle, the arc length also doubles.
This is because the arc length is directly proportional to the radius.
Hence, doubling the radius of a circle results in an increase in the arc length by a factor of 2.
To learn more about “Sector Area” refer to the https://brainly.com/question/22972014
#SPJ11
in a simple linear regression analysis, if the coefficient of correlation is -0.933, then the percentage of the total sum of squares that can be explained by using the estimated regression equation is
In a simple linear regression analysis, the coefficient of correlation (also known as the Pearson correlation coefficient) measures the strength and direction of the linear relationship between the dependent variable and the independent variable.
A value of -0.933 indicates a strong negative correlation, meaning that as one variable increases, the other variable tends to decrease.
To determine the percentage of the total sum of squares that can be explained by using the estimated regression equation, we need to look at the coefficient of determination (R-squared). R-squared is the proportion of the variance in the dependent variable that is explained by the independent variable(s).
The square of the coefficient of correlation (r) gives us the R-squared value. Therefore, in this case, the R-squared value would be:
R-squared = (-0.933)^2 = 0.871
This means that 87.1% of the total sum of squares can be explained by using the estimated regression equation. The remaining 12.9% of the variation in the dependent variable is unexplained and is attributed to other factors that are not included in the model.
For more details about Pearson click here:
https://brainly.com/question/30897203#
#SPJ11
how is 21.3-31.2= -9.9 when it should be 10.1?
Answer: answer is 9.9
Step-by-step explanation: becuz 31.2 - 21.3 = 9.9
u have to substract 21.3 from 31.2 . if u subtract 21.3 from 31.2 then it will be 9.9
but ig u did subtract 31.2 from 21.3....
In an election, there were three candidates;⅔ of the electors voted for the first candidates,¼ for the second candidate and the rest for the third candidate. If the third candidate got 3290 votes, how many votes did the winner get? Solve this and show All your workings
The winner of the election got 26320 votes.
Let's first find the total number of votes cast in the election. We know that 2/3 fraction of the electors voted for the first candidate and 1/4 of the electors voted for the second candidate. Therefore, the remaining 1/12 of the electors voted for the third candidate. So, we have:
2/3 + 1/4 + 1/12 = 8/12 + 3/12 + 1/12 = 12/12 = 1
This means that all the electors voted, and the total number of votes cast is equal to the total number of electors.
Now, let's find the number of votes the third candidate got, which is 1/12 of the total number of votes. We know that this is equal to 3290. So, we have
1/12 x Total Number of Votes = 3290
Multiplying both sides by 12, we get:
Total Number of Votes = 3290 x 12 = 39480
Now, we can find the number of votes the first candidate got, which is 2/3 of the total number of votes. We have:
2/3 x Total Number of Votes = 2/3 x 39480 = 26320 votes
Learn more about fraction here
brainly.com/question/8764267
#SPJ4
GM is tangent to circle O at point G, and GS
is a secant line. If mGS = 84°, find
m/SGM.
Since GM is tangent tο circle O at pοint G, the intercepted arc GE has measure zerο. ,then ∠SGM = 84°.
What is secant line?Secant line is alsο knοwn as average rate οf change οf functiοns between twο pοints and alsο called slοpe.
the tangent line is perpendicular tο the radius that passes thrοugh the pοint οf tangency. Therefοre, we have:
m∠MGS = 90°
Alsο, we knοw that the measure οf an angle fοrmed by a tangent line and a secant line that intersect οutside the circle is half the difference οf the intercepted arcs.
m∠SGM = 1/2 (mSE - mGE)
where SE is the intercepted arc by secant GS, and GE is the intercepted arc by tangent GM.
Since GM is tangent tο circle O at pοint G, the intercepted arc GE has measure zerο.
mSE = 2mGS
mSE = 2(84°) = 168°
m∠SGM = 1/2 (mSE - mGE) = 1/2 (168° - 0°) = 84°
Therefοre, m∠SGM = 84°.
To knοw more about secant line visit,
https://brainly.com/question/14438198
#SPJ1
Roland's family drove 4 6/10 kilometers from their home to the gas station. They drove 2 30/100 kilometers from the gas station to the store. Which expression can be used to determine the number of kilometer Ronald's family drove altogether
The following phrase can be used to calculate the total amount of kilometre that Roland's family travelled: 2 30/100 plus 4 6/10 equals 69/10 kilometres.
The distance from house to the gas station and the distance from the gas station to the store must be added in order to calculate the total number of kilometre driven by Roland's family.
The distance between their house and the petrol station is 4 6/10 kilometres, which can also be expressed using an incorrect fraction as follows:
4 6/10 = (4 × 10 + 6) / 10 = 46/10
The distance between the petrol station and the store can be expressed as 2 30/100 kilometres, which can be written as follows:
2 30/100 = (2 × 100 + 30) / 100 = 230/100
We sum the two distances to get the total distance travelled:
46/10 + 230/100
We must identify a common denominator in order to add these fractions. Both 10 and 100 can be divided into only one single digit, which is 100. Hence, using 100 as the common denominator, we can rewrite the expression as follows:
(46/10) * (10/10) + (230/100) * (1/1)
That amounts to:
460/100 + 230/100 = 690/100
So, by dividing the numerator and denominator by their 10 greatest common factor, we may reduce this fraction:
690/100 = (690 ÷ 10) / (100 ÷ 10) = 69/10
As a result, the following phrase may be used to calculate the total amount of kilometres driven by Roland's family:
2 30/100 plus 4 6/10 equals 69/10 kilometres.
Learn more about kilometer here:
https://brainly.com/question/30581160
#SPJ1
A bag contains 6 red marbles and 1 blue marble. A marble is taken at random, put to one side, and then another marble is taken at random. What is the probability that at least one of the marbles takes was blue?
Give your answer as a fraction in its simplest form
We have 6 red and 1 blue marble thus the probability of drawing blue marble = 1/7
To understand probability as a concept, pay attention to the steps below.
Step 1. Multiply the individual probabilities to obtain the chance of numerous separate events.
Step 2. As there are two separate events in this scenario, double the probabilities of each.
Step 3. Add the individual probabilities to obtain the chance of several events that are mutually exclusive.
In this bag of 7 marbles, there is 1 blue one. Assume that each is marked with a number. Choosing blue-1 has a 1/7 chance of happening. (Why? As there are 7 marbles that may be chosen, each with an equal probability, and since those 7 occurrences are mutually exclusive, the 7 probabilities total up to 1.)
The probability of choosing blue-2 is similarly 1/7; the same goes for blue-3,..., and blue-8. To determine the likelihood of picking a blue, add those up (and blue).
Step 4. Do the same for red next.
Thus the probability of drawing blue marble = 1/7
Learn more about probabilities at
brainly.com/question/30034780
#SPJ4
A regular hexagon and a regular pentagon have a common edge. Work out the value of a.
the answer is below with full explanation
A first-year teacher wants to retire in 40 years. The teacher plans to invest in an account with a 6.95% annual interest rate compounded continuously. If the teacher wants to retire with at least $125,000 in the account, how much money must be initially invested? Round your answer to the nearest dollar.
Therefore, the teacher must initially invest at least $7,725 to retire with at least $125,000 in the account after 40 years at a 6.95% annual interest rate compounded continuously.
What is percent?Percent is a way of expressing a number as a fraction of 100. It is often denoted by the symbol "%". Percentages are commonly used to describe proportions or rates, such as the percentage of students who passed a test, the percentage of a population that belongs to a certain group, or the percentage increase or decrease in a quantity over time. Percentages are also used in calculations involving discounts, taxes, interest rates, and other financial applications.
Here,
The formula for the continuous compounding interest is given by:
[tex]A = Pe^{rt}[/tex]
where A is the final amount, P is the principal amount (initial investment), e is the constant 2.71828..., r is the annual interest rate as a decimal, and t is the time in years.
In this case, we want to solve for the initial investment P, given that the teacher wants to retire with at least $125,000 in the account after 40 years, and the annual interest rate is 6.95% compounded continuously. Therefore, we have:
A = $125,000
r = 0.0695 (annual interest rate as a decimal)
t = 40 years
Substituting these values into the formula, we get:
$125,000 = [tex]Pe^{0.0695*40}[/tex]
Dividing both sides by [tex]e^{0.0695*40}[/tex], we get:
P = $125,000 / [tex]e^{0.0695*40}[/tex]
Using a calculator, we find that [tex]e^{0.0695*40}[/tex] is approximately 16.173, so:
P = $125,000 / 16.173
P ≈ $7,725.32
To know more about percent,
https://brainly.com/question/29172752
#SPJ1