The operation manager at a tire manufacturing company believes that the mean mileage of a tire is 36,30936,309 miles, with a standard deviation of 46934693 miles. What is the probability that the sample mean would differ from the population mean by less than 170170 miles in a sample of 211211 tires if the manager is correct
Answers
The probability that the sample mean would differ from the population mean by less than 170 miles in a sample of 211 tires is approximately 0.994 or 99.4%.
We can use the central limit theorem to find the probability that the sample mean would differ from the population mean by less than 170 miles in a sample of 211 tires.
According to the central limit theorem, the distribution of sample means will be approximately normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
Therefore, we can calculate the z-score as follows:
z = (\(\bar{X}\) - μ) / (σ / √n)
where \(\bar{X}\) is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
In this case, we want to find the probability that the sample mean would differ from the population mean by less than 170 miles, which means we need to find the probability that the z-score is between -170/ (σ / √n) and 170/ (σ / √n).
Plugging in the given values, we get:
z = (\(\bar{X}\) - μ) / (σ / √n)
z = (170) / (4693 / √211)
z ≈ 8.13
Using a calculator, we can find that the probability of getting a z-score less than 8.13 or greater than -8.13 is approximately 1.0. Therefore, the probability is approximately 0.994 or 99.4%.
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Related Questions
at the end of 2024, marin co. has accounts receivable of $673,200 and an allowance for doubtful accounts of $24,010. on january 24. 2025, it is learned that the company's receivable from madonna inc. is not collectible and therefore management authorizes a write- off of $4.147.
Answers
The write-off of the receivable from Madonna Inc. is a necessary adjustment to ensure the accuracy of Marin Co.'s financial statements. Without it, the company's accounts receivable would be overstated and their financial statements would not provide an accurate portrayal of the company's financial position.
At the end of 2024, Marin Co. had accounts receivable of $673,200 and an allowance for doubtful accounts of $24,010. On January 24th, 2025, it was determined that the company's receivable from Madonna Inc. was not collectible and management authorized a write-off of $4,147. This action reduces the accounts receivable balance by $4,147, and reduces the allowance for doubtful accounts by the same amount. The net effect on the balance sheet is a reduction of $4,147 in both accounts receivable and allowance for doubtful accounts.
The impact of the write-off on the company's financial statements is a decrease in net income for the period. This is because a write-off is recognized as an expense, which reduces the amount of net income reported in the period. The amount of the write-off is recorded as an expense on the income statement. In this case, the amount of the write-off is $4,147.
The journal entry to record the write-off would be: Accounts Receivable 4,147; Allowance for Doubtful Accounts 4,147. This entry reduces the accounts receivable and allowance for doubtful accounts by $4,147. The write-off of $4,147 is recorded as an expense on the income statement, and this reduces the net income reported for the period.
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Plzzzz helppp!! Determine the type of triangle that is drawn below
Answers
isosceles Acute
Step-by-step explanation:
I think I'm pretty sure that right sorry if I'm wrong
PLEASE HELP NO ONES ANSWERING SEE IMAGE BELOW
Answers
Answer:
Step-by-step explanation:
A)16
B)25
C)121
Answer:
(1.) 12
(2.) 20
(3.) 110
Step-by-step explanation: The first answer I'm going to use as an example. Because there is 4 people, one person who is shaking everybody's hands does not count. So we wouldn't count that person making the equation 4x3=12.
If we did add that person we would be basically saying that everyone is shaking their own hands as well as everybody else.
Because there is 4 people and even if you wrote this out on paper and put it out... like
1,2,3,4 showing the number of people and underneath it putting 3 and then adding it all up you would still get 12.
hree dice are tossed, one red, one blue, and one green. what outcomes make up the event a that the sum of the three faces showing equals 5?
Answers
The outcome that makes up the event a that the sum of the three faces showing equal 5 is; P(E) = 1/36
There are three dice, thus.
Set the Red die to R.
Set the Blue die to B.
Green Dice should be G.
Now, none of the six potential numbers can be bigger than 3 in order for the sum of the three numbers on all dice to equal 5.
So, P(R) = 3/6.
Now, if P(R) = 3/6, none of the other 2 dice can produce 3 or more because doing so would cause the sum to exceed the necessary 5.
So, P(B) = 2/6.
Now that P(R) and P(B) have been obtained, P(Y) must be 1/6.
As a result, P(E) = 3/6 2/6 1/6 is the result that constitutes the event that the sum of the three faces shown equals 5.
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Ankit reads 1/3 of a story book on firstday and ¼of the book on the second day what part of the book is yet to read by Ankit?
Answers
Answer:
5/12
Step-by-step explanation:
need common denominator
so 1/3 =4/12 and 1/4=3/12
4/12 + 3/12=7/12
whole book is 12/12-7/12=5/12
what is the percent change in 7.50 and 9.00
Answers
Answer:
I believe its 20% not exactly sure tho.
Step-by-step explanation:
You're welcome.
It's easy it's : 7.50=750% 9.00=900
good luck!:)
the use of statistics and probability are critical to continuous improvement projects. explain the role they have in continuous improvement projects?
Answers
Statistics and probability play a critical role in continuous improvement projects by providing tools and methods to gather, analyze, and interpret data.
Continuous improvement projects are aimed at identifying and eliminating waste, reducing defects, improving efficiency, and increasing customer satisfaction. To achieve these goals, it is necessary to collect data and use it to make informed decisions about the process being improved.
Here are some specific ways in which statistics and probability are used in continuous improvement projects:
Data Collection: Statistics provides techniques for collecting data that are accurate, relevant, and representative of the process being studied. By collecting data over time, trends can be identified, and patterns can be discovered.
Data Analysis: Probability and statistics provide tools for analyzing data, including graphical techniques such as histograms and control charts, and numerical techniques such as descriptive statistics and regression analysis.
These techniques can help to identify the root causes of problems and quantify the impact of changes made to the process.
Hypothesis Testing: Probability and statistics provide methods for testing hypotheses about the process being studied.
For example, hypothesis testing can be used to determine whether a change made to the process has had a statistically significant impact on the output.
Process Improvement: Probability and statistics provide methods for optimizing processes, such as design of experiments (DOE) and statistical process control (SPC).
These methods can be used to identify the optimal settings for process parameters, such as temperature or pressure, that will result in the desired output.
In summary, statistics and probability are essential tools in continuous improvement projects. They provide the means to collect, analyze, and interpret data, test hypotheses, and optimize processes.
By using these tools, organizations can make data-driven decisions that lead to continuous improvement and increased efficiency.
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is this the right answer to it?
Answers
Answer:
Yes
Hope i helped
Six times the difference of a number and 9 is 54. Find the number.
Answers
Answer: 6
Step-by-step explanation:
9 x 6 =54
54/9 =6
Answer:
x=18
Step-by-step explanation:
6(x-9)=54
Divide by 6 on each side
x-9=9
Add 6 on both sides
x=18
2(7x-7)=14x-20
with work plss and ty :)
Answers
Answer:
0=-6 (No solution)
Step-by-step explanation:
2(7x-7)=14x-20 - Distribute the 2 to 7x-7
14x -14 = 14x -20 - Subtract +14 from both sides
+ 14 +14
14x = 14x -6
-14x -14x
0=-6
Help me with this, it’s due in a bit!
Answers
Answer:
64 square centimeters
Step-by-step explanation:
The surface are of a pyramid is found by finding the sum of the area of the four sides and the base.
Finding the triangular face:
Area of triangle = \(\frac{1}{2} b h\) = \(\frac{1}{2}*4*6 = 12\)
12 * 4 (4 sides) = 48 square cm
Finding the Base = \(w * l = 4 * 4 = 16\)
Finally, we add it together. 48 + 16 = 64
Your mother is very fond of collecting rare philodendron (an ornamental and
indoor plant). If she has a garden which measures 100 m2 (10 m by 10 m)
and each philodendron will occupy an estimated area of 0. 6 by 0. 6 m of the
garden, what is the maximum number of philodendron plants that will occupy
the whole area?
help me please
Answers
The maximum number of philodendron plants that will occupy the whole area is 256.
The term area in math is defined as the region bounded by the shape of an object
Here we have given that your mother is very fond of collecting rare philodendron and here we have know that If she has a garden which measures 100 m² and each philodendron will occupy an estimated area of 0. 6 x 0. 6 m of the garden.
Here we have to 10 meters divided by 0.6 of a meter gives 16 philodendrons in one direction and the same number in the other direction.
Then the maximum number of plants is calculated as,
=> 16 x 16 = 256
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Consider the seriessum_{n=1}^infty frac{1}{n(n+3)}Determine whether the series converges, and if it converges, determine its value. Converges (y/n): Value if convergent (blank otherwise):
Answers
The value of the series is frac{11}{18}. This series converges. To see why, we can use the comparison test with the series sum_{n=1}^infty frac{1}{n^2}, which is a known convergent series.
Specifically, we have frac{1}{n(n+3)} < frac{1}{n^2} for all n >= 1, and so by comparison, the given series converges as well.
To find the value of the series, we can use partial fractions to write:
frac{1}{n(n+3)} = frac{1}{3n} - frac{1}{3(n+3)}
Then, we can split up the series into two telescoping sums:
sum_{n=1}^infty frac{1}{n(n+3)} = sum_{n=1}^infty (frac{1}{3n} - frac{1}{3(n+3)})
= (frac{1}{3(1)} - frac{1}{3(4)}) + (frac{1}{3(2)} - frac{1}{3(5)}) + (frac{1}{3(3)} - frac{1}{3(6)}) + ...
Notice that most of the terms cancel out, leaving us with just:
sum_{n=1}^infty frac{1}{n(n+3)} = frac{1}{3} (1 + frac{1}{2} + frac{1}{3})
= frac{11}{18}
Therefore, the value of the series is frac{11}{18}.
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(c) A non-uniform but spherically symmetric charge distribution has a charge density: rho(r)=rho 0
(1−r/R)
rho(r)=0
for r≤R
for r>R
where rho 0
=3Q/πR 3
is a positive constant. Show that the total charge contained in this charge distribution is Q. [4] Show that the electric field in the region r>R is identical to that created by a point charge Q at r=0 [2] Derive an expression for the electric field in the region r≤R. [5]
Answers
To show that the total charge contained in the charge distribution is Q, we integrate the charge density over the entire volume. The charge density is given by:
ρ(r) = ρ₀(1 - r/R) for r ≤ R,
ρ(r) = 0 for r > R,
where ρ₀ = 3Q/πR³.
To find the total charge, we integrate ρ(r) over the volume:
Q = ∫ρ(r) dV,
where dV represents the volume element.
Since the charge density is spherically symmetric, we can express dV as dV = 4πr² dr, where r is the radial distance.
The integral becomes:
Q = ∫₀ᴿ ρ₀(1 - r/R) * 4πr² dr.
Evaluating this integral gives:
Q = ρ₀ * 4π * [r³/3 - r⁴/(4R)] from 0 to R.
Simplifying further, we get:
Q = ρ₀ * 4π * [(R³/3) - (R⁴/4R)].
Simplifying the expression inside the parentheses:
Q = ρ₀ * 4π * [(4R³/12) - (R³/4)].
Simplifying once more:
Q = ρ₀ * π * (R³ - R³/3),
Q = ρ₀ * π * (2R³/3),
Q = (3Q/πR³) * π * (2R³/3),
Q = 2Q.
Therefore, the total charge contained in the charge distribution is Q.
To show that the electric field in the region r > R is identical to that created by a point charge Q at r = 0, we can use Gauss's law. Since the charge distribution is spherically symmetric, the electric field outside the distribution can be obtained by considering a Gaussian surface of radius r > R.
By Gauss's law, the electric field through a closed surface is given by:
∮E · dA = (1/ε₀) * Qenc,
where ε₀ is the permittivity of free space, Qenc is the enclosed charge, and the integral is taken over the closed surface.
Since the charge distribution is spherically symmetric, the enclosed charge within the Gaussian surface of radius r is Qenc = Q.
For the Gaussian surface outside the distribution, the electric field is radially directed, and its magnitude is constant on the surface. Hence, E · dA = E * 4πr².
Plugging these values into Gauss's law:
E * 4πr² = (1/ε₀) * Q,
Simplifying:
E = Q / (4πε₀r²).
This is the same expression as the electric field created by a point charge Q at the origin (r = 0).
To derive an expression for the electric field in the region r ≤ R, we can again use Gauss's law. This time we consider a Gaussian surface inside the charge distribution, such that the entire charge Q is enclosed.
The enclosed charge within the Gaussian surface of radius r ≤ R is Qenc = Q.
By Gauss's law, we have:
∮E · dA = (1/ε₀) * Qenc.
Since the charge distribution is spherically symmetric, the electric field is radially directed, and its magnitude is constant on the Gaussian surface. Hence, E · dA = E * 4πr².
Plugging these values into Gauss's law:
E * 4πr² = (1/ε₀) * Q.
Simplifying:
E = Q / (4πε₀r²).
This expression represents the electric field inside the charge distribution for r ≤ R.
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Jessica deposits $4000 into an account that pays simple interest
at a rate of 3% per year. How much interest will she be paid in the
first 5 years
Answers
The following is the response to the query:supposing Jessica puts $4,000 into an account that accrues simple interest at a 3% annual rate.
The answer to the question is as follows:Given that Jessica deposits $4000 into an account that pays simple interest at a rate of 3% per year.To find the amount of interest Jessica will be paid in the first 5 years, we'll need to use the simple interest formula.Simple Interest = (P * r * t) / 100Where,P = principal amount (initial amount deposited) = $4000r = annual interest rate = 3%t = time = 5 yearsSubstituting the given values, we have:Simple Interest = (P * r * t) / 100= (4000 * 3 * 5) / 100= $600Hence, the amount of interest Jessica will be paid in the first 5 years is $600.
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The amount of interest Jessica will be paid in the first 5 years is $600.
The following is the response to the query:
Supposing Jessica puts $4,000 into an account that accrues simple interest at a 3% annual rate.
The answer to the question is as follows:
Given that Jessica deposits $4000 into an account that pays simple interest at a rate of 3% per year.
To find the amount of interest Jessica will be paid in the first 5 years, we'll need to use the simple interest formula.
Simple Interest = \(\frac{(P * r * t)}{100}\)
Where,
P = principal amount (initial amount deposited) = $4000r
= annual interest rate = 3%
t = time = 5 years
Substituting the given values, we have:
Simple Interest = \(\frac{(P * r * t)}{100}\)
= \(\frac{(4000 * 3 * 5)}{100}\)
= $600
Hence, the amount of interest Jessica will be paid in the first 5 years is $600.
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The president wife is leading a humanitarian mission.
A. presidents
B. president's
C. presidents'
D. presidentes'
Answers
Answer:
B
Step-by-step explanation:
Technically it's describing something that belongs to the president.
Answer:
A
Step-by-step explanation:
I chosen A because it is the right answer
for 105 consecutive days, a process engineer has measured the temperature of champagne bottles as they are made ready for serving. each day, she took a sample of 9 bottles. the average across all 945 bottles (105 days, 9 bottles per day) was 52 degrees fahrenheit. the standard deviation across all bottles was .9 degrees fahrenheit. when constructing an x-bar chart, what would be the upper control limit?
Answers
The upper control limit for the x-bar chart for the temperature of champagne bottles is 52.243 degrees Fahrenheit for standard deviation.
To find the upper control limit for an x-bar chart, we use the formula:
Upper Control Limit = X-bar + A2 * (standard deviation / \(\sqrt{(sample size)}\))
Where X-bar is the average temperature across all bottles (52 degrees Fahrenheit), A2 is a constant factor based on the sample size (for a sample size of 9, A2 is 0.729), and the standard deviation is 0.9 degrees Fahrenheit.
Plugging in these values, we get:
Upper Control Limit = 52 + 0.729 * (0.9 / \(\sqrt{9}\))
Upper Control Limit = 52 + 0.243
Upper Control Limit = 52.243 degrees Fahrenheit
Therefore, the upper control limit for the x-bar chart for the temperature of champagne bottles is 52.243 degrees Fahrenheit. This means that if any sample of 9 bottles has an average temperature above this limit, it may indicate a problem with the process that needs to be addressed.
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The upper control limit (UCL) for the X-bar chart is 52.9 degrees Fahrenheit.
We will use the following terms to find the upper control limit (UCL) for an X-bar chart:
Average temperature (µ) = 52 degrees Fahrenheit
Standard deviation (σ) = 0.9 degrees Fahrenheit.
Sample size (n) = 9 bottles
Number of days (m) = 105 days.
To find the UCL, we first need to find the standard error (SE) using the formula:
SE = σ / √n
Substitute the given values into the formula:
SE = 0.9 / √9 = 0.9 / 3 = 0.3 degrees Fahrenheit
Now we'll use the control chart formula to find the UCL, which is:
UCL = µ + 3 * SE
Substitute the values:
UCL = 52 + 3 * 0.3 = 52 + 0.9 = 52.9 degrees Fahrenheit.
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A car trip is 1/2h shorter that a bus trip. How long is the car trip if the bus trip is 3/4h?
Answers
Answer:
1/4h
Step-by-step explanation:
The car trip is 1/2h shorter than the bus trip.
The bus trip is 3/4h long.
Therefore, the length of the car trip is:
3/4h - 1/2h = 1/4h
The car trip is 1/4h long.
1)bowl a contains 2 red chips; bowl b contains two white chips; and bowl c contains 1 red chip and 1 white chip. a bowl is selected at random, and one chip is taken at random from that bowl. what is the probability of selecting a white chip? if the selected chip is white, what is the probability that the other chip in the bowl is red?
Answers
Probability that selected chip is white: 1/2
Probability that the other chip in the bowl is red given if the selected chip is white: 1/3
Let A be the event that bowl A is randomly selected; let B be the event that bowl B is randomly selected; and let C be the event that bowl C is randomly selected. All these three bowls are equally likely to be selected:
P(A) = P(B) = P(C) = 1/3
The probability of selecting a white chip from a bowl depends on from which bowl the chip is selected.
Let W be the event that a white chip is randomly selected.
Attached is the picture solution.
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the probility of alvins mother will server rice with dinner is 0.78 the probilty that she will server carrots is with dinner is 0.30
Answers
The probability of both rice and carrots being served with dinner is 23.4%.
The probability of Alvin's mother serving rice with dinner can be expressed using the formula P(Rice) = 0.78. This means that the probability of Alvin's mother serving rice with dinner is 78%. The probability of Alvin's mother serving carrots with dinner can be expressed using the formula P(Carrots) = 0.30. This means that the probability of Alvin's mother serving carrots with dinner is 30%. To calculate the combined probability of both rice and carrots being served with dinner, we can use the formula P(Rice and Carrots) = P(Rice) * P(Carrots) = 0.78 * 0.30 = 0.2340. This means that the probability of both rice and carrots being served with dinner is 23.4%.
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in a class in which the final course grade depends entirely on the average of four equally weighted 100-point tests, mark has scored 90, 86, and 85 on the first three. what range of scores on the fourth test will give mark a c for the semester (an average between 70 and 79, inclusive)? assume that all test scores have a non-negative value.
Answers
Answer:
b/w 19 & 55
Step-by-step explanation:
average of four equally weighted 100-point tests,
mark has scored 90, 86, and 85 on the first three.
C average = 70 and 79
90+86+85+x = 4*70 = 280, so x=19
90+86+85+x = 4*79 = 316, so x=55
A package of 6 pairs of insulated socks cost 49.74 What is the unit price of the pairs of socks?
Answers
49.74 / 6
= 8.29
What is the slope of a line parallel to the line whose equation is 3x – 3y = -45.
Fully reduce your answer,
Answers
Answer:
One
Step-by-step explanation:
A parallel line has the same slope of the original graph. Because of this, all we need to do is put the equation you gave into slop-intercept form, or:
y = mx + b
Don't forget that m is the slope, and b is the y-intercept!
3x - 3y = 45
-3y = -3x + 45
y = x + 15
Compare this to the equation of the slope-intercept form and look for m:
y = mx + b
There's nothing in front of the variable! No worries, that's the same thing as saying 1x.
But mathematicians are a little lazy (lol) and they don't want to mistake the number 1 for the lowercase letter L or a capital i. Because of that, they made 1x equal x.
Long story short, the slope for the equation (3x – 3y = -45) is one. And because parallel lines have the same slope as their original counterparts, the slope is one as well!
I recommend trying a few other problems like these. You'll end up using them a lot in the future!
Good luck and keep studying!
Find the sum of the interior angles of a dodecagon ( 12 sides ) show work for your answer!  ❤️
Answers
Answer:
Sum of Interior Angles = (Number of Sides -2) • 180 degrees
Sum = (12 -2) * 180
Sum of the interior angles = 1,800 degrees
Source: http://www.1728.org/polygon.htm
Step-by-step explanation:
Determine a feedback control law x1 = x3 + 8x2
x2 = -x2 + x3
x3 = - x3 + x4/1 - x2/1+u
y = x1
exactly linearizing the system.
Answers
Answer:
Step-by-step explanation:
dv/dt + z = x3 + dx4/dt/(1 + u - w - x3) - w*dx2/dt/(1 + u - w - x3)^2
dv/dt + z = x3 + dx4/dt/(1
80t²u(t) For a unity feedback system with feedforward transfer function as 60(8+34) (s+4)(8+8) G(s): 8² (8+6)(8+17) The type of system is: Find the steady-state error if the input is 80u(t): Find the steady-state error if the input is 80tu(t): Find the steady-state error if the input is 80t²u(t): =
Answers
The given unity feedback system is the type-1 system, which can be observed from the given open-loop transfer function G(s).
Steady state error is the difference between the input and the output as time approaches infinity. It is also the difference between the desired value and the actual output at steady-state.
The steady-state error is calculated using the error coefficient, which depends on the type of the system.Find the steady-state error if the input is 80u(t):The transfer function of the given system can be written as follows;G(s) = 80(8²)/(s+4)(8+6)(8+17)The type of the given system is the type-1 system.
As the input to the system is u(t), the error coefficient is given as,Kp = lims→0sG(s) = 80/4(6)(17) = 5/153The steady-state error can be found out by the following formula;
ess = 1/Kp = 153/5.
Therefore, the steady-state error of the given system if the input is 80u(t) is 153/5.Find the steady-state error if the input is 80tu(t):As the input to the system is tu(t), the error coefficient is given as,Kv = lims→0s²G(s) = 0The steady-state error can be found out by the following formula;ess = 1/Kv = ∞.
Therefore, the steady-state error of the given system if the input is 80tu(t) is infinity.Find the steady-state error if the input is 80t²u(t):As the input to the system is t²u(t), the error coefficient is given as,Ka = lims→0s³G(s) = ∞The steady-state error can be found out by the following formula;
ess = 1/Ka = ∞.
Therefore, the steady-state error of the given system if the input is 80t²u(t) is infinity.
By using the error coefficient formula, we have found that the steady-state error of the given system if the input is 80u(t) is 153/5, steady-state error of the given system if the input is 80tu(t) is infinity and steady-state error of the given system if the input is 80t²u(t) is infinity.
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given the equation y = 3x, complete the table of values.
(just give me the output numbers)
Answers
given the equation y = 3x, complete the table of values.
x = -2
y = 3x
y = 3(-2)
y = -6
______________________
x = -1
y = 3x
y = 3(-1)
y = -3
______________________
x = 0
y = 3x
y = 3(0)
y = 0
______________________
x = 1
y = 3x
y = 3(1)
y = 3
______________________
x = 2
y = 3x
y = 3(2)
y = 6
______________________
many academic institutions offer a sabbatical policy. every seven years a professor is given a year free of teaching and other administrative responsibilities at full pay. for a professor earning $70,000 per year who works for a total of 42 years, what is the present value of the amount she will earn while on sabbatical if t
Answers
Present value of the amount she will earn while on sabbatical if the interest rate is 6% is $126,964.34
The value of money reduces as time passes, this is due to the interest factor. $1 is worth more today than tomorrow this is because of the time value of money. The present value of cash flows is discounted value of future cash flows. Discount factors at a given rate of interest are used to find out the present value of cash flows.
Here, the professor will receive $70,000 every 7 years for 42 years.
Hence he will receive $70,000 sabbatical in the 7th, 14th,21st,28th,35th, and 42nd years.
We will find the present value of such receipts and add them.
R=0.06
F=$70,000
\(Present~Value = \displaystyle\frac{FV}{(1+r)^7}+\frac{FV}{(1+r)^{14}}+\frac{FV}{(1+r)^{21}}+\frac{FV}{(1+r)^{28}}+\frac{FV}{(1+r)^{35}}+\frac{FV}{(1+r)^{42}}\)
\(Present~Value = \displaystyle\frac{70,000}{(1.06)^7}+\frac{70,000}{(1.06)^{14}}+\frac{70,000}{(1.06)^{21}}+\frac{70,000}{(1.06)^{28}}+\frac{70,000}{(1.06)^{35}}+\frac{70,000}{(1.06)^{42}}\)
=$126,964.34
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How many even numbers less than 500 can be formed using 1,2 3 4 5?
Answers
28 different even numbers can be formed using 1,2,3,4 and 5 that are less than 500.
To form the even number from a combination of five different numbers 1 to 5 and the even number less that will be formed from such a combination are less than 500. Therefore, in this scenario, 28 different event numbers will be formed. The cases to formed the even number from 1,2,3,4 and 5 are given below:
Case 1: There is only one digit in the number.
The only even integers in this situation are 2 and 4, adding up to a total of 2.
Case 2: There are exactly two digits in the number.
In this instance, the first digit must be one of the other four permitted digits and the last digit must be either 2 or 4, for a sum of 2*4=8.
Case 3: There are exactly three digits in the number.
In this instance, the middle digit must be one of the other four permitted digits, and the last digit must either be 2 or 4.
The total will be 2*3*2=12 if the middle digit is not 5, which means the first digit must be one of two digits other than the final two digits and 5.
As a result, there exist 28 even numbers with the digits 1, 2, 3, and 5 that are less than 500.
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Sketch a graph of f(x) = e−x+ 2. State the domain and range in
interval notation.
Please show me the work in precalculus way thank you
Answers
Sketching a graph of the function f(x) = e-x+ 2 and state its domain and range in interval notation:Let's first discuss the domain of the given function which is all real numbers, as there are no restrictions for the input value (x) of the function. Therefore, the domain of f(x) = e-x+ 2 is:Domain: (-∞,∞)
Next, we will discuss the range of the given function, which is all real numbers greater than or equal to 2. We can see that the function e-x is always greater than zero because e is a constant whose value is approximately 2.718 and x is always negative. When we add 2 to e-x, we get values of f(x) greater than or equal to 2.
the range of f(x) = e-x+ 2 is:Range: [2,∞)Let's now sketch the graph of the given function:Image attached shows the graph of the given function, f(x) = e-x+ 2.
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