14. equation from exercise 2; y(0) = 1, y(1) = 0, y(0) = 6, y(0) = 5.
The solution of the given differential equation is \(y=2e^x-1\).
A differential equation in mathematics is an equation that includes one or more functions and their derivatives. The rate of change of a function at a place is determined by the derivatives of the function. It is mostly employed in disciplines like physics, engineering, biology, and others. Studying equation-satisfying solutions and the solutions' characteristics is the main goal of differential equations.
We have the differential equation -
\(\frac{dy}{dx}-y=1\\\\\frac{dy}{1+y}=dx\\\\log(1+y)=x+c\\1) y(0)=1\\log2=c\\\\1+y=e^{x+c}\\y=2e^x-1\)
2)
y(1)=0
log(1+0)=1+c
c=-1
\(y=e^{x-1}\\\)
3)
y(0)=6
log7=c
\(y=e^{x+log7}-1\\y=7e^x-1\)
4)
c=log5
\(y=5e^x-1\)
The complete question is-
The given differential equation is \(\frac{dy}{dx}-y=1\),
find the particular solution on ivp y(0)=1,y(1)=0 ,y(0)=6 and y(0)=5
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a group of veterinarians at a major veterinary hospital was interested in investigating a possible link between enteroliths, stones that form in the colon of horses, and diet. they decided to conduct a survey of feeding practices of horses in the hospital's state. they created a survey questionnaire and decided to administer it to the owners of every fifth horse being treated at the hospital. the sample is a:
Fron the given question, we can say that systematic sample because not all sample are possible.
What is Systematic sampling?Using the probabilistic sampling technique known as systematic sampling, researchers periodically choose individuals from a community. Choose each 15th of her, for instance, from the population list. You can simulate the advantages of straightforward random sampling by randomly sorting the population.
\(Since every 100th horse is selected in the sample. Thus, Systematic Sampling is used.\)
Further,
Sampling method is said to be Simple Random Sampling if unit from the population are picked randomly without any criteria, so that each unit as similar chance of selection.
If any criteria are used to select every sample, such as selecting every fourth unit, the sampling technique is said to be systematic sampling.
If the population is divided into various groups that share the same characteristic, the sampling method is said to be stratified sampling. Additionally, units are chosen at random from these groups.
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The price of a video game was reduced from $80 to $32.
By what percentage was the price of the video game reduced?
Answer:
40%
Step-by-step explanation:
32/80=0.4
80×0.4=32
Answer:
40%
Step-by-step explanation:
32÷80= .4
80x0.4=32
You believe you can recruit an experienced assembler for $32/hour who can assemble 8 bicycles per hour. You can also recruit a less experienced assembler for $24/hour who can assemble 4 bicycles per hour. At least in the short term, which assembler is more cost effective?.
We make use of unitary method to find out that the first assembler is more cost effective than the second assembler.
It is given to us that -
One experienced assembler can be recruited for $32/hour who can assemble 8 bicycles per hour
Another experienced assembler can be recruited for $24/hour who can assemble 4 bicycles per hour
We have to find out the assembler who is more cost effective.
From the given information, we can say that -
First experienced assembler assembles 8 bicycles per hour and costs $32/hour.
This implies that the first experienced assembler can assemble 1 bicycle for $32/8 = $4/hour
Similarly, the second experienced assembler assembles 4 bicycles per hour and costs $24/hour.
This implies that the second experienced assembler can assemble 1 bicycle for $24/4 = $6/hour.
So, we see that the first experienced assembler is able to assemble 1 bicycle for $4/hour whereas the second experienced assembler is able to assemble 1 bicycle for $6/hour.
This implies that the first experienced assembler is more cost effective than the second experienced assembler because the first assembler can assemble the bicycles in $2/hour less than the second assembler.
Therefore, through unitary method we have concluded that the first assembler is more cost effective than the second assembler.
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Find f/(x). (a) f(x) = xsinx (b) f(x) = sech-1x²
The derivative of f(x) = sech^(-1)(x^2) is f'(x) = 2x/sqrt(1 - x^4).
a) To find f'(x) for f(x) = x*sin(x), we can use the product rule and the derivative of the sine function.
Using the product rule, we have:
f'(x) = (xsin(x))' = xsin'(x) + sin(x)*x'
The derivative of sin(x) is cos(x), and the derivative of x with respect to x is 1. Therefore:
f'(x) = x*cos(x) + sin(x)
So, the derivative of f(x) = xsin(x) is f'(x) = xcos(x) + sin(x).
(b) To find f'(x) for f(x) = sech^(-1)(x^2), we can use the chain rule and the derivative of the inverse hyperbolic secant function.
Let u = x^2. Then, f(x) can be rewritten as f(u) = sech^(-1)(u).
Using the chain rule, we have:
f'(x) = f'(u) * u'
The derivative of sech^(-1)(u) can be found using the derivative of the inverse hyperbolic secant function:
(sech^(-1)(u))' = 1/sqrt(1 - u^2)
Since u = x^2, we have:
f'(x) = 1/sqrt(1 - (x^2)^2) * (x^2)'
Simplifying:
f'(x) = 1/sqrt(1 - x^4) * 2x
So, the derivative of f(x) = sech^(-1)(x^2) is f'(x) = 2x/sqrt(1 - x^4).
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Identify the kind of sample that is described.
Every third day, a computer network administrator analyzes the company's network logs to check for signs of computer viruses.
The sample is a ______________________________ sample.
The sample is a systematic sample.
What is sample?
In statistics, a sample is a subset of individuals or objects selected from a larger population. Samples are used in statistical analyses to draw conclusions or make inferences about the entire population.
A sample is typically less time-consuming and less expensive to collect and analyze than the entire population, making it a practical and efficient way to conduct research.
A systematic sample is a type of probability sampling method in which every nth member of a population is selected to be included in the sample.
In this case, the network administrator is analyzing the company's network logs every third day, which means they are selecting every third day's data for analysis.
This is a systematic approach to selecting the data for analysis, making it a systematic sample.
Therefore, the sample is a systematic sample.
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Identify the dependent and independent variables for each relation
The faster you drive your car, the longer it will take to come to a complete stop
The Spanish classes are having a fiesta lunch. Each student that attends is to bring a Spanish side dish or dessert. The more students that attend, the more food there will be
Answer: The dependent variable is the time it takes to come to a complete stop. The independent variable is the speed at which you drive your car.
The dependent variable is the amount of food there will be. The independent variable is the number of students who attend the fiesta lunch.
Step-by-step explanation:
If the number of tomato growers in the market increases, the supply:
A) of tomatoes increases.
B) of tomatoes decreases.
C) tomatoes remains constant.
D) curve for tomatoes shifts to the left.
If the number of tomato growers in the market increases, it would generally lead to an increase in the supply of tomatoes increases.
The correct answer is A.
This is because an increase in the number of growers means that there are more producers entering the market, resulting in a greater quantity of tomatoes available for sale. As a result, the overall supply of tomatoes would increase.In terms of the supply curve, an increase in the number of growers would cause the supply curve for tomatoes to shift to the right. This signifies that at any given price, there would be a larger quantity of tomatoes supplied in the market. Consequently, consumers would have access to a greater supply of tomatoes, potentially leading to lower prices due to the increased competition among the growers. Thus, supply of tomatoes increases accurately reflects the likely outcome when the number of tomato growers increases.The correct answer is A.
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the frequency polygon and the histogram are two different ways to represent the same data set. True or false?
False. The frequency polygon and the histogram are two different ways to represent data, and they have distinct characteristics.
A frequency polygon is a line graph that displays the distribution of a quantitative variable. It shows the frequency of each value or class interval on the horizontal axis and the corresponding frequencies on the vertical axis. The points on the graph are connected to form a line, which gives a visual representation of the data distribution.
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Select all the ratios that are equivalent to each other. 4:7, 8:15, 16:28, 2:3, 20:35
Answer:
4:7 16:28 20:35
Step-by-step explanation:
Answer:
4:7 = 16:28
Step-by-step explanation:
4 × 4 = 16
7 × 4 = 28
50 points please help!!
The graph of the linear equation y = (1/4)*x - 1 is on the image at the end.
How to graph a linear equation?To graph the line, we need to find two points that belong to the line, and then we can connect them with a line.
So let's evaluate the linear equation.
if x = 0
y = (1/4)*0 - 1 = -1
We have the point (0, -1)
Now let's get another point:
if x = 4
y = (1/4)*4 - 1 = 4 - 1 = 3
We have the point (4, 3)
Now graph these two points and draw a line that connects them.
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Select the correct answer.
The Cohen family started their wheat farm in 1995. The equation models the number of bushels of wheat they produced each year, where tis
the number of years since 1995.
C(t)= 7,000+500 In(t + 1)
The Mason family also started their wheat farm in 1995. The graph models the number of bushels of wheat they produced each year, where t
is the number of years since 1995.
M(t)
A graph is a way to represent a lot of data in such a visual format that it is easy for the user to understand the complete information in one go. The correct statement is D.
What is a graph?A graph is a way to represent a lot of data in such a visual format that it is easy for the user to understand the complete information in one go. Usually, the line of the graph is a function that follows the graph.
If we draw the graph of the Cohen family, then the graph will look as shown below. Therefore, if we observe the graph of the Cohen family and the graph of the Mason family. Then we will observe that the wheat production of both farms will approach a stable amount as the years pass.
Hence, the correct statement is D.
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what is the product of x and y values 2x+8y=24 -7x-6y=26
Answer:
x= -8
y=5
Step-by-step explanation:
2x + 8y =24
2(x+4y)=24
x+4y=24/2
x+4y=12
x=12-4y
-7x-6y=26
-7(12-4y)-6y=26
22y-84=26
22y=26+84
22y=110
y=110/22
y=5
x=12-4y
x=12-4×5
x= -8
4. Landon is cooking soup. He has 15 pinan of vegetable broth, 19 pints of milk, and 14 pints of tomato juice. How many gallons does Landon have, if 1 gallon = 8 pints? 6 gallons.
Answer:
6 gallons
Step-by-step explanation:
1) add 15 and 19 to get 34
2) then add 34 and 14 to get 48
3) then divide 48 by 8 to get 6
Please answer please.
Answer:
Triangles are not similar.
Step-by-step explanation:
Properties of the similarity of two triangles,
1). Corresponding angles of two triangles are equal in measure.
2). Corresponding sides of the similar triangles are proportional.
From the given triangles,
- Corresponding angles of the given triangles are not equal in measure.
- Ratios of the corresponding sides,
\(\frac{KM}{XY}=\frac{CM}{RY}= \frac{KC}{XR}\)
\(\frac{53}{53}= \frac{54}{53}= \frac{64}{53}\)
But these ratios are not equal.
Therefore, both the triangles are not similar.
Suppose payments were made at the end of each month into an ordinary annuity earning interest at the rate of 2.5%/year compounded monthly. If the future value of the annuity after 10 years is $60,000, what was the size of each payment? (Round your answer to the nearest cent.) $
Answer:
Monthly payment= $440.71
Step-by-step explanation:
Giving the following information:
Mothly interest rate (i)= 0.025/12= 0.00208
Number of periods (n)= 12*10= 120 months
Future Value (FV)= $60,000
To calculate the monthly payment, we need to use the following formula:
Monthly payment= (FV*i) / [(1+i)^(n) - 1]
Monthly payment= (60,000*0.00208) / [(1.00208^120) - 1]
Monthly payment= $440.71
Either use an appropriate theorem to show that the given set, W, is a vector space, or find a specific example to the contrary.W = {[\begin{array}{ccc}a\\b\\c\\\d\end{array}\right] : 3a+b=c, a+b+2c=2d}
An appropriate theorem to show that the given set, W, is a vector space. A specific example can be
\(\left[\begin{array}{ccc}p\\q\\r\end{array}\right]\) , -p- -3q = s and 3p = -2s - 3r
Sets represent values that are not solutions. B. The set of all solutions of a system of homogeneous equations OC.
The set of solutions of a homogeneous equation. Thus the set W = Null A. The null space of n homogeneous linear equations in the mx n matrix A is a subspace of Rn. Equivalently, the set of all solutions of the unknown system Ax = 0 is a subspace of R.A.
The proof is complete because W is a subspace of R2. The given set W must be a vector space, since the subspaces are themselves vector spaces. B. The proof is complete because W is a subspace of R. The given set W must be a vector space, since the subspaces are themselves vector spaces.
The proof is complete because W is a subspace of R4. The given set W must be a vector space, since the subspaces are themselves vector spaces. outside diameter. The proof is complete because W is a subspace of R3. The given set W must be a vector space, since the subspaces are themselves vector spaces.
Let W be the set of all vectors of the right form, where a and b denote all real numbers. Give an example or explain why W is not a vector space. 8a + 3b -4 8a-7b. Select the correct option below and, if necessary, fill in the answer boxes to complete your selection OA. The set pressure is
S = {(comma separated vectors as required OB. W is not a vector space because zero vectors in W and scalar sums and multiples of most vectors are not in W because their second (intermediate) value is not equal to -4. OC. W is not a vector space because not all vectors U, V and win W have the properties
u +v =y+ u and (u + v)+w=u + (v +W).
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The value of y is directly proportional to the value of x. If y = 25 when x = 120, what is the value of y when x = 72?
Step-by-step explanation:
y directly proportional to X
y=kx
when k is constant
y is 25 and X is 120
25=k120
divide both sides by 120
25/120
k=25/120
there fore the law connecting is 25/120
what is the value of y when x = 72? 25/120*72=3
therefore y is 3
I need help with things ill give u points
Answer:
012
Step-by-step explanation:
please mark brainliest if correct
A college performs a survey of 424 graduates to estimate the proportion of alumni who are working in the field of study in which they obtained their college degree (e.g., the student earned a degree in biology and works in the field of biology). Of the 424 alumni, 361 reported that they were working in the field of study in which they obtained their college degree. Which of the following is the correct 98% confidence interval for the trus proportion of graduates who are working in the field of study in which they obtained their degree? Find the z-table here. a) (0.108, 0.189) b) (0.115, 0.182) c) (0.807, 0.896) d) (0.811, 0.892) e) 0 (0.818, 0.885)
The correct 98% confidence interval for the true proportion of graduates working in the field of study in which they obtained their degree is (0.811, 0.892).
To calculate the confidence interval, we need to use the formula for estimating proportions and the standard error of the proportion. The formula is:
Confidence interval = sample proportion ± z * standard error
Calculate the sample proportion
In this case, the sample proportion is the number of graduates working in their field of study (361) divided by the total number of graduates surveyed (424):
Sample proportion = 361/424 ≈ 0.852
Calculate the standard error
The standard error of the proportion is calculated using the formula:
Standard error = sqrt((sample proportion * (1 - sample proportion)) / sample size)
Using the given values, we have:
Standard error = sqrt((0.852 * (1 - 0.852)) / 424) ≈ 0.014
Determine the confidence interval
To find the z-value for a 98% confidence level, we look up the corresponding value in the z-table. The z-value for a 98% confidence level is approximately 2.33.
Substituting the values into the confidence interval formula, we have:
Confidence interval = 0.852 ± 2.33 * 0.014
Confidence interval ≈ (0.811, 0.892)
Therefore, the correct 98% confidence interval for the true proportion of graduates working in their field of study is (0.811, 0.892).
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On December 17, 2007 baseball writer John Hickey wrote an article for the Seattle P-I External link about increases to ticket prices for Seattle Mariners games during the 2008 season. The article included a data set that listed the average ticket price for each MLB team, the league in which the team plays (AL or NL), the number of wins during the 2007 season and the cost per win (in dollars). The data for the 16 National League teams are shown below. team league price wins cost/win
Order goes
Team/ League/ Price/ Wins/ cost per win
Arizona Diamondbacks /NL /19.68/ 90 /35.40
Atlanta Braves NL 17.07 /84/ 32.89
Chicago Cubs NL 34.30 /85/ 65.33
Cincinnati Reds NL 17.90 /72 /40.32
Colorado Rockies NL 14.72 /90 /26.67
Florida Marlins NL 16.70 /71 /38.13
Houston Astros NL 26.66 /73 /59.11
Los Angeles Dodgers NL 20.09 /82 /34.64
Milwaukee Brewers NL 18.11 /83 /35.37
N.Y. Mets NL 25.28 /88 /46.56
Philadelphia Phillies NL 26.73 /89 /48.69
Pittsburgh Pirates NL 17.08 /68 /40.67
San Diego Padres NL 20.83 /89 /38.15
San Francisco Giants NL 24.53 /71/ 56.00
St. Louis Cardinals NL 29.78 /78 /61.91
Washington Nationals NL 20.88 /73 /46.30
Compute the correlation between average 2007 price and number of 2007 wins for these 16 teams. (Assume the correlation conditions have been satisfied and round your answer to the nearest 0.001.)
The correlation between average 2007 price and number of 2007 is 0.207
To compute the correlation between the average 2007 price and the number of 2007 wins for the 16 National League baseball teams, we can use the formula for Pearson's correlation coefficient.
First, we need to calculate the following sums:
Sum of prices (ΣX) = 19.68 + 17.07 + 34.30 + 17.90 + 14.72 + 16.70 + 26.66 + 20.09 + 18.11 + 25.28 + 26.73 + 17.08 + 20.83 + 24.53 + 29.78 + 20.88 = 387.47
Sum of wins (ΣY) = 90 + 84 + 85 + 72 + 90 + 71 + 73 + 82 + 83 + 88 + 89 + 68 + 89 + 71 + 78 + 73 = 1296
Sum of products of prices and wins (ΣXY) = (19.68 * 90) + (17.07 * 84) + (34.30 * 85) + (17.90 * 72) + (14.72 * 90) + (16.70 * 71) + (26.66 * 73) + (20.09 * 82) + (18.11 * 83) + (25.28 * 88) + (26.73 * 89) + (17.08 * 68) + (20.83 * 89) + (24.53 * 71) + (29.78 * 78) + (20.88 * 73) = 24839.87
Sum of squared prices (ΣX^2) = (19.68)^2 + (17.07)^2 + (34.30)^2 + (17.90)^2 + (14.72)^2 + (16.70)^2 + (26.66)^2 + (20.09)^2 + (18.11)^2 + (25.28)^2 + (26.73)^2 + (17.08)^2 + (20.83)^2 + (24.53)^2 + (29.78)^2 + (20.88)^2 = 19151.7899
Sum of squared wins (ΣY^2) = (90)^2 + (84)^2 + (85)^2 + (72)^2 + (90)^2 + (71)^2 + (73)^2 + (82)^2 + (83)^2 + (88)^2 + (89)^2 + (68)^2 + (89)^2 + (71)^2 + (78)^2 + (73)^2 = 94518
Using these sums, we can calculate the correlation coefficient (r):
r = (n * ΣXY - ΣX * ΣY) / sqrt((n * ΣX^2 - (ΣX)^2) * (n * ΣY^2 - (ΣY)^2))
where n is the number of data points, which in this case is 16.
Substituting the values:
r = (16 * 24839.87 - 387.47 * 1296) / sqrt((16 * 19151.7899 - (387.47)^2) * (16 * 94518 - (1296)^2))
Calculating this expression gives us:
r ≈ 0.207
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What is the domain of √ 1 x²?
The domain of a function is the set of all possible inputs for the function.
Domain: (−∞,∞),{x|x∈R}
Range: (−∞,1],{y|y≤1}
What are the domain and range?
The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
We have,
f(x) = 1 - x²
The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x).
f(x) = 1 - x² is defined for all Real values of x and therefore the domain is all Real values (R).
x² has a minimum value of 0 (for x ∈ R)
therefore
−x² has a maximum value of 0
and
−x² + 1 = 1 − x² has a maximum value of 1.
Hence, the domain of a function is the set of all possible inputs for the function,
Domain: (−∞,∞),{x|x∈R}
Range: (−∞,1],{y|y≤1}
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If x-1= k and k=3, what is the value of x
3
Answer:
x-1/3 = k where k=3
We must be happy enough to find the value of only one valuable here, that is, x.
therefore, x-1/3=3
To find what is x-1, all we need to do is,
Take the denominator of the fraction to the answer (3)and multiply them. (that's how you'll find the values in the numerator)
So, you'll get,
x-1=3*3
x-1=9
To find the value of x,
The other number (-1) should be taken to the answer (9)
(Remember that the sign changes when the number crosses the equals sign)
therefore,
x= 9 + 1 (-1 will turn to +1 on crossing the equal sign)
Therefore , by addition, normally,
you'll get x=10
Hope this helps:)
determine whether or not the vector field is conservative. f(x,y) = 33x2y2i + 22x3yj
The vector field f(x,y) = 33x^2y^2i + 22x^3yj is conservative, and its potential function is φ(x,y) = 11x^3y^2 + 11x^2y^2 + C.
To determine if a vector field is conservative, we need to check if it is the gradient of a scalar function (i.e., a potential function). We can do this by taking the partial derivatives of each component with respect to their respective variables and checking if they are equal:
∂f_x/∂y = 66xy^2
∂f_y/∂x = 66xy^2
Since these partial derivatives are equal, the vector field is conservative. We can then find a potential function by integrating each component with respect to their respective variable:
φ(x,y) = 11x^3y^2 + 11x^2y^2 + C
where C is the constant of integration.
Therefore, the vector field f(x,y) = 33x^2y^2i + 22x^3yj is conservative, and its potential function is φ(x,y) = 11x^3y^2 + 11x^2y^2 + C.
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The number e is an irrational number approximately equal to 2. 718. Between which pair of square roots does e fall?
The pair of square roots that e fall is √1 and √9
How to determine the pair of square roots that e fall?From the question, we have the following parameters that can be used in our computation:
e = 2.718
Represent as an interval
So, we have
a < e < b
This means that
a < 2.718 < b
The number 2.718 is between 1 and 3
So, we have
1 < 2.718 < 3
Express 1 and 3 as square roots
√1 < 2.718 < √9
Hence, the pair of square roots that e fall is √1 and √9
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The pair of square roots that e falls between is √7 and √8.
What is the range that fits the square roots?The range that the figure falls between is √7 and √8. To get the range, we will find the roots of all the numbers and see the one that the figure falls between.
√2 = 1.414
√3 = 1.732
√4 = 2
√5 = 2.236
√7 = 2.645
√8 = 2.828
Now we will look at the ranges and see the one that figures 2.718 falls between. This is √7 to √8.
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Someone please help me with thisss
Answer:
The equation of the line that passes through points is m = 6/4
Step-by-step explanation: sorry if this is wrong
Due today please help!
Let an = 5n/4n + 1 Determine whether {an) is convergent. convergent divergent
To determine whether the sequence {an} = 5n/4n + 1 is convergent or divergent, we can analyze its behavior as n approaches infinity.
First, let's rewrite the expression for the nth term of the sequence:
an = 5n / (4n + 1)
As n approaches infinity, the denominator 4n + 1 becomes dominant compared to the numerator 5n. Therefore, we can simplify the expression by neglecting the term 5n:
an ≈ n / (4n + 1)
Now, we can consider the limit of the sequence as n approaches infinity:
lim(n→∞) n / (4n + 1)
To evaluate this limit, we can divide both the numerator and denominator by n:
lim(n→∞) (1 / 4 + 1/n)
As n approaches infinity, the term 1/n approaches zero, leaving us with:
lim(n→∞) 1 / 4 = 1/4
Since the limit of the sequence is a finite value (1/4), we can conclude that the sequence {an} = 5n/4n + 1 is convergent.
In other words, as n gets larger and larger, the terms of the sequence {an} get closer and closer to the limit of 1/4. This indicates that the sequence approaches a fixed value and does not exhibit wild oscillations or diverge to infinity. Therefore, we can say that the sequence is convergent.
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Quartile is also called as
SOLUTIONS
Quartile is also called as Quarter
A quartile divides data into three points—a lower quartile, median, and upper quartile—to form four groups of the dataset. The lower quartile, or first quartile, is denoted as Q1 and is the middle number that falls between the smallest value of the dataset and the median. The second quartile, Q2, is also the median.
Quartiles are values that divide your data into quarters. However, quartiles aren't shaped like pizza slices; Instead they divide your data into four segments according to where the numbers fall on the number line. The four quarters that divide a data set into quartiles are: The lowest 25% of numbers.
Therefore Quartile is also called as Quarter
Dianes salary is $32,000 per year. Her car payments total $2,880 per year. What percentage is her salary
Answer:
9%
Step-by-step explanation:
Calculation for What percentage is her salary
Using this formula
Dianes salary percentage=Car payments per year/Salary per year
Let plug in the formula
Dianes salary percentage=$2,880 per year/$32,000 per year
Dianes salary percentage=0.09*100
Dianes salary percentage=9%
Therefore the percentage of her salary is 9%