Check the picture below.
After Verifying that the functions 1 2 satisfy the corresponding homogeneous equation of the given equation, find a particular solution of the non-homogeneous equation and then the general solution of the equation .
x²y'' + xy' + (x² - 0.25 ) y = 3x √xsinx
x> 0
y1(x) = sin (x) / √x
y2(x) = cos (x) / √x
To find a particular solution of the non-homogeneous equation and the general solution of the equation, we can use the method of variation of parameters.
First, let's find the Wronskian of the homogeneous solutions y1(x) and y2(x):
W(y1, y2) = | y1 y2 |
| y1' y2' |
We have y1(x) = sin(x) / √x and y2(x) = cos(x) / √x. Differentiating these functions, we get:
y1'(x) = (cos(x) / √x - sin(x) / (2√x^3))
y2'(x) = (-sin(x) / √x - cos(x) / (2√x^3))
Substituting these values into the Wronskian:
W(y1, y2) = | sin(x) / √x cos(x) / √x |
| (cos(x) / √x - sin(x) / (2√x^3)) (-sin(x) / √x - cos(x) / (2√x^3)) |
Expanding the determinant:
W(y1, y2) = (sin(x) / √x) * (-sin(x) / √x - cos(x) / (2√x^3)) - (cos(x) / √x) * (cos(x) / √x - sin(x) / (2√x^3))
Simplifying:
W(y1, y2) = -1 / (2√x)
Now, we can find the particular solution using the variation of parameters formula:
y_p(x) = -y1(x) * ∫(y2(x) * g(x)) / W(y1, y2) dx + y2(x) * ∫(y1(x) * g(x)) / W(y1, y2) dx
Here, g(x) = 3x√xsin(x). Substituting the values:
y_p(x) = -((sin(x) / √x) * ∫((3x√xsin(x)) * (-1 / (2√x))) dx + (cos(x) / √x) * ∫((3x√xsin(x)) / (2√x)) dx
Simplifying the integrals:
y_p(x) = -(∫(-3sin^2(x)) dx) + (∫(3xcos(x)sin(x)) dx)
Integrating:
y_p(x) = 3/2 (xsin^2(x) - cos^2(x)) - 3/2 (xcos^2(x) + sin^2(x)) + C
Simplifying:
y_p(x) = 3x(sin^2(x) - cos^2(x)) + C
The general solution of the equation is given by the sum of the homogeneous solutions and the particular solution:
y(x) = C1 * (sin(x) / √x) + C2 * (cos(x) / √x) + 3x(sin^2(x) - cos^2(x)) + C
where C1, C2, and C are arbitrary constants.
1. There were 45 more crossword puzzle books than jigsaw puzzles. 5/9 of the crossword puzzle books and 25% of the jigsaw puzzles were sold. Among the items sold, there were 91 more crossword puzzle books than jigsaw puzzles. How many crossword puzzle books and jigsaw puzzles remained in total?
2. In a warehouse, 60% of the table lamps were 30 more than 80% of the standing lamps. Given that there were a total of 155 table and standing lamps in the warehouse at first, how many table lamps were left if 30% of them were removed from the warehouse?
1. The of jigsaw puzzles is 216 and crossword puzzle is 261.
2. 22 table lamps were left in the warehouse.
1. Crossword Puzzle Books and Jigsaw Puzzles:
Let's the number of jigsaw puzzles as "x".
then, the number of crossword puzzle books will be "x + 45"
Now, Number of sold crossword puzzle books = (5/9) (x + 45)
= (25/100) x
= x/4
It is also given that there were 91 more crossword puzzle books sold than jigsaw puzzles. Therefore, we can set up the equation:
(5/9) (x + 45) - (x/4) = 91
(5/9)x + 25 - (x/4) = 91
(20/36)x + 25 - (9/36)x = 91
(11/36)x = 91 - 25
(11/36)x = 66
x = (36/11) 66
x ≈ 216
So, the number of jigsaw puzzles is 216 and the number of crossword puzzle books is 216 + 45 = 261.
2. Table Lamps and Standing Lamps:
Let's the number of table lamps as "x".
then, the number of standing lamps will be "155 - x"
So, Number of table lamps = (60/100) x = 0.6x
and, Number of standing lamps
= (80/100) (155 - x)
= 0.8(155 - x)
= 124 - 0.8x
Therefore, the number of table lamps left will be:
Remaining table lamps = (70/100) * 0.6x = 0.42x
To find the value of x, we can set up the equation:
0.42x = x - 30
Simplifying the equation:
x - 0.42x = 30
0.58x = 30
x = 30 / 0.58
x ≈ 51.72
So, the number of table lamps left is 0.42 x 51.72 ≈ 21.68.
Thus, 22 table lamps were left in the warehouse.
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Whats the value of 14Π and round to the nearest hundredths.
Answer:
43.98
Step-by-step explanation:
43.98 to nearest hundredth
What is the area of this figure?
Answer:
area= 39 square meters
Step-by-step explanation:
10×6=60m²
60m²÷2=30m² is the area of the bigger triangle
6×3=18m²
18m²÷2=9m²
9m²+30m²=39m²
12. What is the percentage increase in miles per gallon from Toyota city driving to highway driving?
Answer: I WOULD SAY 45%
Step-by-step explanation:
The percentage increase in miles per gallon from Toyota city driving to highway driving is 33.33%.
Explanation:The percentage increase in miles per gallon from Toyota city driving to highway driving can be calculated using the formula:
Percentage increase = ((new value - old value) / old value) x 100
Let's say the old miles per gallon for city driving is 30 and the new miles per gallon for highway driving is 40:
Percentage increase = ((40 - 30) / 30) x 100Percentage increase = (10 / 30) x 100Percentage increase = 0.3333 x 100Percentage increase = 33.33%Therefore, there is a 33.33% increase in miles per gallon from Toyota city driving to highway driving.
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Use a calculator to graph f(x) = 2x ^ 3 - 6x ^ 2 - 4x + 1 Which are the approximate x-values of the local maximum and local minimum rounded to the nearest tenth?
A) max ≈ -15.6 , min ≈ 1.6
B) max ≈ 1.6 , min ≈ -15.6
C) max ≈ 2.3 , min ≈ -0.3
D) max ≈ -0.3 , min ≈ 2.3
The approximate x-values for the local maximum and the local minimum are given as follows:
D) max ≈ -0.3 , min ≈ 2.3.
What are the relative minimums and the relative maximums of a function?The relative minimums of a function are given by the points in which the function's behavior changes from decreasing to increasing.The relative maximums of a function, meanwhile, are given by the points in which the function's behavior changes from increasing to decreasing.Hence the critical points of the graphed function are given as follows:
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As part of a physics experiment, a ball is catapulted upward. The height of
the ball is h(t)= -5t²+30t+5 , where t is in seconds and the height of the ball is measured in meters. What was the ball's average velocity
between t=1 andt=2?
To find the average velocity of the ball between t = 1 and t = 2, we need to calculate the displacement of the ball during that time interval and divide it by the duration.
The displacement of an object can be determined by finding the difference in its position at the beginning and end of the interval. In this case, we can find the height of the ball at t = 1 and t = 2 using the given equation:
h(1) = -5(1)² + 30(1) + 5
= -5 + 30 + 5
= 30 meters
h(2) = -5(2)² + 30(2) + 5
= -20 + 60 + 5
= 45 meters
The displacement of the ball between t = 1 and t = 2 is:
Displacement = h(2) - h(1)
= 45 - 30
= 15 meters
The duration of the interval is 2 - 1 = 1 second.
Finally, we can calculate the average velocity using the formula:
Average velocity = Displacement / Duration
= 15 meters / 1 second
= 15 m/s
Therefore, the average velocity of the ball between t = 1 and t = 2 is 15 m/s.
Describe the data set
4, 5, 6, 6, 7, 7, 7, 7, 8, 8, 9, 10
A) Skewed Right
B) Skewed Left
C) Symmetrical
D) None of the other answers are correct
E) Uniform
The given data set: 4, 5, 6, 6, 7, 7, 7, 7, 8, 8, 9, 10 is skewed right or positively skewed due to a cluster of values towards the center and a gradual increase on the right side. The correct answer is A) Skewed Right.
The given data set is: 4, 5, 6, 6, 7, 7, 7, 7, 8, 8, 9, 10.
To determine the shape of the data set, we can analyze its distribution.
Looking at the data set, we can observe that the values are gradually increasing from 4 to 10. However, there are multiple occurrences of the numbers 6, 7, and 8. This indicates that the data set has a cluster or mode around these values.
Since the data set has a cluster of values towards the center and a gradual increase on the right side, it suggests that the data set is skewed right or positively skewed.
Therefore, the correct answer is A) Skewed Right.
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Dustin and Melanie are playing a game, where two standard, six-sided number cubes are rolled, and the sum of their outcomes is found. Each player gets a chance to guess the correct sum, and the player that guesses the correct sum wins the game.
Dustin decides to guess a sum of six. Melanie decides to guess a sum of seven.
Which player made the better decision?
How many complex zeros does the polynomial have?
f(x)=6x^(6)-5x^(4)+2x^(3)-x^(2)+12
We cannot determine the exact number of complex zeros for the given polynomial.
We have,
To determine the number of complex zeros of the polynomial
f(x) = 6x^6 - 5x^4 + 2x^3 - x^2 + 12
We need to analyze the degree and sign changes of the polynomial.
The degree of the polynomial is 6, which means it is a polynomial of degree 6.
According to the Fundamental Theorem of Algebra, a polynomial of degree n can have at most n complex zeros (counting multiplicity).
To analyze the sign changes, we can write down the coefficients of the polynomial in a row:
6, -5, 2, -1, 0, 0, 12
By observing the sign changes in the row of coefficients, we see that there are no sign changes.
This indicates that the polynomial has either zero or an even number of positive real zeros.
Since we are interested in complex zeros, this information alone does not provide conclusive evidence.
To determine the number of complex zeros, we would need more information or further analysis.
It is possible that some of the zeros are complex or imaginary, but without more details or a complete factorization of the polynomial, we cannot determine the exact number of complex zeros.
Thus,
We cannot determine the exact number of complex zeros.
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Lucy is riding on a bike course that is 88 miles long. So far, she has ridden 22 miles of the course. What percentage of the course has Lucy ridden so far?
Answer:
Lucy has ridden 25% of the course so far. This means she has completed a quarter of the total distance.
Step-by-step explanation:
To determine the percentage of the course Lucy has ridden so far, we can use the following formula:
Percentage = (Distance ridden / Total distance) * 100
Given that the total distance of the bike course is 88 miles and Lucy has
ridden 22 miles, we can substitute these values into the formula:
Percentage = (22 miles / 88 miles) * 100
Simplifying the equation:
Percentage = (1/4) * 100
Percentage = 25
Therefore, Lucy has ridden 25% of the course so far. This means she has completed a quarter of the total distance.
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Can someone please help me. I need so much help with these two questions. Find all six trigonometric ratios for the triangle shown. Show all work.
All six trigonometric ratios of the triangle are :
sin (θ) = 3/5, cos (θ) = 4/5, tan (θ) = 3/4
cosec (θ) = 5/3, sec (θ) = 5/4, cot (θ) = 4/3
Given a triangle, which is right angled.
Length of hypotenuse = √(20² + 15²) = 25
Given an angle θ.
We have to find the six trigonometric ratios which are sin, cos, tan, cosec, sec and cot.
sin (θ) = opposite side / hypotenuse = 15/25 = 3/5
cos (θ) = adjacent side / hypotenuse = 20/25 = 4/5
tan (θ) = opposite side / adjacent side = 15/20 = 3/4
cosec (θ) = 1 / sin (θ) = 5/3
sec (θ) = 1 / cos (θ) = 5/4
cot (θ) = 1 / tan (θ) = 4/3
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Alyssa made a pink and white striped blanket for her bed there are 7 pink stripes and 6 white stripes each stripe is 8 inches wide How wide is Alyssa’s blanket?
The blanket's width is determined by adding up the widths of each individual stripe, resulting in a total width of 104 inches.
To find the width of Alyssa's blanket, we need to calculate the total width of all the pink and white stripes combined.
Given that there are 7 pink stripes and 6 white stripes, and each stripe is 8 inches wide, we can calculate the total width as follows:
Total width = (Number of pink stripes [tex]\times[/tex] Width of each pink stripe) + (Number of white stripes [tex]\times[/tex] Width of each white stripe)
Substituting the values into the equation:
Total width [tex]= (7 \times 8) + (6 \times 8)[/tex]
= 56 + 48
= 104 inches.
Therefore, Alyssa's blanket is 104 inches wide.
In this case, we multiply the number of pink stripes by the width of each pink stripe (7 [tex]\times[/tex] 8) and add it to the product of the number of white stripes and the width of each white stripe (6 [tex]\times[/tex] 8) to obtain the total width of the blanket.
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PLEASE HELP AND EXPLAIN HOW YOU GOT THE ANSWER I WILL MARK YOU BRAINLIEST!!
The sequence of transformations that transform the the pre-image and the congruence of the pre-image and image are indicated by the option D.
D. Reflection, then rotation results in an image that is congruent to the original
What is a transformation of a geometric figure?A transformation is the performance of a rotation, reflection, translation, or dilation, that produces an image with a different size, location, orientation or shape.
The coordinates of the points on the triangle ABC are laterally equidistant from the vertical line in the middle between the triangles ABC and triangle DEF, such that the line in the middle is the line of reflection.
The vertical height of the coordinates of the triangle ABC and DEF, which are the same indicates that the transformation from triangle ABC to EFD is a reflection across the line in the middle between the two triangles. The side GH in triangle IGH corresponds to the side EF in the triangle EFD,
The length of GH = EF = 4 units
Similarly, IH = DE, and IG = DF, therefore;
Triangle EFD and triangle HGI are congruent by SSS congruence rule
The orientation of the side EF of the triangle EFD which is vertical and the side HG which is horizontal indicates a rotation of the triangle EFD by 90 degrees to obtain the triangle HGI
The correct option is therefore, the option D.
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A total of 240 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student tickets sold was two times the number of adult tickets sold. How many adult tickets were sold?
The number of adult tickets sold were 80.
Let's denote the number of adult tickets sold as A and the number of student tickets sold as S.
The number of student tickets sold was two times the number of adult tickets sold:
S = 2A
We also know that the total number of tickets sold was 240:
A + S = 240
Substituting the value of S from the first equation into the second equation, we have:
A + 2A = 240
Combining like terms:
3A = 240
Divide both sides of the equation by 3:
A = 80
Therefore, 80 adult tickets were sold.
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good people please help!!!!!!! please!!!!!!
Clearer image, please!
Can you help me with this please? Thank you. : )
In the given diagram, we have a triangle with one angle labeled as 2x + 10° and another angle labeled as 3x - 5°. To solve for x, we can set up an equation using the sum of angles in a triangle, which is 180°.
The sum of the angles in a triangle is given by the equation:
Angle1 + Angle2 + Angle3 = 180°
Substituting the given angle measurements, we have:
(2x + 10°) + (3x - 5°) + 95° = 180°
Combining like terms, we get:
5x + 100° = 180°
Next, we can isolate the variable x by subtracting 100° from both sides:
5x = 180° - 100°
5x = 80°
Finally, we can solve for x by dividing both sides by 5:
x = 80° / 5
x = 16°
Therefore, the value of x is 16°.
You are interested in finding a 95% confidence interval for the mean number of visits for physical therapy patients. The data below show the number of visits for 11 randomly selected physical therapy patients. Round answers to 3 decimal places where possible.
13 6 25 11 11 10 21 20 9 20 9
a. To compute the confidence interval use a
?
distribution.
b. With 95% confidence the population mean number of visits per physical therapy patient is between
and
visits.
c. If many groups of 11 randomly selected physical therapy patients are studied, then a different confidence interval would be produced from each group. About
percent of these confidence intervals will contain the true population mean number of visits per patient and about
percent will not contain the true population mean number of visits per patient.
For calculating a 95% confidence mean range for the typical number of visits for patients receiving physical therapy.
a. We employ a t-distribution to calculate the confidence interval.
b. The population mean number of visits per physical therapy patient is between 9.454 and 19.000 visits, with a 95% confidence interval.
c. If multiple groups of 11 randomly chosen physical therapy patients are examined, roughly 95% of these confidence intervals will contain the genuine population mean number of visits per patient, and around 5% will not.
a. T-distribution is used to calculate the confidence interval for the mean number of visits. This is so because the population standard deviation is unknown and the sample size is tiny (only 11). The t-distribution is used in place of the conventional normal distribution when certain conditions are satisfied.
b. We have two options for calculating the confidence interval: we can do it manually or with statistical software. We determine the sample mean to be 13.182 and the sample standard deviation to be 6.446 using the provided data (13, 6, 25, 11, 11, 10, 21, 20, 9, 20, 9). Given the limited sample size and a 95% level of confidence, we use the t-distribution to establish the critical value. Using a calculator or the t-distribution table, determine the critical value for a 95% confidence level with 10 degrees of freedom is approximately 2.228.
The formula for the confidence interval is:
Sample Mean (Critical Value) * (Standard Error) = Confidence Interval
Sample Standard Deviation / sqrt(sample size) gives the standard error.
By entering the values, we can determine the confidence interval using the formula below:
The confidence interval is equal to 13.182 (2.228) * (6.446 / sqrt(11)).
9.454 visits make up the lower bound and 19.000 visits make up the upper bound of the confidence interval. The population mean number of visits per physical therapy patient is therefore expected to range between 9.454 and 19.000 visits, with a 95% confidence interval.
c. Confidence intervals for each group of 11 randomly chosen physical therapy patients can be constructed, and roughly 95% of these intervals will contain the actual population mean number of visits per patient. This is due to the fact that we are employing a 95% confidence level, which indicates that over time, 95% of the confidence intervals created will accurately reflect the underlying population mean.
On the other hand, around 5% of these confidence intervals won't include the actual population mean for visits per patient. These intervals are referred to as Type I errors or "misses". The likelihood of rejecting the actual null hypothesis is represented by the significance level, or alpha, which is represented by the 5%.
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help me please
with this
Given u =(√3,-1) and v= (3,-4), what is u. v?
O-4√3-3
O-4√3+3
O 3√3-4
3√3+4
[tex]u=(\sqrt{3}~~,~-1)\hspace{5em}v=(3~~,~-4) \\\\\\ u\cdot v\implies (\sqrt{3}\cdot 3)~~ + ~~(-1\cdot -4)\implies \stackrel{ \textit{dot product} }{3\sqrt{3}+4}[/tex]
26. Find the perimeter of the rectangle below.
(Use Pythagorean Theorem to find the length of the rectangle)
27. If the diagonals of a square measure 36 meters, what is the length of a side of
the square?(Use Pythagorean Theorem to find the side of the square)
ONLY 26 and 27 Pls help ASAP for points
The length of one side of the square is 36 meters.In general, the perimeter of a rectangle can be found by adding up the lengths of all four sides.
If we know the length and width of the rectangle, we can use the formula:
Perimeter = 2(length + width)
To find the length of the rectangle using the Pythagorean Theorem, we would need to be given some additional information, such as the width and the length of one of the sides or one of the diagonals. Once we have the length and width of the rectangle, we can use the formula above to find its perimeter.
If the diagonals of a square measure 36 meters, what is the length of a side of the square?(Use Pythagorean Theorem to find the side of the square)
Let s be the length of one side of the square. Since the diagonals of a square are equal in length, we have:
s² + s² = 36²
Simplifying the left-hand side:
2s² = 1296
Dividing both sides by 2:
s² = 648
Taking the square root of both sides:
s = √648 = 18√4 = 36.
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60 cm * 50 cm what is the area covered by one sheet of newspaper if the area of the room is 79.2 msquare
The solution is: 0.003 area of of the room's area is, covered by one sheet of newspaper.
Here, we have,
given that,
60 cm * 50 cm what is the area covered by one sheet of newspaper if the area of the room is 79.2 m square.
we know, that,
area of one sheet of newspaper = 60 cm * 50 cm
= 3000 cm^2
we know that,
100 cm = 1 m
so, 3000 cm^2 = 0.3 m^2
now, we have,
the area of the room is 79.2 m square.
so, we get,
the area covered by one sheet of newspaper = 0.3/ 79.2
= 0.003
Hence, The solution is: 0.003 area of of the room's area is, covered by one sheet of newspaper.
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find the general solution for: cos(x+30)=-1
The required, general solution for x that satisfies the equation cos(x + 30) = -1 is x = (2n + 1)π - 30.
To find the general solution for the equation cos(x + 30) = -1, we can start by considering the general form of the cosine function. The cosine function has a period of 2π, meaning it repeats every 2π radians.
In this equation, we have cos(x + 30) = -1. Since the cosine function has a maximum value of 1 and a minimum value of -1, the only way for cos(x + 30) to equal -1 is if x + 30 is an odd multiple of π. We can write this as:
x + 30 = (2n + 1)π
Here, n is an integer representing the number of periods of the cosine function. To find the general solution, we can solve for x by subtracting 30 from both sides:
x = (2n + 1)π - 30
This equation gives us the general solution for x that satisfies the equation cos(x + 30) = -1. We can see that for each integer value of n, we have a different solution.
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Carlos created a pattern by using the rule "add 2" and starting with 1, as shown below.
1, 3, 5, 7
Carlos plotted the first four terms on a coordinate grid. Which of these would be the
coordinates of one of the points?
A (2,1)
B (2,3)
C (5,7)
D (7,4)
The coordinates of one of the points in Carlos' pattern would be (2, 3).
To determine the coordinates of the points in Carlos' pattern, we can assign the term number as the x-coordinate and the corresponding term value as the y-coordinate. Let's go through each term:
Term 1: 1
The first term is 1. So, the coordinate for this term is (1, 1).
Term 2: 3
The second term is obtained by adding 2 to the previous term. The previous term had the coordinate (1, 1). Therefore, the coordinate for this term is (2, 3).
Term 3: 5
The third term is obtained by adding 2 to the previous term. The previous term had the coordinate (2, 3). Therefore, the coordinate for this term is (3, 5).
Term 4: 7
The fourth term is obtained by adding 2 to the previous term. The previous term had the coordinate (3, 5). Therefore, the coordinate for this term is (4, 7).
From the given options, we can see that the coordinates (2, 3) match one of the points in Carlos' pattern. Therefore, the correct answer is B) (2, 3).
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How do I find the critical values and rejection region? and how is it graphed?
The critical value of the given data set is 3.42.
The two-way chi-square analysis is used to determine if there is a relationship between two categorical variables. In this case, the two variables are shiftwork availability and the union-management relationship.
To conduct the analysis, we need to calculate the expected frequencies for each cell in the table. We can do this by multiplying the row and column totals and dividing by the total number of observations.
For the cell in the top left corner (No Shiftwork/Good Relationship):
Expected Frequency = (36 × 33) / 100 = 11.88
We can then calculate the expected frequencies for the other cells in the same way.
Once we have calculated the expected frequencies, we can then calculate the chi-square statistic using the following formula:
Chi-square = Σ [(Observed Frequency - Expected Frequency)² / Expected Frequency]
Using this formula, we can calculate the chi-square statistic for the above example as follows:
Chi-square = (11 - 11.88)²/11.88 + (22 - 21.12)²/21.12 + (25 - 23.12)²/23.12 + (42 - 40.88)²/40.88 = 3.42
Finally, we can compare the chi-square statistic to the critical value of 3.84 at α = 0.05 (df = 1). Since our chi-square statistic is less than the critical value, we can conclude that there is no relationship between shiftwork availability and the union-management relationship.
Therefore, the critical value of the given data set is 3.42.
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Please
Can someone answer this question
Answer:2nd one
Step-by-step explanation:
- Calculate CV for the following numbers: 5, 8, 9, 2, 6. OA. 40.82 B. 120 OC. 0.4083 OD. 1.2
The coefficient of variation or CV of the given numbers is 45.64%.
Given numbers are,
5, 8, 9, 2, 6
We have to find Coefficient of variation.
CV = (Standard deviation / sample mean ) × 100
Sample mean = Sum of the values / total number of values
= (5 + 8 + 9 + 2 + 6) / 5
= 6
Standard deviation = √[(Σ(x - mean)² / (n - 1)]
Σ(x - mean)² = (5 - 6)² + (8 - 6)² + (9 - 6)² + (2 - 6)² + (6 - 6)²
= 30
Standard deviation = √(30 / (5 - 1) = 2.7386
CV = (2.7386 / 6) × 100
= 45.64%
Hence CV is 45.64%.
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Find an equation for the slope of the graph of y=x²+2x at any point.
Answer:
dy/dx = 2x + 2
Step-by-step explanation:
the slope (gradient) is given by differentiating y = x² + 2x.
dy/dx = 2x + 2
What is the value of x in the equation? 5 1/6x + 2 1/4= 10
Answer:
To solve for x, we need to isolate x on one side of the equation.
First, we can start by subtracting 2 1/4 from both sides of the equation:
5 1/6x = 10 - 2 1/4
5 1/6x = 7 3/4
Next, we can simplify the left side of the equation by multiplying the whole equation by the reciprocal of 5 1/6, which is 6/31:
(6/31) * 5 1/6x = (6/31) * 7 3/4
x = 3/2
Therefore, the value of x in the equation is 3/2.
I NEED HELP PLEASE HELP
Answer:
a. x = licensed riders; y = junior racers
b. x + y = 321; 25x +15y = 6935
c. see attached. (x, y) = (212, 109); 212 licensed riders; 109 junior racers
Step-by-step explanation:
You want to determine the number of racers of each type, given 321 racers total paid $6935 in fees. Licensed racers paid $25 each, and junior racers paid $15 each. You want a system of equations and a graphical solution.
a. VariablesIn general, the variables represent the values the question is asking for. In part (b), we see that we want to find the number of racers of each type. Since our graphing program prefers the variables x and y, we will assign those in the same order the descriptions of the types of racers appear in the problem statement. (Keeping the order can avoid confusion later.)
x = the number of licensed riders
y = the number of junior racers
b. EquationsThe relations given in the problem statement give rise to two equations:
x + y = 321 . . . . . . . . . the total number of racers25x +15y = 6935 . . . . the total income from feesc. GraphThe attached graph shows the solution to these equations is (x, y) = (212, 109). There were 212 licensed riders and 109 junior racers.
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