Answer:
Step-by-step explanation:
Here Is a Quick Explanation :)
To find the axis of symmetry and the vertex of the function, we can use the fact that the function is recursive, and we can write:
f(x) = f(x-1)² + 7
f(x-1) = f(x-2)² + 7
f(x-2) = f(x-3)² + 7
...
f(1) = f(0)² + 7
If we substitute the last equation into the previous one, we get:
f(x-1) = (f(0)² + 7)² + 7
f(x) = ((f(0)² + 7)² + 7)² + 7
This shows that the function depends only on the initial value f(0), and we can use this fact to find the axis of symmetry and the vertex.
To find the axis of symmetry, we need to find the value of x that makes f(x) equal to f(-x). We can write:
f(-x) = f(-(x-1))² + 7 = f(-x+1)² + 7
Now, if we substitute f(x) = f(x-1)² + 7 into the last equation, we get:
f(-x) = (f(x-1)² + 7)² + 7 = f(x)² + 7
This means that the axis of symmetry is the line x = 0, and not y = 7 as stated in option A.
To find the vertex, we need to find the maximum or minimum value of the function. Since f(x) = f(x-1)² + 7, the function is increasing if f(x-1) > -7, and decreasing if f(x-1) < -7. Since f(0) = 7, we can conclude that the function is increasing on the interval -∞ < x < 1, and decreasing on the interval x > 1. Therefore, the vertex is at x = 1, and the corresponding value is f(1) = 7.
Therefore, the correct statements are:
The axis of symmetry of f(x) is x = 0.
The vertex of the function is (1, 7).
f is increasing on the interval -∞ < x < 1.
f is decreasing on the interval x > 1.
triangle ABC has perimeter 22cm
AB= 8cm
BC=5cm
By calculation, deduce whether triangle ABC is a right angle triangle
Answer: ABC is not a right angled triangle
Step-by-step explanation:
total = 22cm
22-8-5= 9cm
Hypotuneus = 9 cm since its the longest angle
pythagoras theorum = a2+b2=c2
so we need to see if 8² +5² =9²
64+25 need to be 81 (9² )
but its 64+25=89
therefore it is not a right angles triangle.
3. SHORT ANSWER Which point on the number line
is closest to the product of the numbers graphed at
points R and T? Explain your answer.
P
QRST
0
1
The closest point will be 0.6 which is point Q.
To determine the product of the numbers graphed at points R and T, we need to find the coordinates of these points on the number line.
So, point R x point T
= 7/10 x 9/10
However, once you have the coordinates of points R and T, you can multiply the corresponding numbers to find their product.
Then, 0.7 x 0.9
= 0.63
From the points given we can write as
P = 0.4
Q = 0.6
R= 0.7
S = 0.8
T = 0.9
Among all the points the most closest is 0.6 which is point Q.
Thus, the closest point will be 0.6 which is point Q.
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Pls help due today xxx
Answer:
x=6
Step-by-step explanation:
25^3=15,625
5^6=15,625
Therefore, x=6
Answer:
x=6.........................................................
I need some help please, Describe the translation that maps DEF onto JKL
Answer: Translate DEF 2 units to the right
Step-by-step explanation:
Each point in DEF is 2 units to the left of JKL. For example, D is at (-3, 4) and J is at (-1, 4). To map the figures on to one another, DEF must be moved 2 units to the right
Craig Rosenberg has a personal injury protection policy that covers each person in, on, around, or under his car for medical expenses as a result of an accident. Each person can collect up to $50,000. Craig is involved in an accident and three people are hurt. One person has$23,000 of medical expenses, one person has $500 worth of medical expenses, and Craig himself has medical expenses totaling$70,000. How much money must the insurance company pay out for these three people?
Based on the policy limit of $50,000, the total amount that the insurance company must pay out for these three people involved in Craig's personal injury protection policy is $73,500.
How is the amount computed?The total amount that the insurance company will indemnify the three persons involved in the accident is determined by the policy or liability limit of $50,000 for each person.
Policy limit in Craig's personal injury protection policy for each = $50,000
The medical expense for the first person = $23,000 (below limit)
The medical expense for the second person = $500 (below limit)
The medical expense for the third person (Craig) = $70,000 (above limit)
Total indemnity = $73,500 ($23,000 + $500 + $50,000)
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(2) There is a total of 20 balls. Some balls weigh 50g each and others weigh 120g each. If the 20 balls weigh 1560g altogether, how many 50g balls and 120g balls are there respectively?
Number of 50 g weigh balls = 12
And, Number of 120g weigh balls = 8
We have to given that;
There is a total of 20 balls. Some balls weigh 50g each and others weigh 120g each.
Let number of 50 g weigh balls = x
And, Number of 120g weigh balls = y
Hence, We can formulate;
x + y = 20 .. (i)
And, 50x + 120y = 1560
⇒ 5x + 12y = 156 .. (ii)
From (i);
x = 20 - y
Plug in (ii);
5 (20 - y) + 12y = 156
100 - 5y + 12y = 156
7y = 56
y = 8
From (i);
x = 20 - y
x = 20 - 8
x = 12
Thus, number of 50 g weigh balls = 12
And, Number of 120g weigh balls = 8
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Match the system of equations graphed to the correct solution.
infinate solutions (1,1) (-1,2) -1.5,4.5
The solution for each system of equations in this problem is given as follows:
First system: no solution.Second system: (1,1).Third system: (-1.5, 4.5).Fourth system: (-1, 2).How to solve a system of equations?Considering the graph containing the equations for the system, the solution of the system of equations is presented by the point of intersection of all the equations of the system.
When the two curves do not intersect, as is the case for the parallel lines in the first graph in this problem, it is said that the system has no solution.
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what is the exponential regression equation to best fit the data where the y values were rounded to the nearest integer. x y 0 2 1 6 2 19 3 56 4 167 question 9 options:
The exponential regression equation to best fit the given data is y = 1.87 * 5.39^x, and this is found by using the logarithmic transformation of the exponential function and linear regression.
To find the exponential regression equation that best fits the given data, we need to use the following formula:
y = ab^x
where a is the y-intercept and b is the base of the exponential function. We can use the logarithmic transformation of this equation to linearize the data:
ln y = ln a + x ln b
We can then use linear regression to find the values of ln a and ln b. Once we have these values, we can use the exponential function to find the best-fit equation.
Using this method, we get the following values:
ln a = 0.6248
ln b = 1.6835
Therefore, the exponential regression equation that best fits the given data is:
y = e^(0.6248) * e^(1.6835x)
This equation can be simplified as:
y = 1.87 * 5.39^x
Note that since the y-values are rounded to the nearest integer, the calculated equation may not perfectly fit the data points, but it will provide a close approximation.
In summary, the exponential regression equation to best fit the given data is y = 1.87 * 5.39^x, and this is found by using the logarithmic transformation of the exponential function and linear regression.
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let A and B be a square matrices of order 3 defined By A={aij}=2i^2+3j and B={bij}=i^2+2j^2. Compute matrices A and B
(b) find the sum of their determinant
(c) 2A^-1
Matric A = [[5, 8, 11],
[11, 14, 17],
[21, 24, 27]]
Matric B = [[3, 9, 19],
[6, 12, 22],
[11, 17, 27]]
(b) The sum of their determinant is 102.
(c) The inverse of matrix A, you can use matrix inversion techniques such as the adjugate matrix or row reduction.
To compute the matrices A and B, we substitute the given expressions for each element into their respective matrices.
Matrix A:
A = [aij] where aij = 2i² + 3j
Substituting the values of i and j from 1 to 3, we get:
A = [[2(1)² + 3(1), 2(1)² + 3(2), 2(1)² + 3(3)],
[2(2)² + 3(1), 2(2)² + 3(2), 2(2)² + 3(3)],
[2(3)² + 3(1), 2(3)² + 3(2), 2(3)² + 3(3)]]
Simplifying each element:
A = [[2 + 3, 2 + 6, 2 + 9],
[8 + 3, 8 + 6, 8 + 9],
[18 + 3, 18 + 6, 18 + 9]]
A = [[5, 8, 11],
[11, 14, 17],
[21, 24, 27]]
Matrix B:
B = [bij] where bij = i² + 2j²
Substituting the values of i and j from 1 to 3, we get:
B = [[1² + 2(1)², 1² + 2(2)², 1² + 2(3)²],
[2² + 2(1)², 2² + 2(2)², 2² + 2(3)²],
[3² + 2(1)², 3² + 2(2)², 3² + 2(3)²]]
Simplifying each element:
B = [[1 + 2, 1 + 8, 1 + 18],
[4 + 2, 4 + 8, 4 + 18],
[9 + 2, 9 + 8, 9 + 18]]
Next, we move on to the remaining parts of the question.
To find the sum of the determinants of matrices A and B, we compute the determinants separately and add them together:
det(A) = |A|
= 5(14 - 17) - 8(11 - 17) + 11(11 - 14)
= -6
det(B) = |B| = 3(12 - 17) - 9(6 - 17) + 19(6 - 12)
= 108
Sum of determinants = det(A) + det(B)
= -6 + 108
= 102
To compute 2A⁻¹, we need to find the inverse of matrix A and multiply it by 2:
A⁻¹ = inverse of matrix A
Once you have the inverse, you can multiply it by 2:
2A^-1 = 2 × A⁻¹
Since matrix A is not given in the question and we've only computed its elements based on the given formula
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11. How many combinations of four can you make from the set?
25 baseball cards
Put your answer in the form [XXXXX]. Please do not insert a comma.
PLEASE HELP ME I NEED HELP
A makeup artist purchased some lipsticks and wants to wrap them individually with gift wrap. Each lipstick has a radius of 0.6 inch and a height of 2.4 inches. How many total square inches of gift wrap will the makeup artist need to wrap 5 lipsticks? Leave the answer in terms of π.
18π square inches
14.4π square inches
11.3π square inches
2.26π square inches
Answer:
I think that it is 18π sq in
Step-by-step explanation:
U do surface area of a cylinder
SA=2πrh+2πr^2
. estimate a regression equation for sales as a function of population, advertising in the current year, and advertising in the previous year. can you expect predictions of sales in future years to be very accurate if they are based on this regression equation? explain.
It's also worth noting that there may be other factors that impact sales that are not included in the regression equation. For example, changes in consumer preferences, economic conditions, or competition from other businesses could all have an impact on sales that is not captured by the variables included in the equation.
So while a regression equation can be a useful tool for predicting sales, it's important to keep in mind that it's not a perfect predictor and should be used in conjunction with other information and analysis. To estimate a regression equation for sales as a function of population, advertising in the current year, and advertising in the previous year, you would need to gather data on sales, population, and advertising expenditures for both the current and previous years. Once you have this data, you can use regression analysis to determine how much of the variation in sales can be explained by population and advertising. As for whether or not predictions of sales in future years would be very accurate based on this regression equation, it really depends on how well the equation fits the data.
If the equation has a high R-squared value (meaning that a large percentage of the variation in sales can be explained by the independent variables), then predictions based on the equation are likely to be more accurate. However, if the equation has a low R-squared value, then predictions based on the equation may not be very accurate.
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How many ounces of gatoradae would marcus drank if he walked 12 miles
The amount of Gatorade that Marcus would drink while walking 12 miles depends on several factors such as his personal preference, level of exertion, and the weather conditions.
However, a general rule of thumb is to drink about 8 ounces of fluid (water or sports drink) for every 20 minutes of exercise. If we assume that Marcus takes about 2 hours to walk 12 miles, he would be walking for 120 minutes, and he would need to drink about 48 ounces (8 ounces x 6 cycles of 20 minutes) of fluid during his walk. Therefore, Marcus would drink about 48 ounces of Gatorade (or any other fluid) during his 12-mile walk.
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Juan's family took a road trip to the Grand Canyon. Juan fell asleep after they had travelled 177 miles. If the total length of the trip was 300 miles, what percentage of the total trip had they travelled when Juan fell asleep?
When Juan fell asleep, his family had traveled approximately 59% of the total trip to the Grand Canyon.It's important to note that this calculation assumes that the distance traveled is proportional to the progress made in the trip and that no significant detours or changes in speed occurred.
To calculate the percentage of the total trip that Juan's family had traveled when he fell asleep, we need to divide the distance traveled by the total length of the trip and then multiply by 100.
The distance traveled before Juan fell asleep is given as 177 miles, and the total length of the trip is 300 miles.
Percentage = (Distance traveled / Total length of trip) * 100
Substituting the given values, we have:
Percentage = (177 miles / 300 miles) * 100Performing the calculation:
Percentage = (0.59) * 100 = 59%.
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Water flows back and forth between a small and large tank. When water is moving into a tank the flow rate is positive, and when water is moving from a tank the flow rate is negative. The large tank begins with 300 gallons of water, and the small tank begins with 200 gallons of water. After a period of 5 minutes, the large tank has the same amount of water as the small tank. Which statement describes the flow rate?
The flow rate of the large tank is 10 gal/min, and the flow rate of the small tank is –10 gal/min.
The flow rate of the large tank is –10 gal/min, and the flow rate of the small tank is 10 gal/min.
The flow rate of the large tank is 20 gal/min, and the flow rate of the small tank is –20 gal/min.
The flow rate of the large tank is –20 gal/min, and the flow rate of the small tank is 20 gal/min.
The correct statement regarding the flow rate is given as follows:
The flow rate of the large tank is –10 gal/min, and the flow rate of the small tank is 10 gal/min.
How to define a linear function?The slope-intercept equation for a linear function is presented as follows:
y = mx + b
The parameters of the definition of the linear function are given as follows:
m is the slope, representing the rate of change of the function.b is the intercept, representing the value of y when the graph of the function crosses the y-axis.The functions are given as follows:
Large tank: V(x) = 300 - mx. (rate of -m).Small tank: V(x) = 200 + mx. (rate of m).After 5 minutes, the two tanks have the same rate, hence the value of m is obtained as follows:
300 - 5m = 200 + 5m
10m = 100
m = 10 gal/min.
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A jar full of marbles is displayed the following table shows the guesses for 10 people. The actual number of marbles in the jar is 145. Calculate the absolute guessing error for all 10 guesses.
Answer:
Step-by-step explanation:
To calculate the absolute guessing error, we need to find the absolute difference between each guess and the actual number of marbles (145).
Guess Absolute Guessing Error
190 45
150 5
125 20
133 12
167 22
160 15
148 3
200 55
170 25
115 30
To check, we can verify that each absolute guessing error is the positive difference between the guess and 145.
Como se resuelve esta ecuación?
Answer:
-33-7x=
[tex] - 33 - 7x = 2(3 - 8x) - 3 [/tex]
[tex] - 33 - 7x = 6 - 16x - 3[/tex]
[tex] - 33 - 6 + 3 = - 16x + 7x[/tex]
[tex] \frac{ - 36}{ - 9 ?} = \frac{ - 9x}{ - 9?} [/tex]
Step-by-step explanation:
x=4
a group of 11 women and 16 men must select a 6-person committee. how many committees are possible if it must consist of 5 men?
To answer your question, we need to use a combination formula, which is nCr = n! / (r! * (n-r)!).
In this case, we want to select 5 men out of 16 men, which can be done in 16C5 = 4368 ways. Then, we need to select 1 woman out of 11 women, which can be done in 11C1 = 11 ways. Therefore, the total number of committees possible if it must consist of 5 men is 4368 * 11 = 48,048.
In summary, there are 48,048 committees possible consisting of 5 men and 1 woman, out of a total of 11 women and 16 men. Finally, to find the total number of possible committees, multiply the number of ways to select the men by the number of ways to select the women: C(16, 5) * C(11, 1). This results in 4368 possible committees that consist of 5 men and 1 woman.
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The price of a CD radio cassette has been reduced from $16,999 to $13,999 . Calculate the rate of discount
Answer:
The difference between the original price of $16,999 and the discounted price of $13,999 is:
$16,999 - $13,999 = $3,000
So the discount is $3,000.
To calculate the rate of discount as a percentage, you need to divide the discount by the original price, and then multiply by 100.
($3,000 / $16,999) x 100% ≈ 17.65%
Therefore, the rate of discount is approximately 17.65%.
Step-by-step explanation:
Answer:
0.17648 (round to whatever you need) is the RATE of discount
17.648% is the PERCENTAGE of discount
Step-by-step explanation:
(16,999 - 13,999)/ 16,999 = 0.17648
Because of the formula (og price - discount price)/ og price
olve the system of differential equations the lesser of the two eigenvalues is its corresponding eigenvector is . what is ? the greater of the two eigenvalues is its corresponding eigenvector is . what is ?
The solution to the system of differential equations is x(t) = -29[tex]e^{-0.2t}[/tex] + 18[tex]e^{0.1t}[/tex] and y(t) = -9[tex]e^{-0.2t}[/tex] + 5[tex]e^{0.1t}[/tex] with initial conditions x(0)=-7 and y(0)=-2. The eigenvalues and eigenvectors are also given.
We can solve the system of differential equations using the eigenvalues and eigenvectors as follows
Let V be the matrix whose columns are the eigenvectors of the system
V = [ -7 4 ]
[ -2 1 ]
Then the diagonal matrix D whose diagonal entries are the eigenvalues of the system is
D = [ -0.2 0 ]
[ 0 0.1 ]
We can express the solution of the system as
[ x(t) ] [ -7 4 ] [ [tex]e^{-0.2t}[/tex] 0 ] [ x(0) ]
[ y(t) ] = [ -2 1 ] * [ 0 [tex]e^{0.1t}[/tex]] * [ y(0) ]
Substituting the given initial conditions, we get:
[ x(t) ] [ -7 4 ] [ [tex]e^{-0.2t}[/tex] 0 ] [ -7 ]
[ y(t) ] = [ -2 1 ] * [ 0[tex]e^{0.1t}[/tex] ] * [ -2 ]
Simplifying, we get
x(t) = (-7[tex]e^{-0.2t}[/tex] + 4[tex]e^{0.1t}[/tex](-7) + (-2[tex]e^{-0.2t}[/tex] + [tex]e^{0.1t}[/tex](-2)
= -29[tex]e^{-0.2t}[/tex] + 18[tex]e^{0.1t}[/tex]
y(t) = (-7[tex]e^{-0.2t}[/tex] + 4[tex]e^{0.1t}[/tex](-2) + (-2[tex]e^{-0.2t}[/tex] + [tex]e^{0.1t}[/tex](1)
= -9[tex]e^{-0.2t}[/tex] + 5[tex]e^{0.1t}[/tex]
Therefore, the solution to the system of differential equations with the given initial conditions is
x(t) = -29[tex]e^{-0.2t}[/tex] + 18[tex]e^{0.1t}[/tex]
y(t) = -9[tex]e^{-0.2t}[/tex] + 5[tex]e^{0.1t}[/tex]
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--The given question is incomplete, the complete question is given below " Solve the system of differential equations { x'=2.2x−8.4y, y' =0.6x−2.3y}
with the initial condition x(0)=−7,y(0)=−2 The eigenvalues and their eigenvectors are found as follows. The lesser of the two eigenvalues is −0.2 and its corresponding eigevector is [ −7 −2]. The greater of the two eigenvalues is 0.1 and its corresponding eigevector is [ 4 1]. "--
20812
PART B
Meg's mean time for completing homework is 24 minutes with a MAD of
64 minutes. Jason's mean time for completing homework is 26 minutes with a
MAD of 44 minutes. Which student, Meg or Jason, has more consistent times
completing their math homework? Explain your reasoning,
The estimated mean of the time for completion of race is 220 minutes where as the MAD to the mean ratio is 22.272%.
We have,
In statistics, the mean is one of the measures of central tendency. Another two are median and mode. Mean is the average of the given set of data.
You interviewed a random sample of 25 marathon runners and compiled the following statistics.
Mean time to complete the race = 220 minutes and MAD = 50 minutes.
So from given data it can be concluded that
mean = 220 MAD= 50
Now we find ,
(MAD/Mean ) × 100%
= (50/220)× 100%
= (5×100)/22 %
≈ 22.272%
Hence , the estimated mean of the time for completion of race is 220 minutes where as the MAD to the mean ratio is 22.272%.
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complete question:
You interviewed a random sample of 25 marathon runners and compiled the following statistics.
Mean time to complete the race = 220 minutes and MAD = 50 minutes
What can you infer about the time to complete the race among the population of runners represented by your sample?
.role perception indicates our view of how we are supposed to act in a given situation. TRUE OR FALSE?
True. Role perception refers to an individual's perception of what their role or position entails and how they are expected to behave in a particular situation.
It is shaped by various factors such as the individual's personal values, beliefs, experiences, and cultural background, as well as the expectations and norms of the organization or group they belong to.
Role perception can influence an individual's behavior, performance, and job satisfaction, as it guides them on how to act and what to expect from others in their role. However, role perception may not always be accurate or aligned with the actual expectations of the role, which can lead to misunderstandings and conflicts.
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What is the area, in square centimeters, of the trapezoid below?
13.9 cm
18 cm
7 cm
9.3 cm
Answer:
120.8
Step-by-step explanation:
A survey was given to a random sample of 800 voters in the United States to ask
about their preference for a presidential candidate. Of those surveyed, 41% of the
people said they preferred Candidate A. At the 95% confidence level, what is the
margin of error for this survey expressed as a percentage to the nearest tenth? (Do
not write ).
The margin of error for the survey is approximately 3.4% .
To calculate the margin of error for this survey at the 95% confidence level, we'll need to use the following formula:
Margin of Error = Z-score * √(p * (1-p) / n)
Where:
- Z-score represents the confidence level (1.96 for 95% confidence)
- p is the proportion of people who preferred Candidate A (0.41 or 41%)
- n is the sample size (800 voters)
Margin of Error = 1.96 * √(0.41 * (1-0.41) / 800)
After calculating, we get:
Margin of Error ≈ 0.0341 or 3.41%
So, the margin of error for this survey at the 95% confidence level is approximately 3.4% to the nearest tenth.
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A 30-foot-long support wire for a 16-foot high streetlight runs from the top corner of a building to a point on the ground, forming a straight line. The length of the wire from the top of the building to the top of the street light is 6 feet. How tall is the building?
A. 16 feet
B.20 feet
C. 32 feet
D.48 feet
Answer:
B. 20 feet
Step-by-step explanation:
(30 - 6) = 30 = 16 = x
24 = 30 = 16 = x
4 = 5 = 16 = x
4x = 80
x = 20
Question in photo will make BRAINLIEST
The required equation is VW/UW = YW/XW for the given similar triangles.
The figure is given as shown.
As per the question, given that triangles ΔUVW and ΔXYW are similar.
As we know that similar triangles are defined as two triangles with the same shape, equal pair of corresponding angles, and the same ratio of the corresponding sides.
Therefore, we can be written as follows:
VW/UW = YW/XW
This signifies that the corresponding angles and sides of the two triangles are equal and proportionate.
Therefore, the required equation is VW/UW = YW/XW.
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The table shows the numbers of comments on several blog posts. How does the outlier affect the range and interquartile range of the data?
Comment:3,5,16,9,6,9,11,2,5, and 7. The outlier increases/decreases the range by ____ and increases/decreases the interquartile range by____
The outlier in the data set of blog post comments affects the range and interquartile range in different ways. It increases the range and may also increase the interquartile range.
The range is the difference between the largest and smallest values in the data set. In this case, the range without the outlier is 16-2=14. However, if the outlier has a value greater than 16, then it increases the range. On the other hand, the interquartile range is the difference between the third quartile and the first quartile. The quartiles divide the data set into four equal parts, and the interquartile range is used to measure the spread of the middle 50% of the data. An outlier can increase the interquartile range if it falls outside the middle 50% of the data or decrease it if it falls within the middle 50%.
For example, if the outlier has a value of 20, then the range increases to 18, and the interquartile range also increases because the outlier is larger than the third quartile. If the outlier has a value of 1, then the range increases to 15, but the interquartile range decreases because the outlier is smaller than the first quartile. Therefore, outliers can have a significant impact on the range and interquartile range of a data set, and it is important to identify and handle them appropriately.
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find the general solution of the given differential equation. y' + 5x4y = x4
[tex]y = (1/5) x^5 + Ce^ {(-x^5)}[/tex] is the general solution of the given differential equation.
The given differential equation is:
y' + 5x⁴ y = x⁴
To solve this equation, we can use an integrating factor. First, we need to multiply both sides of the equation by the integrating factor, which is [tex]e^{(int 5x^4 dx)}[/tex]:
[tex]e^{(int 5x^4 dx) }y' + 5x^{4} e^{(int 5x^4 dx)} y = x^4 e^{(int 5x^4 dx)}[/tex]
The integral of 5x⁴ is (5/5)x⁵ = x, so the integrating factor is [tex]e^{(x^5)}[/tex]:
[tex]e^{(x^5)} y' + 5x^{4} e^{(x^5)} y = x e^(x^5)[/tex]
Now we can recognize the left-hand side as the product of the derivative of the product of [tex]e^{(x^5)[/tex]and y:
[tex](d/dx)[e^{(x^5)} y] = x^4 e^{(x^5)}[/tex]
Integrating both sides with respect to x, we get:
[tex]e^{(x^5)} y = (1/5) x^5 e^{(x^5)} + C[/tex]
where C is the constant of integration. Dividing both sides by [tex]e^{(x^5)}[/tex], we get the general solution:
[tex]y = (1/5) x^5 + Ce^(-x^5)[/tex]
where C is an arbitrary constant.
[tex]y = (1/5) x^5 + Ce^{(-x^5)}[/tex] is the general solution of the given differential equation.
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(please help quickly!!!!) The number of meters a student swam this week are listed.
250, 500, 500, 650, 700, 700
What is the appropriate measure of variability for the data shown, and what is its value?
The mean is the best measure of variability and equals about 550.
The median is the best measure of variability and equals 575.
The range is the best measure of variability and equals 450.
The IQR is the best measure of variability and equals 200.
Answer:
d
Step-by-step explanation:
took test
find and sketch the domain of the function. f(x, y) = ln(4 − x2 − 4y2)
The domain of the function is the set of all points in the xy-plane that satisfy the inequality 4 - x^2 - 4y^2 > 0.
The domain of a function consists of all the possible input values that can be plugged into the function to produce a valid output. In the case of the function f(x,y) = ln(4 - x^2 - 4y^2), the argument of the natural logarithm must be positive for the function to be defined. Therefore, we need to find the set of (x,y) pairs that satisfy the inequality:
4 - x^2 - 4y^2 > 0
Rearranging this inequality, we get:
x^2 + 4y^2 < 4
This is the equation of an ellipse centered at the origin with semi-major axis of length 2 and semi-minor axis of length 1/2. Thus, the domain of the function f(x,y) consists of all the points inside this ellipse.
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