The series [infinity]Σn=1 (-1)^n -1. 1/n^0.1 is absolutely convergent the given statement is true..
We are to determine whether the series ∞Σn=1(−1)n−11/n0.1 is absolutely convergent.
Let's start with the definition of absolute convergence.
A series is said to be absolutely convergent if the sum of the absolute values of the terms of the series converges. If the series is conditionally convergent and the sum of the series diverges to infinity when absolute values are taken, then the series is said to be divergent.
The general term of the series is given by
a_n = (-1)^n - 1/n^0.1
Let's take the absolute value of a_n
a_n| = 1/n^0.1
Since 0.1 < 1, the p-series p = 0.1 is a convergent series.
Therefore, |a_n| = 1/n^0.1 is a convergent series by comparison test.
Since the absolute value series converges, we can say that the original series also converges absolutely.
Thus, the given series ∞Σn=1(−1)n−11/n0.1 is absolutely convergent.
Hence, the given statement is true.
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If (x-9) is a factor of 2x^2 - 19x + k what is the value of k
Answer:
The answer is 18.
What is 12x+8-7x-10 simplified
What are the domain restrictions?
X-8/x² + 6x - 7
a. x1,x=7
b. x#8
c. x1,x#-7
d. x-1, x*7
Answer: The correct answer is the function domain is x<-7 or x>1
Your available options (a-d) appear to have some incorrect values, I am assuming the correct answer is "c. x1,x#-7" provided it matches "c. x>1, x<-7"
Step-by-step explanation:
The domain of a function is the set of input or argument values for which the function is real and defined.
Equation: x-8/x^2+6x-7
Define the domain of (x-8)/(x^2+6x-7)
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If x^2 = 40, what is the value of x? ±80 ±20 plus or minus square root 80 plus or minus square root 40
Answer:
Step-by-step explanation:
x^2 = 40
To find the value of x you must take the square root of both x^2 and 40.
When you do, you get
sqrt(x^2) = sqrt(40)
Answer x = + sqrt(40)
Simplification
x = + sqrt(2 * 2 * 2 * 5)
The square root of 2 equal primes is one of them. That root can be shown outside the root sign.
x = + 2*sqrt( 2 * 5)
physically Stephanie bought a used one for 1500naira and sold it to her friend at profit of 4%
The amount by which Stephanie sold the item is given as follows:
1560 naira.
How to obtain the amount?The amount by which Stephanie sold the item is obtained applying the proportions in the context of the problem.
The amount at which the item was purchased is given as follows:
1500 naira.
Hence the amount at which the item was sold is given as follows:
1.04 x 1500 = 1560 naira.
Missing InformationThe problem asks for the amount by which Stephanie sold the item.
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Each minute, a faucet allows 4/7 gallons of water to enter a large tub, and the drain allows 5/7 gallons to leave the tub.
What is the change in the amount of liquid in the tub after 1/4 minute?
Enter your answer as a fraction in lowest terms in the box.
gal.
Answer: -1/28 gallon
Step-by-step explanation:
divide both numbers by 4 since its 1/4 a minute (-5/7 ÷ 4 and 4/7 ÷ 4) then add them, (-5/28 + 4/28= -1/28)
Answer: -1/28 gallon
Step-by-step explanation:
Can someone help me? I had the notes in my notebook but I threw it away when it got full, not thinking that I was ever gonna need these notes again.. ;,)
Figure A is a scale image of Figure B. What is the value of x?
Answer:
4.4
Step-by-step explanation:
To find the answer we would need to find by how much the amount reduced from Figure B to Figure A.
10/4=2.5.
Now we just need to divide 11 by 2.5 which equals 4.4.
So, if I'm correct, the answer should be 4.4.
Hope this helps! <3
Find x in each triangle
Answer:
15
Step-by-step explanation:
BY PYTHAGORAS THEOREM
Answer:
x = 15 ft
Step-by-step explanation:
using the Pythagorean theorem:
x² = 17² - 8² = 289 - 64 = 225
x = √225 = 15
factors of the number 81 as 1,3,27,81
Answer:
Great
Step-by-step explanation:
However, you're missing a factor of 9.
Answer:
1x81 =81
3x27=81
9 x 9 =81
1,3,27,81 These are factors too, but you missed of the number 9.
3. Pilihan ganda30 detik1 ptQ. How does the arrival of George Murchison change the mood of the scene?George's arrival changes the mood because he doesn't take part in the danceGeorge's arrival changes the mood because he complains that Beneatha is giving them a lecture on their African pastGeorge's arrival changes the mood because he was rich, and they didn't like that a rich white person was in their houseGeorge's arrival changes the mood because he had a gun
Option B) George's arrival changes the mood because he complains that Beneatha is giving them a lecture on their African past
In Act 2 of A Raisin in the Sun, George Murchison's arrival changes the mood of the scene as he complains that Beneatha is giving them a lecture on their African past. George's comments create tension and conflict among the characters, particularly with Beneatha, who is exploring her African heritage. His attitude towards Beneatha's interest in her roots is dismissive and condescending, which generates discomfort and disagreement among the characters. George's arrival highlights the cultural differences between him and the Younger family and demonstrates the generational and ideological divides within the African American community. Thus, his presence is a catalyst for revealing deeper tensions and conflicts within the play.
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Complete question:
How does the arrival of George Murchison change the mood of the scene?
A) George's arrival changes the mood because he doesn't take part in the dance
B) George's arrival changes the mood because he complains that Beneatha is giving them a lecture on their African past
C) George's arrival changes the mood because he was rich, and they didn't like that a rich white person was in their house
D) George's arrival changes the mood because he had a gun
2.3 divided by 5.06
help, please
Answer: 0.454
2.3/5.06
0.45454545
Brainliest pweaseee if the answer is correct! <3
What is the domain and range of this function?
I’ll put Brainliest! :)
Answer:
Step-by-step explanation:
The Domain of a function is the x value, and the Range of a function is the y value. For example, in the ordered pair (9,4) the Domain is 9, or the x value, and the Range is 4, or the y value. So to find the Domain and Range, write ordered pairs for each plotted point on your graph (the dot at the end of each line) and then go through and identify the Domain and Range from there. When you list them, write the numbers in numeric order from least to greatest. Hope this helps!
What is the equation in standard form of the line that passes through the point (6,-1) and is parallel to the line represented by 8x+3y=15.
The equation of line that passes through the point (6, -1) & is parallel to the line represented by 8x + 3y = 15, in standard form is: 8x + 3y = 45.
Equation of a line in standard form is:
Ax + By = C
where A, B & C are constants.
As the required line is parallel to the given line, that is 8x + 3y = 15, the slope of the required line will be same as that of the given line.
Slope intercept form of a line is:
y = mx + b
where, m is slope of the line, b is a constant.
Re-writing the equation of the given line in slope-intercept form:
⇒ 3y = -8x + 15
⇒ y = (-8/3)x + 5
⇒ slope = m = -8/3
Now as the required line is parallel to the given line, hence its slope-intercept form will be
y = (-8/3)x + b
As the line passes through the point (6, -1),
⇒ -1 = (-8/3)×6 + b
⇒ b = 15
Hence, the slope-intercept form of the required line is
y = (-8/3)x + 15
Re-writing it in standard form, the equation comes out to be
8x + 3y = 45
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Tell what each of the residual plots to the right indicates about the appropriateness of the linear model that was fit to the data. (a). Choose the best answer for residuals plot A. The fanned pattern indicates that the linear model is not appropriate. The model's predicting power decreases as the values of the explanatory variable increases. B. The fanned pattern indicates that the linear model is not appropriate. C. The model's predicting power increases as the values of the explanatory variable increases. The scattered residuals plot indicates an appropriate linear model. (b). Choose the best answer for residuals plot A. The scattered residuals plot indicates an appropriate linear model. B. The curved pattern in the residuals plot indicates that the linear model is not appropriate. The relationship is not linear. C. The fanned pattern indicates that the linear model is not appropriate. The model's predicting power decreases as the values of the explanatory variable increases.
Residual Plot A indicates that the linear model is not appropriate because the fanned pattern shows that the model's predicting power decreases as the values of the explanatory variable increases. Residual Plot B indicates that the linear model is appropriate because the scattered residuals suggest a linear relationship.
Residual Plot A shows a fanned pattern which indicates that the linear model is not appropriate. This means that the model's predicting power decreases as the values of the explanatory variable increases. This suggests that the relationship between the dependent and independent variables is not linear and a different model may be necessary. Residual Plot B, on the other hand, shows a scattered pattern which suggests that the linear model is appropriate. The scattered pattern indicates that the data points are randomly distributed, which is a sign of a linear relationship. This indicates that the linear model is an appropriate fit for the data.
the complete question is :
Tell what each of the residual plots to the right indicates about the appropriateness of the linear model that was fit to the data. (a). Choose the best answer for residuals plot A. The fanned pattern indicates that the linear model is not appropriate. The model's predicting power decreases as the values of the explanatory variable increases. B. The fanned pattern indicates that the linear model is not appropriate. C. The model's predicting power increases as the values of the explanatory variable increases. The scattered residuals plot indicates an appropriate linear model. (b). Choose the best answer for residuals plot A. The scattered residuals plot indicates an appropriate linear model. B. The curved pattern in the residuals plot indicates that the linear model is not appropriate. The relationship is not linear. C. The fanned pattern indicates that the linear model is not appropriate. The model's predicting power decreases as the values of the explanatory variable increases.
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Find the x-intercept and y-intercept
from the following linear equation:
-3x + 11y = 66
x - intercept (-22, [?])
y - intercept ([],[])
Answer:
x - intercept: (-22, 0)
y - intercept: (0, 11)
Step-by-step explanation:
Given the linear equation
-3x + 11y = 66
Determining the x-intercept
We know that the x-intercept can be computed by setting the value y=0 and solving for x.
substitute y = 0
-3x + 11y = 66
-3x + 11(0) = 66
-3x + 0 = 66
-3x = 66
Divide both sides by -3
-3x/-3 = 66/-3
x = -22
Thus, the ordered pair representing the x-intercept : (-22, 0)
Determining the y-intercept
We know that the y-intercept can be computed by setting the value x=0 and solving for y.
substitute x = 0
-3x + 11y = 66
-3(0) + 11y = 66
0 + 11y = 66
11y = 66
Divide both sides by 11
11y/11 = 66/6
y = 11
Thus, the ordered pair representing the y-intercept : (0, 11)
Therefore, we conclude that:
x - intercept: (-22, 0)
y - intercept: (0, 11)
Answer:
X=(-22,0)
Y=(0,6)
Two six-sided dice are rolled and the sum of the faces showing is recorded after each roll. Let �
=
the number of rolls required to obtain a sum greater than 7
. If 100
trials are conducted, which of the following is most likely to be the result of the simulation?
Based on probability, it is most likely that the result of the simulation will be close to the expected value of 4. This means that on average, it will take around 4 rolls to obtain a sum greater than 7.
To determine the most likely result of the simulation, we need to understand the possible outcomes and their probabilities.
When rolling two six-sided dice, there are a total of 36 possible outcomes. Each die has 6 possible outcomes (1, 2, 3, 4, 5, 6), so the total number of outcomes is 6 × 6 = 36.
Let's analyze the possible sums of the faces showing after each roll:
If the sum is less than or equal to 7, we need to roll again.
If the sum is greater than 7, we have successfully obtained a sum greater than 7 and the process is complete.
Let's calculate the probabilities for each scenario:
The sum is less than or equal to 7 (not successful):
The possible outcomes for this scenario are (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (3, 1), (3, 2), (3, 3), (3, 4), (4, 1), (4, 2), (4, 3), (5, 1), (5, 2), (6, 1).
The number of possible outcomes in this scenario is 21 out of 36.
The probability of this scenario is 21/36 = 7/12.
The sum is greater than 7 (successful):
The possible outcomes for this scenario are (2, 6), (3, 5), (3, 6), (4, 4), (4, 5), (4, 6), (5, 3), (5, 4), (5, 5), (5, 6), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6).
The number of possible outcomes in this scenario is 15 out of 36.
The probability of this scenario is 15/36 = 5/12.
Based on the probabilities, the probability of a successful outcome (sum greater than 7) is higher than that of an unsuccessful outcome (sum less than or equal to 7). Therefore, the most likely result of the simulation would be a sum greater than 7.
Therefore, the result "a sum greater than 7" is the most likely outcome of the simulation.
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Graph the line x = - 1.
Answer: see below
Step-by-step explanation:
x=-1 is a vertical line at x=-1
A truck is traveling at a constant speed. The diagram represents the truck's distance and time. What is the speed of the truck?
Answer:
distance divided by time
Step-by-step explanation:
distance is the speed of the moving object multiplied by the time taken to complete a certain distance therefore the speed is the distance covered divided by the time taken.
please help with these 3 questions
Answer:
1. D) Both b) and c)
2. B) Cosine Law
3. B) Find the measures of angles and sides that we can't physically measure.
Step-by-step explanation:
1. To solve non-right triangles we use Sine Law and Cosine Law.
2. If 3 sides lengths were given and you were asked to find an angle, you would use the Cosine Law.
3.Trigonometry is used in real life to find the measures of angles and sides that we can't physically measure.
Am i the only one that watches Osman??
Someone else in the world may watch it but personally i do not.
Answer:
Please Give Brainliest
Step-by-step explanation:
Ivan runs each lap in 4 minutes. He will run at most 28 minutes today. What are the possible numbers of laps he will run today?
Use n for the number of laps he will run today.
Write your answer as an inequality solved for n.
Answer:
7 laps
Step-by-step explanation:
4n = 28
n = 7
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Look at the Screenshot
The value for m is -5
Putting the x⁵ on the denominator is just a way to get rid of the negative exponent.
How can I solve x - y = -8
Is y alone?
Answer:
x - y = -8
+ y +y
x = -8y
A population has a mean of
= 50 and a standard deviation of
= 10.
A) If 3 points were added to every score in the population, what would be the new values for the mean and standard deviation?
B) If every score in the population were multiplied by 2, then what would be the new values for the mean and standard deviation?
A) The new values for the mean and standard deviation, after adding 3 points to every score, would be a mean of 53 and a standard deviation of 10. B) The new values for the mean and standard deviation, after multiplying every score by 2, would be a mean of 100 and a standard deviation of 20.
A) Adding 3 points to every score in the population would result in a shift of the entire distribution. The new mean would be the original mean plus 3, so the new mean would be 50 + 3 = 53. The standard deviation would remain the same since it measures the spread of the data relative to the mean. Therefore, the new standard deviation would still be 10.
B) Multiplying every score in the population by 2 would affect both the mean and the standard deviation. The new mean would be the original mean multiplied by 2, so the new mean would be 50 * 2 = 100. The new standard deviation would also be multiplied by 2 since it measures the spread of the data relative to the mean. Therefore, the new standard deviation would be 10 * 2 = 20.
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a researcher in campaign finance law wants to estimate the proportion of elementary, middle, and high school teachers who contributed to a candidate during a recent election cycle. given that no prior estimate of the population proportion is available, what is the minimum sample size such that the margin of error is no more than 0.03 for a 95% confidence interval?
A minimum sample size of 1069 is required to estimate the proportion of elementary, middle, and high school teachers who contributed to a candidate during a recent election cycle such that the margin of error is no more than 0.03 for a 95 percent confidence interval.
In order to estimate the proportion of elementary, middle, and high school teachers who contributed to a candidate during a recent election cycle, a researcher in campaign finance law wants to determine the minimum sample size such that the margin of error is no more than 0.03 for a 95 percent confidence interval.
Assuming that the researcher wants to establish a 95% confidence interval, the level of significance (α) is 1 - 0.95 = 0.05. Furthermore, we can assume that there is no prior knowledge of the population proportion, which is the proportion of elementary, middle, and high school teachers who contributed to a candidate during the election cycle. The standard deviation of a proportion is calculated using the following formula:
\(σ_p=√(p(1−p)/n)\)
Here, n is the sample size and p is the proportion of elementary, middle, and high school teachers who contributed to a candidate during the election cycle. Because there is no prior knowledge of p, it is assumed that the sample proportion, p-hat, is equal to 0.5.
Using these values, we can calculate the minimum sample size required for a margin of error of 0.03 for a 95 percent confidence interval.
α/2=0.025 can be determined by dividing the level of significance (α) by two. This will allow us to calculate the appropriate critical value. To calculate the critical value, we can look up the value of 0.025 in a standard normal distribution table.
Z_α/2=1.96 is the corresponding z-value for a 95% confidence interval.With the critical value, we can now calculate the minimum sample size using the formula below:
\(n = (Z^2) (p) (1 - p) / (E^2)\)
where, Z = critical valueα = level of significance (0.05)
E = margin of error (0.03)
p-hat = 0.5
The minimum sample size for a 95% confidence interval with a margin of error of 0.03 and no prior knowledge of the population proportion is as follows:
\(n = (1.96)^2 (0.5) (0.5) / (0.03)^2n = 1068.44444 ≈ 1069\)
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It takes a snail 50 hours to travel 22 miles. At this rate, how many hours will it take the snail to travel 11 miles?
Answer: 25 hours
Step-by-step explanation:
Answer:
25 hours
Step-by-step explanation:
A quadratic function y=f(x) is plotted on a graph and the vertex of the resulting parabola
(−4,−5). What is the vertex of the function defined as g(x)= f(-x)−4?
Answer:
(-2,6)
Step-by-step explanation:
y=f(x) has vertex (-4,6)
g(x)=-f(x-2) shifts the graph 2 units to the right, not to the left, and the graph is reflected over the x-axis
therefore the vertex is (-2,6) and the reflection over the x-axis has no affect on the vertex
Unit #2 - Lesson #7 Exit Ticket: Solve the equation shown below for the variable x. Place your answer in the answer box.
Answer:
doctor
Step-by-step explanation:
feature-length capacitor chromatographic filesystems crinkled
I forgot how to do these, and i don’t remember whether they have two answers or not.
Solve for d.
-7| d - 1 | = -11
Answer:
=18/7
=−4/7
Step-by-step explanation:
Divide both sides by -7
−7|−1|=−11
The negatives are canceled.
Simplify
|−1|=11/7
Split the problem into two cases: one positive and one negative
=18/7
=−4/7