The following series are geometric series. Determine whether each series converges or not. For the series which converge, enter the sum of the series. For the series which diverges enter "DNE" (without quotes). 67 DNE 5" 1 6 X (c) (d) n=2 5 23 5 6(2) ³ 3" DNE 37+4 5" + 3" 31 6" 6 n=1 Question Help: Message instructor Submit Question (e) n=0 n=5 37 n=1 37 52n+1 5" 67 || = X
Answers
Each series are : (a) DNE (b) Converges with a sum of 3/2. (c) DNE (d) Diverges and (e) Diverges.
To determine whether each geometric series converges or diverges, we can analyze the common ratio (r) of the series. If the absolute value of r is less than 1, the series converges.
If the absolute value of r is greater than or equal to 1, the series diverges.
Let's analyze each series:
(a) 67, DNE, 5, 1, 6, X, ...
The series is not clearly defined after the initial terms. Without more information about the pattern or the common ratio, we cannot determine whether it converges or diverges. Therefore, the answer is DNE.
(b) 1, 6, (2)³, 3, ...
The common ratio here is 2/6 = 1/3, which has an absolute value less than 1. Therefore, this series converges.
To find the sum of the series, we can use the formula for the sum of an infinite geometric series:
Sum = a / (1 - r), where a is the first term and r is the common ratio.
In this case, the first term (a) is 1 and the common ratio (r) is 1/3.
Sum = 1 / (1 - 1/3) = 1 / (2/3) = 3/2.
So, the sum of the series is 3/2.
(c) DNE, 37 + 4/5 + 3/5² + 3/5³, ...
The series is not clearly defined after the initial terms. Without more information about the pattern or the common ratio, we cannot determine whether it converges or diverges. Therefore, the answer is DNE.
(d) 31, 6, 6², 6³, ...
The common ratio here is 6/6 = 1, which has an absolute value equal to 1. Therefore, this series diverges.
(e) n = 0, n = 5, 37, n = 1, 37, 52n + 1, 5, ...
The common ratio here is 52/37, which has an absolute value greater than 1. Therefore, this series diverges.
In summary:
(a) DNE
(b) Converges with a sum of 3/2.
(c) DNE
(d) Diverges
(e) Diverges
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Related Questions
A continuous random variable X has probability density function f(x) = c(1+x)(1 - 2 over the domain -1<<1. (a) i. Evaluate the constant e (the integration can be done by MATLAB). ii. Plot the probability density function over the domain (-1,1). Is this density function skewed to the right, skewed to the left, or symmetric? (b) Use MATLAB to evaluate I i. the mean y = E(X)= |- «f(x) dx; ii. E(X)= (- 22 f(x) dx; iii. the variance o2 = Var(X) = E(X) – H?, and the standard deviation o. *(c) i. Use MATLAB to find an expression for the cumulative distribution function F(x). ii. Check the result in (i) by differentiation. Hint: simplify (ans) might help! iii. Evaluate P(-0.2 X <0.2).
Answers
(a)i. Evaluating the constant:
\($$\int_{-1}^{1} c(1+x)(1-2x) dx = 1$$$$\implies c = \frac{3}{4}$$\)
Therefore, the probability density function is:
\($$f(x) = \frac{3}{4} (1+x)(1-2x), -1< x < 1$$\) ii. Plotting the probability density function:
From the graph, it is observed that the density function is skewed to the left.
(b)i. The mean:
\($$E(X) = \int_{-1}^{1} x f(x) dx$$$$E(X) = \int_{-1}^{1} x \frac{3}{4} (1+x)(1-2x) dx$$$$E(X) = 0$$\)
ii. The second moment about the origin:
\($$E(X^2) = \int_{-1}^{1} x^2 f(x) dx$$$$E(X^2) = \int_{-1}^{1} x^2 \frac{3}{4} (1+x)(1-2x) dx$$$$E(X^2) = \frac{1}{5}$$\)
Therefore, the variance is:
\($$\sigma^2 = E(X^2) - E(X)^2$$$$\implies \sigma^2 = \frac{1}{5}$$\)
iii. The standard deviation:
$$\sigma = \sqrt{\sigma^2} = \sqrt{\frac{1}{5}} = \frac{\sqrt{5}}{5}$$(c)
i. The cumulative distribution function:
\($$F(x) = \int_{-1}^{x} f(t) dt$$$$F(x) = \int_{-1}^{x} \frac{3}{4} (1+t)(1-2t) dt$$\)
ii. The probability density function can be obtained by differentiating the cumulative distribution function:
\($$f(x) = F'(x) = \frac{3}{4} (1+x)(1-2x)$$\)
iii. Evaluating\(P(-0.2 < X <0.2):$$P(-0.2 < X <0.2) = F(0.2) - F(-0.2)$$$$P(-0.2 < X <0.2) = \int_{-0.2}^{0.2} f(x) dx$$$$P(-0.2 < X <0.2) = \int_{-0.2}^{0.2} \frac{3}{4} (1+x)(1-2x) dx$$$$P(-0.2 < X <0.2) = 0.0576$$\)
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how to solve −3/4n≤3.
Answers
Answer:
n ≥ -4
Step-by-step explanation:
-3/4n ≤ 3
-4/3(-3/4n) ≤ 3(-4/3)
n ≥ -12/3
n ≥ -4
CHECK:
correct
-3/4(-4) ≤ 3
12/4 ≤ 3
3 = 3
correct
-3/4(5) ≤ 3
-15/4 ≤ 3
-3.75 < 3
incorrect
-3/4(1) ≤ 3
-3/4 is not ≤ 3
If a fee for a balance transfer is 3% and b = amount of the balance and f= the fee transfer show the formula used to calculate the relationship?
Answers
Answer:
f=0.03b
Step-by-step explanation:
Amount of balance = b
Fee charged on balance = f = 3%
Amount of fee charged on balance = 3% of amount of balance
Amount of fee charged = 0.03b
Thus,
f=0.03b
Consider the following counter-espionage puzzle to find whether there is a spy among n guests at a party. Every spy knows everyone else's name but nobody will know theirs. Fortunately, if you ask any person at this event the name of any other person (other than yourself), they'll tell you honestly whether they know. The non-spies will do so because they're good, honest people, and the spy will do so because they want to seem like they fit in. So all you need to do is ask every pair at the party whether each knows the other's name, right? Here's the problem. If the spy happens to notice you doing this, they'll get spooked and leave. You'll need to ask as few questions as possible. Describe a protocol for finding a spy that: 1. Finds the spy if there is one. 2. Uses 3(n−1) or fewer questions of the form "do you know that person's name?" Your protocol should be recursive. Prove by induction on n that your protocol satisfies the two properties above.
Answers
The questions asked in the final step, between potential_spy_A and potential_spy_B, are independent of the group size. Therefore, the protocol still requires 3(n-1) or fewer questions overall. By induction, the protocol satisfies the two given properties for any number of guests n.
Here is a recursive protocol for finding a spy among n guests at a party using 3(n-1) or fewer questions:
Base case (n = 2): Ask the first person if they know the second person's name. If they answer "yes," the first person is not the spy. If they answer "no," the first person is the spy.
Recursive case (n > 2):
a. Divide the group into two equal-sized subgroups, A and B, each containing n/2 guests.
b. Apply the protocol recursively to subgroup A, which will find a potential spy, if any, among them. Let's call this person "potential_spy_A."
c. Now, we need to determine whether potential_spy_A is the actual spy or not. We do this by asking potential_spy_A if they know anyone in subgroup B.
If potential_spy_A answers "yes," we know they are not the spy, as the spy does not know anyone's name.
If potential_spy_A answers "no," we know they might be the spy. However, we can't be certain yet.
d. Apply the protocol recursively to subgroup B, excluding potential_spy_A, which will find a potential spy, if any, among them. Let's call this person "potential_spy_B."
e. Now, we need to determine whether potential_spy_B is the actual spy or not. We do this by asking potential_spy_B if they know anyone in subgroup A.
If potential_spy_B answers "yes," we know they are not the spy, as the spy does not know anyone's name.
If potential_spy_B answers "no," we know they might be the spy. However, we can't be certain yet.
Final step:
a. Now we have two potential spies: potential_spy_A and potential_spy_B.
b. To determine the actual spy, ask potential_spy_A if they know potential_spy_B's name.
If potential_spy_A answers "yes," potential_spy_B is the spy.
If potential_spy_A answers "no," potential_spy_A is the spy.
Proof by induction:
Base case (n = 2): In this case, we ask one question, satisfying the requirement of 3(n-1) or fewer questions.
Recursive case (n > 2): Assuming the protocol works for n guests, let's prove it for (n+1) guests.
In the recursive step, we divide the group into two equal-sized subgroups, A and B. Each subgroup has (n+1)/2 guests, which is greater than 1.
Applying the protocol recursively to subgroups A and B ensures that we find potential spies, if any, among them, satisfying the property of finding the spy if there is one.
The questions asked in the final step, between potential_spy_A and potential_spy_B, are independent of the group size. Therefore, the protocol still requires 3(n-1) or fewer questions overall.
Hence, the protocol satisfies both properties for (n+1) guests.
By induction, the protocol satisfies the two given properties for any number of guests n.
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Does anyone know how to divide 4/3 by 7/11?
Answers
Answer:
Well, when you are dividing fractions, you can turn 4/3 into 3/4 and do 3/4*7/11 and you will get the same answer as 4/3 divided by 7/11. I hope this easier way to divide fractions helped you!
Step-by-step explanation:
Also, the answer is 21/44
I need some help please it’s due in 20 minutes!
Answers
Answer:C
Step-by-step explanation:
I am not that sure.. but I think the answer is C.
pls help 50 points!!!!!!
it is on khan!!!
Answers
Answer:
5
Step-by-step explanation:
Well, there are 4 "s" blocks that make up one "20" units block. So all you have to do is to divide 20/4 to get 5.
If the point (x, y) is in Quadrant III, which of the following must be true?
x < 0 and y>0
x < 0 andy<0
Submit
x > 0 and y>0
x > 0 and y < 0
Answers
Answer: x < 0 and y < 0
Step-by-step explanation:
quadrant three is here
|
II | I
|
--------------------|-------------------
|
III | IV
|
here /\
so, the x is to the left which is negative, and the y is down which is negative. x is less than zero, and y is less than zero
help me find the perimeter please:)
Answers
Answer:
79.2 cm
Step-by-step explanation:
Add up all the lengths of all of the sides of the figure:
16.2 + 7.5 + 7.5 + 18 + 18 + 12 = 79.2
Answer:
79.2 m
Step-by-step explanation:
Well since all the units are the same and you have already labeled the missing/ congruent sides. Just add up all the sides and you’d end up with 79.2
At 4:00 AM, the temperature is – 12 °F. If the temperature drops 3 °F per hour, what will the temperature be at 6:00 AM?
Answers
Hope this helps ?(:
Answer:
-18
Step-by-step explanation: -12 - 3 - 3 sence 2 hours passed
i think is the answer
Without dividing how can you decide which quotient is greater: 51 +31 or 5 1/4÷2 1/2
Answers
Answer:
51 + 31
Step-by-step explanation:
To compare which quotient is greater between 51+31 and 5 1/4 ÷ 2 1/2, we can use estimation.
First, we can estimate 51+31 to be around 80.
Then, for the second quotient 5 1/4 ÷ 2 1/2, we can convert the mixed numbers to improper fractions to get 21/4 ÷ 5/2. We can then multiply the divisor (5/2) by 2/2 to get a common denominator of 10. This gives us 21/4 ÷ 5/2 = 21/4 ÷ 5/10. We can then invert the divisor and multiply to get 21/4 x 10/5 = 21/2 or 10.5.
Since 80 is greater than 10.5, we can conclude that 51+31 is greater than 5 1/4 ÷ 2 1/2.
Use the CER strategy to solve the following questions.
1. As an accountant, you keep track of invoices and payments. You received a payment of
$4, 823.28 from a client. Your company's money transfer provider charges a fee that
reduces the amount paid by 1 %. To match the amount you received to the invoice, you
need to know the original amount the client paid before the transfer fee was charged.
What was the original amount the client paid?
Answers
Answer:
48,232.8
Step-by-step explanation:
4,823.28 x 0.01
NEED HELP ASAP 25 pointsWhich equation best describes the data in the table?x y-2 -41 -73 1 6 28options:a. y=x-2b. y=3x-4c. y=x^2-8d. y=2x^2-3
Answers
To determine the equation that best describe the data in the table, let us substitute the value of x given on the table into each equation and check for the equation that gives us the corresponding values of y;
for x = -2, y=-4; substituting x= -2 into each equation, we have;
\(\begin{gathered} a)y=x-2=-2-2=-4 \\ b)y=3x-4=3(-2)-4=-16 \\ c)y=x^2-8=-2^2-8=4-8=-4 \\ d)y=2x^2-3=2(-2)^2-3=5 \end{gathered}\)From the first substitution, only equation a and c gave us the corresponding value of y.
Secondly, let's substitute another value of x into the two right right equaabove to confirm the best;
At x=1, y= -7; substituting x=1 into equation a and c we have;
\(\begin{gathered} a)y=x-2=1-2=-1 \\ c)y=x^2-8=1^2-8=-7 \end{gathered}\)From the above only equation c gave us the corresponding value of y at x=1.
Since only equation c gave us the corresponding values of y for both substituttions. The equation that best describe the data on the table is equation cequatio
\(c\text{. }y=x^2-8\)the probability that paul can solve the crossword puzzle in an hour is 0.4. the probability that annie can do that is 0.6. Find the probability that a)both of them can solve the puzzle in an hour; b) neither can solve the puzzle in an hour; c)only Mary can solve the puzzle in an hour; d)Mary or Burt can solve the puzzle in an hour;
Answers
The probabilities are given as follows:
a) Both: 0.24.
b) Neither: 0.24.
c) Only Mary: 0.36.
d) Mary or Burt: 0.76.
How to calculate a probability?The parameters that are needed to calculate a probability are listed as follows:
Number of desired outcomes in the context of a problem or experiment.Number of total outcomes in the context of a problem or experiment.Then the probability is then calculated as the division of the number of desired outcomes by the number of total outcomes.
For both people, we multiply the probabilities, hence:
0.6 x 0.4 = 0.24.
For neither people, we multiply the complement of the probabilities, hence:
(1 - 0.6) x (1 - 0.4) = 0.24.
For only Mary, we have that:
(1 - 0.4) x 0.6 = 0.36.
For at least one, we subtract the total of 1 from neither, hence:
1 - 0.24 = 0.76.
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in 2021, the national highway traffic administration said that, based on survey data, 84% of drivers use seat belts regularly. if four drivers are randomly selected, what is the probability that at least one of them is not wearing a seatbelt?
Answers
The probability that at least one of them is not wearing a seatbelt is 0.5021.
What is meant by probability?Potential is described by probability. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of events. Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true.
These concepts now have an axiomatic mathematical formalization thanks to probability theory, which is widely employed in disciplines including statistics, mathematics, science, finance, gambling, artificial intelligence, machine learning, computer science, and philosophy.
Let X be the proportion of drivers who do not use a seat belt. It has a binomial distribution, as shown by,
n=4, p=1-0.84
p=0.16
The likelihood that at least one of them is not wearing seatbelt is:
P(X≥1)=1-P(X<1)
=1-P(X=0)
=1-{(4₀)(0.16)⁰(1-0.16)⁴⁻⁰
=1-0.4979
=0.5021.
Therefore, the probability that at least one of them is not wearing a seatbelt is 0.5021.
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The area of a circle is 169π
What is the value of r?
Answers
Answer:
radius is 7.33...
Step-by-step explanation:
I think that is the answer but i am not very sure
Triangle A B C. The length of side A C is 10, B C is 6, and A B is 8. Triangle A prime B prime C prime. Side A prime C prime has a length of 5.
Triangle ABC is dilated to get triangle A'B'C'. Which is the length of A'B'?
Options:
3
4
5
16
Answers
The measure of side A'B' for the triangle A'B'C' is equal to 4 using a scale factor of 1/2 to dilate it.
What is scale factorScale factor is the ratio between the scale of a given original object and a new object, which is its representation but of a different size either bigger or smaller.
The dilation if the triangle ABC implies it is bigger than the triangle A'B'C' with a scale factor 1/2 since AC = 10 and A'C' = 5
side A'B' = 8 × 1/2
side A'B' = 4
Therefore, the measure of side A'B' for the triangle A'B'C' is equal to 4 using a scale factor of 1/2 to dilate it.
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Answer:
the answer is B, 4. :)
Find the elapsed time.
from 2:08 A.M. to 11:03 A.M.
3 h 5 min
8 h 55 min
8 h 45 min
9 h 5 min
Answers
4x-3y-23=0
2x-5y=36
solve this question as a simultaneous linear equation
Answers
Answer:
x=1/2, y=-7
Step-by-step explanation:
4x-3y=23 (1)
2x-5y=36
4x-3y=23
(-2)*(2x-5y=36)
4x-3y=23
-4x+10y=-72 +
----------------------
7y=-49
y=-49/7
y=-7
(1)--> 4x-3*(-7)=23
4x+21=23
4x=23-21
4x=2
x=2/4
x=1/2
Answer:
x = 1/2, y = -1/7
Step-by-step explanation:
All other units of measure are defined and compared to the four basic measurements of: _____?
Answers
The four basic measurements that serve as the foundation for other units of measure are length, mass, time, and temperature.
Length is a measure of distance between two points, typically measured in meters (m) within the International System of Units (SI). Mass is the amount of matter in an object, measured in kilograms (kg) in the SI system. Time refers to the duration or interval between events and is measured in seconds (s) within the SI system.
Lastly, temperature is a measure of the average kinetic energy of particles in a substance, represented in degrees Celsius (°C) or Kelvin (K) in the SI system.
All other units of measure are defined and compared to these four basic measurements. For instance, speed is derived from the combination of length and time (e.g., meters per second). Similarly, force is derived from mass and acceleration, which itself is derived from the change in velocity over time (e.g., newtons).
The combination and comparison of these fundamental measurements enable scientists, engineers, and other professionals to quantify and analyze various phenomena in the physical world.
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What number is the opposite of the opposite of 68?
Answers
Answer:
it's(-68) if you mean negative positive wise
yesterday, eric had m baseball cards. today, he got 10 more. using m , write an expression for the total number of baseball cards he has now. as an equation
Answers
Answer:
m+10
Step-by-step explanation:
We know that yesterday, eric had m baseball cards. Thus, we can denote that the total number of baseball cards he had yesterday is m.
We know that he got 10 more today. Since he is receiving more, he is adding to his collection. Since he is getting more, we have to add 10 to how many baseball cards he used to have. He used to have m baseball cards, so today he has m+10 baseball cards.
This is the answer as we cannot combine 10 and m. Since m is a variable with no set value as of now, and 10 is a constant number that has no variable, they are not like terms and cannot be added. So the answer is m+10 baseball cards.
I hope this helped.
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Type the correct answer in the box. Use numerals instead of words.
For this item, if the answer is not a whole number, enter it as a fraction in simplest form using / as the fraction bar.
Isolde is stacking books. The stack of books forms a rectangular prism.
Each book is the same size. Isolde knows the area of the base of one book is 22 1/2 square inches and each book is 3/4 inch thick.
The volume of a stack of 9 books is cubic inches.
Answers
The volume of a stack of 9 books is 1368.75 cubic inches.
Volume of a book stackTo find the volume of a stack of 9 books, we first need to find the height of the stack. Since each book is 3/4 inch thick, the height of the stack is 9 times 3/4 inch, which is 6 3/4 inches.
Now we need to find the area of the base of the rectangular prism formed by the stack of books. Since each book has an area of 22 1/2 square inches, the total area of the base of the stack is 9 times 22 1/2 square inches, which is 202 1/2 square inches.
Therefore, the volume of the stack of 9 books is:
Volume = Area of base x heightVolume = (202 1/2 square inches) x (6 3/4 inches)Volume = 1368.75 cubic inchesMore on volume of stacked books can be found here: https://brainly.com/question/1058070
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-2(3x + 2) > -6x - 4
Answers
Answer: All real numbers are solutions.
Step-by-step explanation:
−2(3x+2)≥−6x−4
Step 1: Simplify both sides of the inequality.
−6x−4≥−6x−4
Step 2: Add 6x to both sides.
−6x−4+6x≥−6x−4+6x
−4≥−4
Step 3: Add 4 to both sides.
−4+4≥−4+4
0≥0
"Match the justifaction with each step"
Answers
I also want to know the answer...........................................
If you can buy 5 packs of gum for $4.99 how much does 1 pack of gum cost? (1 mark)
Answers
Step-by-step explanation:
5 packs = $4.99 => $5
1 packs = $5 ÷ 5
= $1
So, much on 1 packs of gum cost is $1
Sorry, if i wrong. Im newbie in USA server
Answer:
divide 4.99 by 5 and that should be your answer
Step-by-step explanation:
6) What is the measure of angle bpc?
Answers
find the f-test statistic to test the claim that the population variances are equal. both distributions are normal. the standard deviation of the first sample is 2.1971 7.32 is the standard deviation of the second sample.
Answers
the f-test statistic to test the claim that the population variances are equal is F test = 2.54
We are given two samples
Standard deviation of the first sample = 2.1971
Standard deviation of the second sample = 7.32
F test statistic = Variance of the Larger sample/ Variance of the smaller sample
Variance = (Standard deviation)²
Variance for the first sample = 2.1971²
= 4.8272
Variance for the second sample = 7.32² = 53.5824
F test = 53.5824/4.8272
= 11.100
Therefore, the F test approximately = 11.100
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it takes a 1/4 bottle glue to make slime if teacher has 15 bottles of glue how many bottles of slime can the 5th graders make
Answers
Answer:
60students
Step-by-step explanation: 4 x 15=60
This is because each bottle can make 4 slimes and if there are 15 bottles you multiply 4 by 15. Now you will receive 60.
The width of a rectangle is 5x -9.5 feet and the length is 9.5x + 10 feet. Find the perimeter of the
rectangle
Answers
Answer:
Perimeter of the rectangle is 29x + 1 feet
Step-by-step explanation:
Length of the rectangle = 9.5x + 10 feet
Width of the rectangle = 5x - 9.5 feet
perimeter of rectangle = 2 ( length + width )
perimeter = 2 { (9.5x + 10) + (5x-9.5) }
perimeter = 2 ( 9.5x + 5x + 10 - 9.5 )
perimeter = 2 (14.5x + 0.5)
perimeter =29x + 1 feet