Use the comparison test or limit comparison test to determine whether the following series is convergent or divergent. 1 5 sinn (a) Švh-1 (b)Σ ( n=2 n=1 n! 6. Use the alternating series test to determine whether the series Inn coverges. n Σ(-1): n=3
Answers
The problem involves using convergence tests to determine whether two given series converge or diverge.
In the first part, we are asked to use either the comparison test or the limit comparison test to determine the convergence of the series Σ(sinn)/n^(1/2), where n ranges from 1 to infinity. To use the comparison test, we need to find a known series that is either greater than or less than the given series and whose convergence is already known.
To use the limit comparison test, we need to find a known series whose ratio with the given series approaches a finite non-zero limit. In the second part, we are asked to use the alternating series test to determine whether the series Σ((-1)^n)/n) converges or diverges, where n ranges from 3 to infinity. The alternating series test states that if a series alternates in sign and its absolute values decrease monotonically to zero, then the series converges. If the absolute values do not decrease monotonically, then the series diverges.
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Related Questions
Select the correct answer.
Which expression is equivalent to this polynomial expression?
(5xy^2 + 3x^2–7) + (3x^2y^2 – xy^2 + 3y^2 + 4)
Answers
Answer:
Option B
Step-by-step explanation:
\((5xy^2 + 3x^2-7) + (3x^2y^2-xy^2 + 3y^2 + 4)\\\)
if we solve this lets rewrite it order
\(3x^2y^2-xy^2 + 3y^2 + 4+5xy^2+3x^2-7\)
\(3x^2y^2-xy^2 +5xy^2+3y^2+3x^2-7+4\)
\(3x^2y^2+4xy^2+3y^2+3x^2-4\)
The solution of the given polynomial is 3x²y² + 4xy² +3x² +3y² +3x²y² -3. The correct option is B.
What is a polynomial?A polynomial in mathematics is an expression made up of coefficients and indeterminates and involves only the operations of multiplication, addition, subtraction, and non-negative integer exponentiation of variables.
Given that the expression is (5xy² + 3x²–7) + (3x²y² – xy² + 3y² + 4).
The polynomial can be solved as:-
E = (5xy² + 3x²–7) + (3x²y² – xy² + 3y² + 4)
E = 3x²y² + 4xy² + 3x² + 3y² -3
Hence, the solution of the polynomial would be 3x²y² + 4xy² +3x² +3y² +3x²y² -3.
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F(x)=-2^2+16x-13
In vertex form
Answers
Answer:
f(x) = - (x - 8)² + 51Step-by-step explanation:
Assumed it is:
f(x) = - x² + 16x - 13Converting into vertex form:
f(x) =- x² + 16x - 13 = - (x² - 16x + 64 - 64) - 13 = - (x - 8)² + 64 - 13 = - (x - 8)² + 51Given :-
x² + 16x -13 [correct]To Find :-
To convert it in vertex form .Answer :-
We have ,
x² + 16x -13 x² + 2*8*x -13Add and subtract 8² .
x² + 2*8*x + 8² - 8² -13 ( x² + 2*8*x +8²) -64 -13 ( x +8)² - 77Hence the required answer is (x+8)² -77.
Find the value of x in this equation.
1/6 (6x-5) - x = 1/3 - 2(x + 1)
Answers
Explanation:
1/6(6x-5) - x = 1/3 - 2(x + 1)
(6x - 5)/6 - 6x/6 = 2/6 - 6(2x + 2)/6
6x - 5 - 6x = 2 - 12x - 12
-5 = -12x - 10
12x = -5
x = -5/12
Therefore, x = -5/12
which sampling method divides the population up into sections, then chooses sll the members from the selected sections to cstudy
Answers
The sampling method which divides the population up into sections and then chooses all the members from the selected sections to study is called the cluster sampling method. The answer is cluster sampling method.
Cluster sampling is a probability sampling technique in which the population is divided into smaller groups or clusters. The clusters are then randomly selected, and all members within the chosen clusters are included in the sample. This method is commonly used when the population is large and dispersed over a wide area, making it difficult or impossible to sample from the entire population. Cluster sampling has several advantages. It is less time-consuming and less costly compared to other methods of sampling. It also allows for a greater representation of the population as all members within the chosen clusters are included in the sample. However, it is important to note that cluster sampling can lead to increased sampling error due to the fact that members within a cluster may be more similar to each other than to members in other clusters. Overall, cluster sampling is a useful method of sampling when dealing with large, dispersed populations.
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Find the slope of the line passing through the pair of points. (−4, −5) and (5, 4) A. −1 B. 1 C. 9 D. −9
Answers
Answer: A. -1
Explanation: 4-5/5-4= -1/1 = -1
The probability of success of an event is p and that of failure is q. Find the expected number of trials to get a first success.
Answers
The expected number of trials to get a first success in an event with probability of success p and probability of failure q is 1/p.
The expected number of trials to get a first success in an event with probability of success p and probability of failure q can be calculated using the formula:
Expected number of trials = 1/p
Therefore, the expected number of trials to get a first success in this event is 1/p.
For example, if the probability of success is 0.2 (or 20%), then the expected number of trials to get a first success is 1/0.2 = 5 trials.
It is important to note that this formula assumes that each trial is independent of the previous trials, meaning that the probability of success or failure does not change from one trial to the next.
In summary, the expected number of trials to get a first success in an event with probability of success p and probability of failure q is 1/p.
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calculate the volume of of a cylinder of diameter 5.93cm and length 10cm in log and antilog
Answers
Archaeologists used pieces of burned wood, or charcoal, found at the site to date prehistoric paintings and drawings on walls and ceilings of a cave in Lascaux, France. Considering that the half-life of carbon-14 (C-14) is 5730 years, determine the appropriate age of a piece of burned wood, if it was found that 76.1% of the C-14 found in living trees of the same type had decayed.
Answers
The appropriate age of the piece of burned wood is approximately 20945 years.
Carbon-14 dating is based on the principle that living organisms continuously exchange carbon with their environment. When an organism dies, the intake of carbon-14 stops, and the existing carbon-14 begins to decay at a predictable rate. The half-life of carbon-14 is 5730 years, which means that after 5730 years, half of the carbon-14 in a sample will have decayed.
In this case, if 76.1% of the carbon-14 found in living trees of the same type had decayed, it implies that the remaining carbon-14 represents approximately 23.9% of the original amount. By applying the concept of half-life, it can be determined that the elapsed time is approximately 4 half-lives (since 23.9% is close to 25%). Therefore, 4 times the half-life of carbon-14 (5730 years) gives an estimated age of approximately 20945 years for the piece of burned wood.
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Which is equivalent to 23/25
Answers
Answer:
I don’t see any answer choices??
(Answer to ur question in the comments)
⬇️
Step-by-step explanation:
Of the 24 items that Jamal has sold, 25% are CDs. Jamal has sold
4 more T-shirts than CDs. How much profit has the band earned
from Jamal's sales?
Answers
Answer: Not applicable
Step-by-step explanation:
To determine the profit earned from Jamal's sales, we need more information such as the price of each item and the total profit earned from each item. Without this information, it is impossible to calculate the profit earned from Jamal's sales.
please help mi i really need it XD
Answers
Answer:
q^3
Step-by-step explanation:
xd xd xd okay ill help xd xd
youre just symplifying by the way
Whats the answer y’all
Answers
The expressions that will give you a difference of 5 are: -3 - (-8) and 1 - (-4).
What is the Difference of Two Expressions?The difference of two expressions is determined by subtracting one from the other.
Find the difference of each of the expressions given to determine which will give us 5.
-3 - (-8)
= -3 + 8
= 5
-2 - 3 = -5 [this is not the same as 5]
1 - (-4)
= 1 + 4
= 5
7 - (-2)
= 7 + 2
= 9
-3 - (-8) and 1 - (-4) will give us a difference of 5.
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which expression is equivalent to 4^7 x 4^-5
Answers
please mark this answer as brainlist
Construct a truth table for each of these compound propositions
a) p → ⇁p
b) p ↔ ⇁p
c) p ⊕ (p V q) d) (p ∧ q) → (p V q) e) (p → ⇁p) ↔ (p ↔ q) f) (p ↔ q) ⊕ (p ↔ ⇁q)
Answers
After considering the given data we conclude that there truth table is possible and is placed in the given figures concerning every sub question.
A truth table is a overview that projects the truth-value of one or more compound propositions for each possible combination of truth-values of the propositions starting up the compound ones.
Every row of the table represents a possible combination of truth-values for the component propositions of the compound, and the count of rows is described by the range of possible combinations.
For instance, if the compound has just two component propositions, it comprises four possibilities and then four rows to the table. The truth-value of the compound is projected on each row comprising the truth functional operator.
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I am unsure how to solve problems H through L and it's due by Friday!!! pls help! (solve for variable listed on paper from equation)
Answers
Answer:
Step-by-step explanation:
(h)
\(KE= \frac{1}{2}mv^{2} \\KE=\frac{mv^{2} }{2} \\2KE=mv^{2}\\2KEm=v^{2} \\v=\sqrt{2KEm}\)
(g)
\(s=\frac{(u+v)t}{2} \\2s=(u+v)t\\\frac{2s}{t}=u+v\\u= \frac{2s}{t}-v\)
(i)
\(s=ut+\frac{1}{2} at^{2} \\s-ut=\frac{at^{2} }{2} \\2s-2ut=at^{2} \\\sqrt{2s-2ut}=at\\a=\sqrt{2s-2ut}-t\)
(j)
\(\frac{pV}{T} =nR\\T=\frac{pV}{nR}\)
(k)
\(a^{2} -b^{2} +c^{2} \\a^{2} +c^{2} =b^{2} \\b=\sqrt{a^{2} +c^{2} }\)
(i)sinθ\(=\frac{a}{b}\)
θ=\(\frac{a}{sin(b)}\)
Z 3. Give/Describe a generator, a directrix and the rulings of the cylinder x = (1/z)^z. Draw a sketch of the cylinder.
Answers
The cylinder x = (1/z)^z has a unique shape defined by its generator curve, a directrix line at x = 1, and rulings connecting the generator curve to the directrix.
The cylinder x = (1/z)^z represents a cylindrical surface in three-dimensional space. The generator of the cylinder is obtained by fixing the x-coordinate and allowing z to vary. By doing so, we generate a curve that lies on the surface of the cylinder. This curve is known as the generator.
The directrix of the cylinder is the line x = 1. It acts as a reference line parallel to the z-axis and helps determine the position of the ruling lines. The rulings of the cylinder are straight lines that connect corresponding points on the generator curve to the directrix. These lines create a grid-like pattern that extends across the surface of the cylinder.
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Two coins are flipped. The sample space representing all the outcomes of this action is the set S ={ HH,HT,TH,TT}. Which
subset of represents the event "At least one HEAD is flipped"?
Answers
The subset of represents the event "At least one HEAD is flipped" is {HH, HT, TH}.
The event "At least one HEAD is flipped" refers to the outcome of flipping two coins where there is at least one head showing. To find the subset of the sample space S = {HH, HT, TH, TT} that represents this event, we need to identify the outcomes that satisfy the condition.
Looking at the sample space, we can see that three out of the four possible outcomes have at least one head: HH, HT, and TH. These outcomes represent the scenarios where at least one of the coins shows heads.
The outcome HH represents the scenario where both coins show heads, HT represents the scenario where the first coin shows heads and the second shows tails, and TH represents the scenario where the first coin shows tails and the second shows heads.
The outcome TT represents the scenario where both coins show tails and does not satisfy the condition of "at least one head."
Therefore, the subset of the sample space S that represents the event "At least one HEAD is flipped" is {HH, HT, TH}. These outcomes encompass all the possibilities where there is at least one head in the outcome of flipping two coins.
In summary, the subset {HH, HT, TH} represents the event "At least one HEAD is flipped" because these outcomes fulfill the condition of having at least one head in the result of flipping two coins, while the outcome TT does not satisfy this condition.
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Un jugador de basquetbol ha realizado los 2/5 del número de puntos conseguidos por su equipo en un partido y otro la tercera parte del resto. Si los demás jugadores han conseguido 34 puntos, ¿cuántos puntos obtuvo el equipo en el partido?
Answers
Answer:
85 points
Step-by-step explanation:
Let :
Total points made by team = x
Points made by the player :
2/5 of total = 2x/5
1/3 of the rest :
Points left = x - 2x/5= 3x /5
1/3 of 3x /5
1/3 * 3x / 5
= 3x / 15 = x / 5
Points made by rest of the players = 34 points
Hence, total points scored, x :
x = 34 + 2x /5 + x /5
x = 34 + 3x / 5
x - 3x/5 = 34
2x / 5 = 34
2x = 34 * 5
2x = 170
x = 170 / 2
x = 85
Total points scored by team = 85
In interval estimation, as the sample size becomes larger, the interval estimate.
Answers
The interval estimate becomes narrower.
An interval estimate is the use of sample data to calculate an interval of possible (or probable) values of an unknown population parameter, as opposed to a point estimate, which is a single number.
Estimation is a method of drawing conclusions about an unknown population parameter from a sample. An estimate is a statistic that is used to calculate the value of a parameter that is not defined. Intervals are statistical estimation approaches that use survey data to generate ranges of values that are likely to contain the population value of interest. Point estimates, on the other hand, are single-valued estimates of the population value. Confidence intervals are the most familiar of the various forms of statistical intervals. Certain types of analysis and scenarios, on the other hand, require the use of different scopes that provide different details.
Hence in interval estimation, as the sample size becomes larger, the interval estimate becomes narrower.
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Which of the following are solutions to the inequality below? Select all that apply.
5 ≥ s
Answers
Answer:
: w ≤ - 6
Step-by-step explanation:
What is the result of subtracting the second equation from the first -2x+7y=-5 -2x-4y=6
Answers
Answer:
0x+11y=-11
Step-by-step explanation:
hope this helps
plzz mark me brainliest
Answer:
y=-1
Step-by-step explanation:
-2×+7y=-5
- -2×-4y=6
11y=-11
But you don't leave the answer like that
You need to simplify
So
11y=-11
y=-11
11
y=-1
Which set of points below represents a function
0 (4,2), (6, 2), (6,4), (8,4)}
O {(1,2), (1,3), (1.4), (1,5)}
O (-1.8), (0, 10), (1, 12), (2, 14)
O . 9,2
{(11. 6), (11.4), (9.2). (7.0)}
I don’t know the answer some help
Answers
Answer:
I believe it's the 3rd option:
(-1, 8), (0, 10), (1,12), (2, 14)
Step-by-step explanation:
Part D
At one point on the trip, the miles are recorded as 15,121 when the gas tank is
75% full. Use a ratio equation to determine the miles per gallon the sedan
averages. Round your answer to the nearest whole number.
Answers
The sedan gets 1090 miles per gallon on average, according to the ratio equation.
What exactly is a ratio?A ratio is an ordered pair of numbers a and b, denoted by the a / b, where b is not equal to zero.
What is a ratio example?If there are eight oranges and six lemons in a bowl of fruit, the orange-to-lemon ratio is eight to six.
Given: When the gas tank is 75% full, the mileage is recorded as 15,121.
A sedan tank is typically 18.5 gallons in size. So it holds 13.875 gallons of gas if it is 75% full. If it traveled 15,121 miles, the mileage per gallon is 1090, rounded to the nearest whole number.
The calculation of miles per gallon using the ratio equation:
Let, x = miles per gallon
15121:13.875 is the ratio.
x/1= 15121/13.875
13.875x = 15121
x = 15121/13.875
x = 1089.80, which equates to 1090 miles per gallon
As a result, the ratio equation used to calculate the sedan's miles per gallon averages 1090 miles per gallon.
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What is the circumference of a circle whose radius is 20 feet. Leave awnser in terms of pi
Answers
Answer:
40π
Step-by-step explanation:
cricumference: 2πr (or πd)
2π(20) = (40)π ≈ 125.66
Answer: 40
Step-by-step explanation:
First, you have to multiply the radius by 2 which gives us 40. Then, 40 x 3.14 (pi) = 125.6 After, you divide 125.6 by 3.14 which once again gives you 40. :)
What is the class width for the class (65-72)kg?
Answers
Answer: Super Lightweight to Middleweight
Step-by-step explanation: I'm assuming you're talking about boxing weight class. If not, please let me know.
i dont know how to do these and i have to finish the subject in an hour so sorry for spamming
Answers
Answer:
x = 45°.
Step-by-step explanation:
∠AED is a vertical angle with ∠BEC. That means the m∠AED = m∠BEC.
x + 115 = 160
x = 160 - 115
x = 45
So, x = 45°.
Hope this helps!
what is 7x8 pls i need some help
Answers
Answer:
56
Step-by-step explanation:
Work out the size of angle 0.
Give reasons for your answer.
Answers
Answer:
θ = 56°
Step-by-step explanation:
As OA and OB are both radii, triangle AOB is an isosceles triangle:
⇒ m∠ABO = m∠OAB = 48°
Interior angles of a triangle sum to 180°:
⇒ m∠ABO + m∠OAB + m∠AOB = 180°
⇒ 48° + 48° + m∠AOB = 180°
⇒ m∠AOB = 180° - 48° - 48°
⇒ m∠AOB = 84°
Angles on a straight line sum to 180°:
⇒ m∠AOB + m∠DOB = 180°
⇒ 84° + m∠DOB = 180°
⇒ m∠DOB = 180° - 84°
⇒ m∠DOB = 96°
The tangent of a circle is always perpendicular to the radius.
Therefore, tangent BC is perpendicular to radius OB, and tangent DE is perpendicular to radius OD, so:
m∠OBC = 90°m∠ODE = 90°OBCD is a quadrilateral.
The interior angles of a quadrilateral sum to 360°:
⇒ m∠OBC + m∠BCD + m∠CDO + m∠DOB = 360°
⇒ 90° + θ + 28° + 90° + 96° = 360°
⇒ θ + 304° = 360°
⇒ θ = 360° - 304°
⇒ θ = 56°
paige just finished a road trip where she visited the following square pyramids: the bent pyramid and the red pyramid. the table below shows the approximate dimensions of the two pyramids. dimensions of pyramids base side length height bent pyramid 619 feet 332 feet red pyramid 722 feet 341 feet paige has to write a paper on volume for school and needs some help. what is the difference in volume of the two pyramids, rounded to the nearest cubic foot?
Answers
The difference in volume between the two pyramids is 12,371,740 cubic feet.
To find the volume of a square pyramid, you use the formula :
V = (1/3)Bh, where B is the area of the base and h is the height.
Using the dimensions given in the table, we can calculate the volumes of the two pyramids:
- Volume of Bent Pyramid = (1/3)(619 feet * 619 feet)(332 feet) = 26,384,053.33 cubic feet
- Volume of Red Pyramid = (1/3)(722 feet * 722 feet)(341 feet) = 38,755,793.33 cubic feet
To find the difference in volume between the two pyramids, we subtract the smaller volume from the larger volume:
38,755,793.33 - 26,384,053.33 = 12,371,740 cubic feet.
Rounding to the nearest cubic foot, the difference in volume between the two pyramids is 12,371,740 cubic feet.
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-1=(5+x)/6
Please help me
Answers
Answer:
-11
Step-by-step explanation:
Answer:
\(x=-11\)
Step-by-step explanation:
\(-1=\frac{\left(5+x\right)}{6}\)
Switch sides:
\(\frac{\left(5+x\right)}{6}=-1\)
Multiply both sides by 6:
\(\frac{6\left(5+x\right)}{6}=6\left(-1\right)\)
\(5+x=-6\)
Subtract 5 from both sides:
\(5+x-5=-6-5\)
\(x=-11\)