Consider the series Σ n=1 [infinity] (-1)^n-1 3n+7/n²+7 he a) Determine whether or not the series is absolutely convergent. b) Determine whether or not the series is conditionally convergent.
Answers
we can conclude that the series Σn=1∞ (-1)^(n-1) * (3n+7)/(n²+7) is absolutely convergent and not conditionally convergent.
Given series: Σn=1∞ (-1)^(n-1) * (3n+7)/(n²+7)
To determine whether or not the series is absolutely convergent, we need to calculate the absolute sum of the series.So,
|aₙ|= |(-1)^(n-1) * (3n+7)/(n²+7)|
= (3n+7)/(n²+7)
Now, we need to check if the series ∑|aₙ| converges or not. Let's calculate the limit of the sum of absolute values of terms of the series. When n approaches infinity, we can get the limiting sum as:
limn → ∞ [(3n+7)/(n²+7)]
= 0
Hence, the sum of absolute values of terms of the series is zero. Since the sum of absolute values of terms of the series is less than infinity and it converges, it can be concluded that the series is absolutely convergent. Now, we need to determine whether or not the series is conditionally convergent.To check this, we need to examine if the original series is convergent or not. In this case, since the series is absolutely convergent, it is also convergent.
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Related Questions
AH = Actual Hours SH = Standard Hours AR = Actual Rate SR = Standard Rate Compute the direct labor rate and efficiency variances for the period and classify each as favorable, unfavorable or no variance
Answers
To compute the direct labor rate and efficiency variances, we will use the given terms: Actual Hours (AH), Standard Hours (SH), Actual Rate (AR), and Standard Rate (SR). Here's a step-by-step explanation:
Step 1: Calculate the Actual Labor Cost
Actual Labor Cost = AH * AR
Step 2: Calculate the Standard Labor Cost
Standard Labor Cost = SH * SR
Step 3: Calculate the Labor Rate Variance
Labor Rate Variance = (AR - SR) * AH
Step 4: Classify the Labor Rate Variance
If the Labor Rate Variance is positive, it is unfavorable. If it is negative, it is favorable. If it is zero, there is no variance.
Step 5: Calculate the Standard Labor Cost for Actual Hours
Standard Labor Cost for Actual Hours = AH * SR
Step 6: Calculate the Labor Efficiency Variance
Labor Efficiency Variance = (AH - SH) * SR
Step 7: Classify the Labor Efficiency Variance
If the Labor Efficiency Variance is positive, it is unfavorable. If it is negative, it is favorable. If it is zero, there is no variance.
By following these steps, you can compute the direct labor rate and efficiency variances for the period and classify each as favorable, unfavorable, or no variance.
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Which ratios have a unit rate greater than 17 Choose ALL that apply.
1
4 miles: 3 hours
miles: hour
6
915
miles: 3 hours
miles: 3 hours
3
7 miles:-hour
4
S
mile: 2 hours
8
Answers
Answer:
4 miles: 3 hours has a unit rate of 4/3 = 1.33 miles/hour which is greater than 17
7 miles: 1 hour has a unit rate of 7 miles/hour which is greater than 17.
PLEASE HELP ASAP!! will mark brainlest!
Answers
Answer:
1. Axis of Symmetry: x=-4, Vertex: (-4, -6)
2. Axis of Symmetry: x=2, Vertex: (2, 8)
Step-by-step explanation:
PLS HELP!!!!!!!!!!!!!!!!!! THIS IS DUE SOON AND I DONT GET IT
PLSSSSSSSS HEELPPPP BRAINLIEST PROMISED AND 24 POINTS. PLS HELP!
Answers
Answer:
80
Step-by-step explanation:
im not sure i ever done this but 1x2=2 and 2x 40= 80
i dont know sorry im trying my bets
I NEED HELP ON THIS ASAP!!!
Answers
The system of inequalities to represent the constraints of the situation are x ≤ 260, y ≤ 320, and x + y ≤ 360.
What is system of inequalities?A group of two or more linear inequalities are grouped together and graphed on a coordinate plane to discover the solution that concurrently solves all of the inequalities. Each inequality forms a half-plane on the coordinate plane, and the location where all the half-planes overlap is where the system is solved. Each point inside the feasible area meets all of the system's inequalities. This region is known as the feasible region. To identify the optimum solution given a set of constraints, systems of linear inequalities are frequently utilised in optimization issues.
Let us suppose the number of boards of Mahagony sold = x.
Let us suppose the number of black walnut boards sold = y.
According to the given problem the equation can be set as follows:
x ≤ 260 (the company has 260 boards of mahogany available)
y ≤ 320 (the company has 320 boards of black walnut available)
x + y ≤ 360 (the company expects to sell at most 360 boards of wood)
Hence, the system of inequalities to represent the constraints of the situation are x ≤ 260, y ≤ 320, and x + y ≤ 360.
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please help thnx...
hi
Answers
Answer:
-17/5
Step-by-step explanation:
Multiply ten to everything to get
6x-1= x+2-20
Simplify to 5x= -17
Solve to get x = -17/5
Please help me out here! Precalc :))
Answers
Domain are the x values where the line starts and stops.
A bracket is used for a solid circle and a parentheses is used for open circles
The answer would be the second choice: (1,2)
if In = 5 x" (1+x)0.5 dx ,n= 0,1,2....
where the integral is for x e [0,1].
By first finding a bound on the integrand, which of these is an upper bound on In?
Pick ONE option
O 1/(n+1)
O 1/2(n+1)
O 1/(n+1) + 1/(n+2)
O N^N
Answers
The correct option is 1/(n+1).The upper bound for the integral is 1/(n+1).
To determine the upper bound, we can use the fact that the integrand is bounded by its maximum value on the interval. The maximum value of the integrand on the interval [0, 1] is:
f(x) = 5x(1 + x)^(0.5)
At x = 1, f(x) = 5(1 + 1)^(0.5) = 5√2.
Therefore, an upper bound for the integral is:
In ≤ 5√2∫x^n dx
0
Using integration by parts, we obtain:
In ≤ 5√2[x^(n + 1)/(n + 1)]_0^1
= 5√2/ (n + 1)
Therefore, the upper bound for the integral is 1/(n+1).
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The cost of ground beef is proportional to the number of pounds bought. Suppose 2 pounds cost $8.40. How much would 10.5 pounds of beef cost?
Answers
Cycle City charges an initial price of $15 plus $0.75 per hour for bike rentals, which is
represented by the expression 15 +0.75h.
Complete each statement to describe the terms.
The variable h represents ?
The constant 15 represents ?
The variable term 0.75h represents ?
Answers
The constant 15 represents the initial price charged by Cycle City for bike rental.
The variable term 0.75h represents the additional price charged by Cycle City for each hour of bike rental.
Make a number line and mark all the points that represent the following values of x
-1
Answers
all the points that represent the following values of x-1 on number line is -3 -2 -1 0 1 2 3.
What is number line ?
A number line is a visual representation of numbers placed along a straight line, where each point corresponds to a unique number. It helps in visualizing the relative position of numbers and their magnitudes. The numbers to the right of zero on the number line are positive and the numbers to the left of zero are negative. The distance between two consecutive points on a number line is the same and represents the unit distance. Number lines can be used to represent integers, fractions, decimals, and even irrational numbers.
According to the question:
Make a number line and mark all the points that represent the following values of x: -1" is simply to mark the point -1 on the number line.
Here is the number line with -1 marked:
-3 -2 -1 0 1 2 3
---------------------------------------
○
The circle (○) represents the point that corresponds to x = -1.
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Q) Make a number line and mark all the points that represent the following values of x=-1,-2,-3,0,1,2,3 ?
In the given figure, find the value of x?
Answers
60 + 3x = 180 ( linear pair)
3x = 180 - 60
3x = 60
x = 60/3
x = 20
- BRAINLIEST answerer ❤️✌
Answer:
40°
Step-by-step explanation:
As per the provided information in the given question, we have :
∠AOC = 60°∠BOC = 3xAB is a straight line.We've been asked to calculate the measure of ∠BOC.
Here, ∠AOC and ∠BOC are making linear pair of angles.
\(\odot \) Linear pair : Linear pair of angles are nothing but the two adjacent angles of which non-common arms are two opposite rays. Now, as these both angles are making linear pair so,
\( \longrightarrow \sf{\quad { \angle AOC + \angle BOC = 180^\circ }} \\ \)
Substitute the measure of ∠AOC and the expression of ∠BOC.
\( \longrightarrow \sf{\quad { 60^\circ+ 3x = 180^\circ }} \\ \)
Transposing the like terms.
\( \longrightarrow \sf{\quad {3x= 180^\circ -60^\circ }} \\ \)
Performing subtraction of the terms in RHS.
\( \longrightarrow \sf{\quad {3x= 120^\circ }} \\ \)
Now, transpose 3 from LHS to RHS, its arithmetic operator will get changed.
\( \longrightarrow \sf{\quad {x= \cancel{\dfrac{120^\circ}{3}} }} \\ \)
Dividing 120° by 3.
\( \longrightarrow \quad\underline {\boxed{ \textbf{\textsf{ x= 40}}^\circ }} \\ \)
∴ The value of x is 40°.
\( \underline{ \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad} \\ \)
Learn More :○ Measure of straight angle = 180°
○ If a ray stands on a line then the sum of the adjacent angles so formed is 180°.
○ The sum of the angles of a linear pair is 180°.
\( \setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\put(5,1){\vector(1,0){4}}\put(5,1){\vector(-1,0){4}}\put(5,1){\vector(1,1){3}}\put(2,2){$\underline{\boxed{\large\sf a + b = 180^{\circ}}$}}\put(4.5,1.3){$\sf a^{\circ}$}\put(5.7,1.3){$\sf b^{\circ}$}\end{picture}\)
I need to know the area
Answers
Answer:
67.5 units²
Step-by-step explanation:
We can break this problem down in two parts: The upper triangle and the lower trapezoid.
The upper triangle:
Use the formula \(\frac{1}{2} (b)(h)\) to compute the area of the triangle. Base = 10 and Height = 7.
1/2 (10)(7)
1/2 (70)
=35 units².
The lower trapezoid:
Use the formula \(\frac{1}{2}(base_{1} + base_{2}) (height)\) to compute the area of the trapezoid. Base 1 = 10, Base 2 = 3 and Height = 5.
1/2 (10 + 3)(5)
1/2 (13)(5)
1/2 (65)
=32.5 units²
So, add the two areas of each shape:
35 + 32.5 = 67.5 units².
Answer:
Step-by-step explanation:
67.5 is the answer and thanks for asking
Round 161.69 to the nearest tenth
Answers
Answer:
To the Nearest Tenth?!
I got's you my G
= 161.7
Step-by-step explanation:
ashley jogged at most 10 1/2 miles this week. use a variable to write each sentence as an inequality.
Answers
x ≤ 10.5
Compare the rates of change of the following items.
Answers
Write an equation of the line in slope-intercept form
Y= ?
Answers
Answer:
y=-7x+4
Hope it helps!
The volume of a right cone is 5137 units³. If its diameter measures 18
units, find its height.
Answers
The height of right cone is roughly 60.58 units .
We can use the formula for a cone's volume and play around with it to solve for the height in order to determine a right cone's height given its volume and diameter. V = (1/3) * * r2 * h, where V is the volume, r is the radius (half the diameter), and h is the height, is the formula for a cone's volume.
By dividing the cone's 18-unit diameter by 2, we can determine the radius, which comes out to r = 18/2 = 9 units.
Now that we know the quantities, we can enter them into the volume formula: \(5137 = (1/3) * * 9^2 * h.\)
We can rewrite the equation as follows to find h:
\(h = (3 * V) / (\pi * r^2)\)
If we substitute the values provided, we get:h =\((3 * 5137) / (\pi * 9^2)\)
When we evaluate the expression using the approximation of 3.14159 for, we get the following result: h (3 * 5137) / (3.14159 * 81)
h ≈ 15411 / 254.469
h=60.58 units
As a result, the right cone is roughly 60.58 units tall.
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Give one pair of vertical angles and one pair of supplementary angles shown in the figure below.
Answers
Answer:
Vertical : Angles 1 & 4 Supplementary: 5 & 6
Step-by-step explanation:
Vertical angels are angles that have the same measure that are opposites of each other (1 & 4) and supplementary angles are 2 angles that equal 180 degrees that are right next to each other or right above each other (5 & 6) (3 & 5)
Simplify this expression.
–6w + (–8.3) + 1.5+ (–7w)
Answers
The simplified form of the expression -6w + (–8.3) + 1.5+ (–7w) is -13w - 6.8.
What is the simplified form of the expression?Given the expression in the question;
-6w + (–8.3) + 1.5+ (–7w)
To simplify, first remove the parenthesis
Note that;
- × + = -- × - = ++ × + = +-6w + × - 8.3 + 1.5 + × - 7w
-6w - 8.3 + 1.5 - 7w
Next collect and add like terms
-6w - 7w - 8.3 + 1.5
Add -6w and -7w
-13w - 8.3 + 1.5
Add -8.3 and 1.5
-13w - 6.8
Therefore, -13w - 6.8 is the simplified form.
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(4c+3d) - (6c-6d) - (3c-5d)
Simplify please <3
Answers
Answer:
Solution
−5+14
Step-by-step explanation:
Distribute
(4+3)−1(6−6)−1(3−5)
(4+3)−6+6−1(3−5)
Distribute
(4+3)−6+6−1(3−5)
(4+3)−6+6−3+5
(4c+3d) - (6c-6d) - (3c-5d) (4+3)−6+6−3+5
4+3−6+6−3+5
Combine like terms
4+3−6+6−3+5
−5+3+6+5
Combine like terms
−5+3+6+5
−5+14
Solution
−5+14
What is the mean of the data set (3, 2, 2, 12, 6, 5, 14, 4]? O 2 O 4 O 6 O 7
Answers
Answer: 6
Step-by-step explanation:
{3, 2, 2, 12, 6, 5, 14, 4}
To find the mean,add everything up, the divide it by how many numbers you added up.
So, do :
3 + 2 + 2 + 12 + 6 + 5 + 14 + 4 = 48
Then, because you added 8 numbers together, you would divide 8 from 48.
48 ÷ 8 = 6
So, your mean is 6
PLEASE HELP ME IT'S DUE TODAY AND IT COULD HELP MY GRADE A LOT
Answers
Answer:
c = 13
m∡A = 60°
m∡B = 30°
Step-by-step explanation:
This is a 5-12-13 triangle. However, to make sure, I will put the steps.
Allow for each sides to be denoted as a-b-c, in which c is the hypotenuse (longest side). Set the equation:
a² + b² = c²
Plug in the corresponding numbers to the corresponding variables:
5² + 12² = c²
Simplify. First, solve the exponents, and then add:
(5²) = 5 * 5 = 25
(12²) = 12 * 12 = 144
25 + 144 = c²
c² = 169
Note the equal sign, what you do to one side, you do to the other. Isolate the variable, c, by rooting both sides:
√c² = √169
c = √169 = √(13 * 13) = 13
c = 13
13 is your answer for c.
Note the measurements of the angles. We know that this is a 30-60-90 triangle, and so it will be easy to figure it out. Note that the corresponding angles will depend on that of the opposite side's measurement lengths. The hypotenuse will always be on the opposite side of the largest angle (as given), as c, the longest side, is opposite of ∡C, which is the largest angle (90°). Based on this information, it means that ∡A would be 60° (as it is opposite of the middle number, 12), and ∡B would be 30° (opposite of the smallest number, 5).
PROBLEM
5
A box contains 81 chits with numbers 1 to 81 written on them. If a chit is drawn at random, what is the
probability of the following cases?
The number is not a perfect square
• The number is greater than 50
• The number is negative 0
.
Answers
The probability of number is not a perfect square, Probability number is greater than 50 and the probability of number is negative 0 are 73/81, 31/81 and 0 respectively
How to find the probability of the cases?
Probability is a measure of the likelihood of an event occurring. Probability is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
Given: A box contains 81 chits with numbers 1 to 81 written on them
The probability that the number is not a perfect square:
Perfect squares are 1, 4, 16, 25, 36, 49, 64, and 81.
Thus, we have eight perfect squares. So the numbers that are not perfect squares will be 73 in number.
Probability (not a perfect square) = 73/81
Probability(number is greater than 50) = 31/81
Probability(number is negative 0) = 0/81 = 0
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what is the value of 30-2(7+2)-1
Answers
Answer:
11
Step-by-step explanation:
30-2(7+2)-1
30-2(9)-1
30-18-1
12-1
11
Answer: Thy answer to ye question is 11
Step-by-step explanation:
Solve the following equation for a. Be sure to take into account whether a letter is capitalized or not.
n/q=b/a
please help
Answers
Answer:
\(a = \frac{bq}{n}\)
Step-by-step explanation:
If we are trying to solve for "a", then we need it to be alone on one side of the equation.
\(\frac{n}{q} = \frac{b}{a}\)
\(\frac{an}{q} = b\)
\(a = \frac{bq}{n}\)
On a map where each unit represents 100 miles, two airports are located at P(1,17) and Q(12,10). What is the distance, to the nearest whole mile, between the two airports? A. 1,800 miles B. 1,304 miles C. 1,122 miles D. 900 miles
Answers
Using the distance formula, the distance, to the nearest whole mile, between the two airports is: B. 1,304 miles.
How to Apply the Distance Formula?The distance formula is: d = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\).
Given the following locations:
P(1,17) = (x1, y1)
Q(12,10) = (x2, y2)
Use the distance formula to find the PQ:
PQ = √[(12−1)² + (10−17)²]
PQ = √[(11)² + (−7)²]
PQ = √170
PQ ≈ 13.04 units
1 unit = 100 miles
PQ = 13.04 × 100
PQ = 1,304 mils
Thus, using the distance formula, the distance, to the nearest whole mile, between the two airports is: B. 1,304 miles.
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Answer: B. 1,304 miles.
Jennifer is shopping with her mother. They pay $2 per pound for tomatoes at the vegetable stand.
A. Find the constant of proportionality in the situation.
B. Write an equation to represent the relationship.
Answers
hopefully this helpssss
evaluate the expression 6x + 4 9/10 when x = 2/3.
Answers
x=2/3
6(2/3) + 4 9/10 =4 + 4 9/10 = 8 9/10
Answer:
2x-1=y,2y+3=x
Step-by-step explanation:
no explanation
2.
Problem 2 Statement
At the kennel, the ratio of cats to dogs is 4:5. There are 27 animals in all Here is a tape diagram
representing this ratio.
number of cats
number of dogs
a.
What is the value of each small rectangle?
How many dogs are at the kennel?
b.
C.
How many cats are at the kennel?
Answers
Step-by-step explanation:
For these type of problems, add the ratio numbers together - in this case 4+5. Then do the total number (27) divided by those two ratio numbers added.
Hope this helps.