Answers
If nth partial sum of series S is given by Sₙ = n+1/n²+1, the value of S is equal to 0.7834.
To find the sum S of the series, we need to take the limit of the nth partial sum as n approaches infinity. This is because the series contains an infinite number of terms, and the sum is the value that the series approaches as we add more and more terms.
We can write the formula for the nth partial sum as:
Sₙ = 1/2 + 2/5 + 3/10 + ... + n/(n²+1)
To find the sum S, we take the limit of Sₙ as n approaches infinity:
S = [tex]\lim_{n \to \infty}[/tex] Sₙ
We can use the formula for the nth partial sum to simplify Sₙ:
Sₙ = 1/2 + 2/5 + 3/10 + ... + n/(n²+1)
= [1/(1²+1)] + [1/(2²+1)] + [1/(3²+1)] + ... + [1/(n²+1)]
= Σ[1/(k²+1)], k=1 to n
Using calculus or other advanced techniques, we can find that the limit of Σ[1/(k²+1)] as n approaches infinity is approximately 0.7834. Therefore, the sum of the series S is approximately:
S ≈ 0.7834
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Related Questions
Kiet needs to observe a science experiment every 6 minutes for one hour. He makes his first observation at 1:00 p.m. At what time will he make another observation?
Answers
Kiet will make his another observation at every multiples of 6 until it reaches at 60 which is at 2 : 00 pm.
Given that,
Kiet needs to observe a science experiment every 6 minutes for one hour.
He makes his first observation at 1:00 p.m.
Now he needs to make the observation every 6 minutes.
This means that his second observation will be at 1:06 pm.
Third observation will be at 1:12 pm.
Fourth will be at 1:18 pm.
It goes on like this for every multiples of 6.
His last observation will be at 2:00 pm which is at the 60th minute after 1.
Hence Kiet will make his observations at every multiples of 6 until it reaches 60.
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3.11 Graded Assignment: Quadratic Equations - Part 2
Answers
At the north end mall, the food court in the court hallways are parallel, in the west hall in east hall are perpendicular. The angle made between the east hall in mid court hallways is 45°. What is the measure of angle X 
Answers
The measure of angle X in the figure is 135 degrees
What is the measure of angle XFrom the question, we have the following parameters that can be used in our computation:
Court hallways are parallel, in the west hall In east hall are perpendicular.Using the above as a guide, we have the following:
x = 90 + angle made between the east hall in mid court hallways
So, we have
x = 90 + 45
Evaluate
x = 135
Hence, the angle is 135 degrees
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1) Find each set is (All Real Numbers) is the universal set.
{x ∈ (All Real Numbers) : -1≤x≤4}^c
In the format of : {x∈_(N, Q, R, W, or Z)__; _____(Equation)____
2) Find each set if R is the universal set.
{x ∈ (All Real Numbers) : x² ≥ 0 }^c
3)
A woman has seven blouses, five skirts, and twenty-one pairs of shoes in her closet. How many outfits can she create) (Note that an outfit consists of one blouse, one skirt, and one paire of shoes. )
Thank you :)
Answers
Answer:
{x∈R : x<-1 or x>4 }
emptyset
735
Step-by-step explanation:
1) Find the points that are not in the original set.
2) same as above
3) 7 possibilities for blouse times 5 possibilities times 21 possibilites
1. {x ∈ R : x < -1 or x > 4}
2. {x ∈ R : x ∈ ∅}
3. The number of outfits = 735.
What is set?Sets are groups of well-defined objects or components in mathematics. A set is denoted by a capital letter, and the cardinal number of a set is enclosed in a curly bracket to indicate how many members there are in a finite set.
1. The set {x ∈ (All Real Numbers) : -1≤x≤4}^c represents the complement of the set {x ∈ (All Real Numbers) : -1≤x≤4}.
The universal set is (All Real Numbers).
The set {x ∈ (All Real Numbers) : -1≤x≤4} contains all real numbers between -1 and 4, including -1 and 4.
Therefore, the complement of this set {x ∈ (All Real Numbers) : -1≤x≤4}^c contains all real numbers that are not between -1 and 4, or outside the interval (-∞, -1) U (4, ∞).
In set builder notation, this can be written as:
{x ∈ R : x < -1 or x > 4}
2. The set {x ∈ (All Real Numbers) : x² ≥ 0 }^c represents the complement of the set {x ∈ (All Real Numbers) : x² ≥ 0}.
The universal set is R.
The set {x ∈ R : x² ≥ 0} contains all real numbers, since any real number squared is always greater than or equal to 0.
Therefore, the complement of this set {x ∈ R : x² ≥ 0}^c contains no real numbers, since all real numbers satisfy the condition x² ≥ 0.
In set builder notation, this can be written as:
{x ∈ R : x ∈ ∅}
3. To find the number of outfits the woman can create, we need to multiply the number of options for each clothing item together.
The number of outfits = number of blouses × number of skirts × number of pairs of shoes
= 7 × 5 × 21
= 735
Therefore, the woman can create 735 outfits.
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Given f(x)= what is the
value of f(12)?
Answers
The value of f(12) for the function f(x) = (x - 4)/16 is 0.5.
Here we have been given the function
f(x) = (x - 4)/16
This function models the expression (x - 4)/16. This implies that we will get a different value of f(x) for every different value of x.
Now here we have been given to find the value of f(12). This implies that we need to find the value of f(x) = (x - 4)/16 when the value of x is 12.
Hence, to find f(12) we need to replace x with 1 in the function. This will give us
(12 - 4)/16
= 8/16
= 0.5
Therefore, f(12) is 0.5
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appomixe the value in the log
Answers
The approximation of log(12) from log(2) and log(3) is 1.544
Appomixe the value in the logFrom the question, we have the following parameters that can be used in our computation:
log(2) = 0.4307
log(3) = 0.6826
So, we have
log(12) = log(4 * 3)
Applying the law of logarithm, we h\ave
log(12) = log(4 + log(3)
So, we have
log(12) = 2log(2) + log(3)
substitute the known values in the above equation, so, we have the following representation
log(12) = 2 * 0.4307 + 0.6826
Evaluate
log(12) = 1.544
Hence, the approximation is 1.544
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Robert just purchased a house for $186,000 after down payment and fees, his loan is for 20 years at an APR of 4.8%. His monthly payment is $1,207.06. Using this information fill in the amortization chart for his first monthly payment.
Answers
Answer:
Step-by-step explanation:
What unit of measurement would you use to weigh an elephant? (2 points)
a
Ounce
b
Ton
c
Millimeter
d
Pound
Answers
Michael lives in Geo City. A map of the city is found below. If Michael walks directly from school to the park, how far must he travel? Round your answer to the nearest tenth if necessary.
Answers
Answer:
The school is at (2, 1), and the park is at (-6, 5).
[tex] \sqrt{ {(2 - ( - 6))}^{2} + {(1 - 5)}^{2} } [/tex]
[tex] \sqrt{ {8}^{2} + {( - 4)}^{2} } [/tex]
[tex] \sqrt{64 + 16} = \sqrt{80} = 4 \sqrt{5} [/tex]
4√5 is about 8.9.
A random sample of n=1200
�
=
1200
registered voters and found that 620 would vote for the Republican candidate in a state senate race. Let p
�
represent the proportion of registered voters who would vote for the Republican candidate.
Consider testing
H0:p=.50
�
0
:
�
=
.50
Ha:p>.50
�
�
:
�
>
.50
(a) The test statistic is z
�
=
(b) Regardless of what you acutally computed, suppose your answer to part (a) was z = 1.28. Using this z,
p-value =
Answers
The critical t value for a confidence level of 80% with a sample size of 11 is 1.833.
What is value?
Value in math is the numerical representation of a concept or quantity. It can be used to measure, compare, or describe a range of concepts, including distance, speed, time, money, and more. Value is an essential part of mathematics, as it allows for the comparison of different numbers and is used in equations and formulas to solve problems. Value is also used to represent specific ideas, such as the value of pi or the value of "infinity".
The critical t value represents the boundary between the middle two categories of a t-distribution with a confidence level of 80%. To calculate this value, we must first calculate the degrees of freedom (DF) which is equal to the sample size minus 1. In this case, the DF is 10.
Next, we must use a t-table to find the t value. Using the chart, we can see that for a confidence level of 80%, the t value is 1.833. This means that any value of t that is higher than 1.833 will fall within the highest category of the t-distribution and is considered statistically significant. Therefore, the critical t value for a confidence level of 80% with a sample size of 11 is 1.833.
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You are going to use an incline plane to lift an heavy object to the top of a shelving unit with a height of 8 ft. The base of the incline plane is 9 ft from the shelving unit. What is the length of the incline plane?
Answers
length = square root of (height^2 + base^2)
In this case, the height is 8 ft and the base is 9 ft, so we can substitute those values into the formula:
length = square root of (8^2 + 9^2)
length = square root of (64 + 81)
length = square root of 145
length ≈ 12.04 ft
the length of the incline plane is approximately 12.04 ft.
Can you help me with this
Answers
Answer:
Step-by-step explanation:
116 because on the graph it said that 116 sophmores were a no
What lump sum should be deposited in an account that will earn 9% compounded every 2 months, to grow to $100,000 in 32 years? Show your step process, when you are solving the problem.
Answers
Answer:
We should deposit approximately $14,408.92 in the account to grow to $100,000 in 32 years, assuming a 9% annual interest rate compounded every 2 months.
Step-by-step explanation:
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
where:
A = the future value of the investment
P = the initial principal (the lump sum we need to deposit)
r = the annual interest rate (9% in this case)
n = the number of times the interest is compounded per year (since interest is compounded every 2 months, or 6 times per year, n = 6)
t = the number of years (32 years in this case)
We are given that we want the investment to grow to $100,000 in 32 years, so we can set A = $100,000 and solve for P:
$100,000 = P(1 + 0.09/6)^(6*32)
Simplifying the expression inside the parentheses:
$100,000 = P(1.015)^192
Dividing both sides by (1.015)^192:
P = $100,000 / (1.015)^192
Using a calculator:
P ≈ $14,408.92
Therefore, we should deposit approximately $14,408.92 in the account to grow to $100,000 in 32 years, assuming a 9% annual interest rate compounded every 2 months.
Here are the numbers of children in 13
elementary school classes.
19, 20, 18, 17, 17, 18, 18, 16, 17, 17, 18, 20, 20, 20
Find the modes of this data set.
If there is more than one mode, write them separated by commas.
If there is no mode, click on "No mode."
Answers
The modes of the given data set are 17, 18, and 20 because they appear most frequently.
The given set of data is as follows:
{19, 20, 18, 17, 17, 18, 18, 16, 17, 17, 18, 20, 20, 20}
A mode can be described as an observation with the highest frequency of occurrence among the values that appear most frequently in the provided data.
As per the question, we can see that the values 17, 18, and 20 appear four times, which is more than any other value.
Therefore, the modes of the given data set are 17, 18, and 20.
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what is 85 divided by 15
Answers
Answer:
Step-by-step explanation:
5.666666666667
Answer:
5.66 repeating
or
17/3
Step-by-step explanation:
85/5 = 17
15/5 = 3
Please lmk if you need me to explain!
Have a great day!!
please show the full answer to this question
Answers
Answer:
1/1
Step-by-step explanation:
The table represents equivalent ratios. Which statements are true? (pick two please!)
The missing y-value is -4
The missing x-value is 2
The ordered pair (-1,2) is part of the ratio table.
The points will be in quadrants | and |||
Answers
The missing value of y is -4 and the ordered pair (-1,2) is part of the ratio table. thus, Options (A) and (C) are correct.
The fact that analogous ratios have the feature that the ratio of the corresponding words is constant must be used to determine whether claims are true. Let's utilize this property to add the values that are missing:
x y
-1 2
x 4 -> since (-1/2) = (x/4), we can solve for x: x = -2
1 -2
2 y -> since (2/(-2)) = (-1/2), we can solve for y: y = -4
Therefore, the missing x-value is -2, and the missing y-value is -4. Also, the ordered pair (-1,2) is part of the ratio table.
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An average silt loam soil with a depth of 4 ft has how many inches of available water capacity?
(Hint: Review the following USDA FAQ on Available Water Capacity and identify the AVERAGE value of the plant available water capacity for a silt loam soil. Note that this value is given as a fraction of the total volume. Thus, if the fraction is 0.18 and the rooting depth is 2.5 feet (30 inches), the Available Water Capacity would be 0.18*30 = 5.4 inches)
Answers
There are 48 inches of available water capacity.
Given that;
An average silt loam soil with a depth of 4 ft has.
Now, We know that;
1 feet = 12 inches
Hence, We get;
4 feet = 4 x 12 inches
= 48 inches
Thus, There are 48 inches of available water capacity.
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Round 2.6123 to 2 SF
Answers
Step-by-step explanation:
2.6 1 2 3 Look at the THIRD figure ...if it is 5 or greater , then round the SECOND number up by 1....o/w leave it alone to get :
2.6 to two SF
The table below represents a linear function. A C Which relationship represents a function with the same rate of change as the function represented above?
Answers
Answer: B
Step-by-step explanation:
The y intercept must be 1 from the chart. So when y=mx+b b is your intercept. A and C do not have b=1
D does not hit y-axis at 1
Must be B
Snow is piling on a driveway so its depth is changing at a rate of r(t) = 10sqrt(1 - cos(0.5t)) centimeters per hour, where t is the time in hours, 0 <= t <= 5 At time t = 0 , the depth of the snow is 20 centimeters. Use a graphing calculator and round your answer to three decimal places. What is the snow's depth at time t = 5 hours? centimeters
Answers
Answer:
58.731 cm
Step-by-step explanation:
You want the depth of accumulated snow after 5 hours if it is 20 cm at 0 hours and is increasing depth at the rate r(t) = 10√(1 -cos(0.5t)) cm/hour.
IntegrationThe attached calculator screen shows the result of the integration. The mode is set to RADians. It took this calculator just over 1 minute to provide its result to 13 significant figures.
The snow's depth at t = 5 hours is 58.731 cm.
__
Additional comment
A different graphing calculator provided the same result to 12 significant figures "instantly." That is shown in the second attachment.
When scientific calculators were rare and expensive, their capability for numerical integration was more limited. Generally one had to specify the tolerance the calculator was to use for its result. These calculators both provided the result to full calculator precision.
The exact result is 20+80(√2)sin(5/8)² ≈ 58.731216038167283412... cm.
We're not quite sure the point of an answer precise to 0.001 cm. The diameter of a snowflake may range from 0.050 to 0.500 cm.
What number comed next 10 9 8 7 6 5 4 3 2
Answers
¿Que es mayor? 50% de 400 o 70% de 200
Answers
70% of 200 is 140.
200 is greater than 140. or 200>140.
200 es mas higher
please help! Naira paddled 4.5 km with the current in the same amount of time as it took her to paddle 3 km against the current. Naira paddled at an average rate of 5 kmh relative to the water each way. Assume the speed of the current was constant.
What was the speed of the current?
Answers
When Naira paddles with the current, her effective speed is (v + c) km/h.
When she paddles against the current, her effective speed is (v - c) km/h.
We know that Naira paddled 4.5 km with the current in the same amount of time as it took her to paddle 3 km against the current.
Using the formula:
time = distance / speed
We can write two equations based on the given information:
4.5 / (v + c) = 3 / (v - c)
and
(v + c) = 5
We can simplify the first equation by cross-multiplying:
4.5(v - c) = 3(v + c)
Expanding the brackets:
4.5v - 4.5c = 3v + 3c
Combining like terms:
1.5v = 7.5c
Dividing both sides by 1.5:
v = 5c
Substituting v = 5 into the second equation:
5 + c = 5
c = 0
Therefore, the speed of the current is 0 km/h. This means that Naira paddled at a speed of 5 km/h relative to the water both with and against the current.
1. To deliver mail in a particular neighborhood, the postal carrier needs to walk along each of the streets with houses (the dots). Create a graph with edges showing where the carrier must walk to deliver the mail.
Answers
The graph for the mail is attached below.
What is graph?
A function, which is a relation that matches every element in its domain with exactly one element in its range, can also be represented as a graph.
Linear function graph. Every linear function has the formula f(x)=ax+b, where an is not zero and a and b are real numbers. ...
Squaring Function Graph. A parabola, or U-shaped curve, is the common name for a squaring function graph. ...
A reciprocal function's graph.
Step Function's graph.
Piece-Wise Function Graph.
The dots on the given figure denoted the houses where the postal carrier needs to go.
The graph is attached below.
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The volume of this cone is 1,186.92 cubic inches. What is the height of this cone? Use ≈ 3.14 and round your answer to the nearest hundredth.
Answers
The height of the cone is determined as 6.45 inches.
What is the height of the cone?
The height of the cone is calculated by applying the formula for the volume of a cone.
V = ¹/₃ π r²h
where;
r is the radius of the coneh is the height of the conelet the radius of the cone = 5.6 inches
The height of the cone is calculated as follows;
h = ( 3V ) / (π r²)
h = (3 x 1,186.92 ) / (π r²)
h = 6.45 inches
Thus, the height of the cone is determined by using the formula for the volume of a cone.
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Find the area of this triangle.
Answers
Answer:
6[tex]cm^{2}[/tex]
Step-by-step explanation:
0.5bh=0.5*3*4=6
Solve (x – 3)2 = 49. Select the values of x. –46 -4 10 52
Answers
Which expressions are equivalent to 31-(-3)?
Select all that apply.
A 3 1/4 - (5/8)
B 3 1/4 + (5/8)
C 3 1/4 + (- 5/8)
D 3 1/4 + (+ 5/8)
E -3 1/4 + (- 5/8)
F -3 1/4 + (+ 5/8)
Answers
The value that is equivalent to 31 - (-3) is none of the options
Evaluating the expressions equivalenceFrom the question, we have the following parameters that can be used in our computation:
31 - (-3)
Evaluate the expressions in bracket
So, we have
31 - (-3) = 31 + 3
Evaluate the sum and the difference
So, we have
31 - (-3) = 34
Hence, the soluton is 34
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Find the quotient WITHOUT a calculator .
7.29 divided (-9) = (-0.81)
Show your work how did you get your answer
Answers
Answer: -0.81
Step-by-step explanation:
Long divide 729 by 9.
Since 7.29 has two decimal places and 9 has none the answer will have 2-0 decimal places. Since 7.29 is positive and -9 is negative, the answer will be negative.
