Convergent Series:
A Convergent Series is a series whose partial sums tend to a specific member is called a limit.
∑ 1/2n = 1/2+ 1/4 + 1/8 + 1/16 +........
Given an infinite series ∑₁ ∞ an determine the series is convergence. Recall that we can actually do better with geometric series not only we can determine convergence but also divergence. We can also calculate geometric series.
Suppose we are given a series ∑ aₙ which is not quite a geometric series but becomes a geometric series for sufficiently large n. That is we can find an integer N such that aₙ = aₓⁿ for all n > N. we don't have a general formula for aₙ when n ≤ N. The values of aₙ for small n don't effect Sₙ is convergence or not.
As a moment of fact, we never used the fact that aₙ eventually become geometric. More general ∑aₙ is convergent series, we can add a finite number of terms to the be gaining of this series or remove a finite number of terms from the be gaining of the series without affecting the convergence of the series. For Example: if ∑aₙ convergence then so does
10 + 10¹⁰ + 10 ¹⁰⁰ + 10¹⁰⁰⁰ + ∑aₙ
Similarly, if ∑aₙ convergence then,
a₁₀₀₀ +a₁₀₀₁ +a₁₀₀₂ + ..... = ∑₁₀₀₀ ∞ aₙ
However, the fact that we are only adding finitely many terms to the series is essential. That is, when it comes to determining convergence of a series ∑aₙ , we can see that only the asymptotic behavior of ∑aₙ matter, that is, only the behavior of the sequence aₙ as n--- ∞ affects convergence.
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Rahul invested $1,100 in an account paying an interest rate of 3 3/8% compounded
quarterly. Caleb invested $1,100 in an account paying an interest rate of 3 1/4%
compounded daily. After 8 years, how much more money would Rahul have in his
account than Caleb, to the nearest dollar?
Answer:
$13
Step-by-step explanation:
You want to know how much more Rahul's investment of $1100 at 3 3/8% compounded quarterly for 8 years is worth than Caleb's investment of $1100 at 3 1/2% compounded daily for 8 years.
Rahul's accountThe amount in Rahul's account is given by ...
A = P(1 +r/n)^(nt) . . . . . P invested at rate r compounded n times per year
A = $1100(1 +0.03375/4)^(4·8) = $1100(1.0084375^32) ≈ $1439.33
Caleb's accountThe same formula is used for Caleb's account, but with different numbers.
A = $1100(1 +0.0325/365)^(365·8) ≈ $1426.61
DifferenceThe difference in account values is ...
Rahul's - Caleb's = $1439.33 -1426.61 = $12.72 ≈ $13
Rahul will have about $13 more in his account.
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What is the function of the following graph?
Answer:
I can't see the graph anywhere.
Step-by-step explanation:
X^2 - x - 6 simplified
pluto is the furthest planet in our solar system and moves in an orbit at an average of 5900 million km from the sun. find this distance in standard form.
Answer: 5.9 × 10 to the power of 9
You have a summer job that pays time and a half for overtime. That means if you work
more than 40 hours in a week, your hourly wage for the extra hours is 1.5 times your
rate of $12 per hour.
How much will you get paid if you work 47 hours?
You have a summer job that pays time and a half for overtime. That means if you work more than 40 hours in a week, your hourly wage for the extra hours is 1.5 times your rate of $12 per hour.
If you work for 47 hours you will get paid $606.
Define overtime. What does overtime pay mean?
The amount of time spent working past the regular working day is known as overtime. The word is also applied to the compensation for this period of extra time.
Employees covered by the Act must receive overtime compensation, unless they are exempt, at an overtime rate that is at least time and a half their usual rates of pay for hours worked beyond 40 in a workweek.
Solution Explained:
Given,
Normal rate = $12 per hour
Overtime rate = 1.5 times more than the normal rate per hour
= (15 X 12) / 10 = $18 per hour
First we will see the normal total pay for 40 hours
= 40 X 12 = $480
The overtime pay = 7 X 18 = $126
Therefore, the pay for 47 hours is = 126 + 480 = $606
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HELLLLPPP WILL GIVE BRAINLIST HELP PLEASE DUE SOON
Find the equation of the parabola with the given x-intercepts and point on the graph. Use y = a(x-p)(x-q).
2. x-int: (-4,0) , (-10, 0)
P (-6,-12)
Answer:
y = 1.5(x + 4)(x + 10)=========================
Givenx- intercepts (-4, 0) and (-10, 0),Point P (- 6, - 12).SolutionThe given translates as:
p = - 4, q = - 10, x = - 6, y = - 12Use given x - intercepts to get the equation:
y = a(x + 4)(x + 10)Use the coordinates of P to find the value of a:
- 12 = a(-6 + 4)(-6 + 10)- 12 = a*(-2)*4- 12 = - 8aa = - 12 / - 8a = 1.5The equation of this parabola is:
y = 1.5(x + 4)(x + 10)Answer:
[tex]\textsf{Intercept form}: \quad y=\dfrac{3}{2}(x+4)(x+10)[/tex]
[tex]\textsf{Standard form}: \quad y=\dfrac{3}{2}x^2+21x+60[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6 cm}\underline{Intercept form of a quadratic equation}\\\\$y=a(x-p)(x-q)$\\\\where:\\ \phantom{ww}$\bullet$ $p$ and $q$ are the $x$-intercepts. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]
If the x-intercepts are (-4, 0) and (-10, 0) then:
p = -4q = -10Substitute the values of p and q into the formula:
[tex]\implies y=a(x-(-4))(x-(-10))[/tex]
[tex]\implies y=a(x+4)(x+10)[/tex]
To find a, substitute the given point on the curve P (-6, -12) into the equation:
[tex]\implies -12=a(-6+4)(-6+10)[/tex]
[tex]\implies -12=a(-2)(4)[/tex]
[tex]\implies -12=-8a[/tex]
[tex]\implies a=\dfrac{-12}{-8}[/tex]
[tex]\implies a=\dfrac{3}{2}[/tex]
Substitute the found value of a into the equation:
[tex]\implies y=\dfrac{3}{2}(x+4)(x+10)[/tex]
Expand to write the equation in standard form:
[tex]\implies y=\dfrac{3}{2}(x^2+14x+40)[/tex]
[tex]\implies y=\dfrac{3}{2}x^2+21x+60[/tex]
Compare -2.655 and 4 square root
Answer:
-2.655 < -√4
Step-by-step explanation:
-√4 = -2
-2.655 < -2
I assume that's what the question is asking for?
of the grid is blank?
bers, insert a less-than symbol (<), a greater-than symbol
pol (=) between the numbers to make a true statement.
b. 0.123 2 0.1002
0.123 < 2 > 0.1002, is the true statement after inserting symbols.
What is greater than symbol refer?
In mathematics, the larger than sign is used between two numbers to indicate that the first number is greater than the second. For instance, 10 > 5. 10 is more than 5 in this case.The greater than symbol, which consists of two strokes of equal length joined at an acute angle at the right, is always pointed toward the greater value in inequality. ( >).What is lesser than symbol refer?
In a situation when one number is less than another, a less than symbol is positioned between the two numbersWhen referring to an inequality, the less than symbol () represents the smaller value where two strokes of equal length meet at a sharp angle on the left.The reader may easily understand the message thanks to the larger than less than sign, which also decreases the time complexity.What is equal to symbol refer?
The "equal to" symbol is used to indicate that two numbers or values are equal. The greater than and less than signs are in conflict with this one. We employ the equal to symbol even while writing equations. '=' is used to indicate it.Hence, 0.123 < 2 > 0.1002, is the true statement after inserting symbols.
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the correlation between variables x and y is .50. You compute a least squares regression line wit this bivariata data. Which of the following is true?
a. the r^2 is greater than .50
b. the regression constant is positive
c. the regression coefficient is positive
d. the slope of the regression line is negative
e. all of the above
The correlation between variables x and y is 0.50 . The true option is option (c) .
that's the regression coefficient is positive for given bivariata.
Correlation: Correlation is a statistical measure of how linearly two variables are related (meaning they change together at a constant rate). The
sample correlation coefficient r quantifies the strength of the relationship.
Correlation Coefficient: The Correlation Coefficient formula is used to examine the strength of the relationship between data. The formula returns a value between -1 and 1.
Here:
1 indicates a strong positive relationship.-1 indicates a strong negative relationship.A result of zero indicates no relationship at allPearson's correlation coefficient is denoted by "r" and is
r = (n∑xy - ∑x∑y )/√( n ∑x² - (∑x )² ) ( √ n∑y² - (∑y)²)
We have given that correlation between x and y is 0.50.
cor(x,y) = √r^2 => √r^2 = 0.50 => r ^2 = (0.50)^2
=> r^2 = 0.25 > 0 but less than 0.50 ---( 1)
Regression coefficient is the constant "b" in the regression equation that gives the change in the value of the dependent variable equal to the unit change in the independent variable.
Symbolically it can be expressed as:
bₓᵧ= r σ ₓ /σ ᵧ
where x and y are correlated
σ ₓ --> standard deviation of X
σᵧ ---> standard deviation of y
We know that standard deviations is square root value of variance of observations. we also know square root any quantity is always positive or zero.
Using the above fact about standard deviations and correlation coefficient (r) is also positive we see that bₓᵧ is postive.
Hence, Regression cofficient is positive.
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factor -1/2 out of 1/2x+6.
Answer:
-1/2(x - 12). Hope this helped out for you!
HELLP ME LOL PLEASE THHANK
Answer:
Clara will call 1 more person than Toby
Step-by-step explanation:
Every 10 phones call is 4 people so 40 phone calls will be 16 people
If every 8 phones calls is 3 people then 40 phones calls will be 15 people
By 1 person
Sorry about previous answer I read question wrong
Hopes this helps please mark brainliest
Answer:
if times 40 it is clara by 40
Step-by-step explanation:
in the moring the temputure starts out around 50 F As the day gose on the temperature rises first slowly then more quickly it stays constant for an hour before droping slowly select the graph that best represents this description
What is the first time after 1 PM at which the inute hand and hour hand of a clock point in exactly opposite directions?
Answer:
9 : 30
Step-by-step explanation:
1 PM - 1 hour = 12 PM
12 PM - 2 hours = 10 PM
10 PM - 20 minutes = 9 : 40
9 : 40 PM - 10 minutes = 9 : 30 PM
So, it is 9 : 30 PM
At a water park, 26 out of 52 tickets sold were child tickets. What percentage of the tickets
were child tickets?
Answer:
50%
Step-by-step explanation:
[tex]\frac{26}{52}[/tex] x 100 = 50
The price of a football season ticket is £1200 Next season the price will increase by 6% Work out how much the season ticket will cost next season.
Answer:
Step-by-step explanation:
34567
ANSWER
1. Your friend decides you should go to a clothes store next. Your friend has one hundred dollars. They pick out 10 items. The first three are $15.99, the second three are $10.40 and the last four are $4.50. Explain how you would estimate if your friend has enough money to buy all the items. Then setup an expression to find out if your friend has enough money to buy all the items. Lastly, find the total from your expression.
2. The weather man says the temperature will increase by 32 degrees by 12 pm then decrease by 14 degrees at 6pm where it remains constant. Setup an expression for finding temperature throughout the day. Find the final temperature from your expression.
In order to determine if your friend has enough money to buy all the items, the total cost of the items have to be determined. The total cost is the sum of all the items bought.
Total cost = total cost of the first three items + total cost of the second three + total cost of the last three
Total cost = (3 x 15.99) + (3 x 10.40) + (4 x 4.50)
Total cost = $47.97 + $31.20 +18
Total cost = $97.17
An increase in temperature would be represented with a positive number. While, a decrease in temperature would be represented with a negative number. The final temperature can be determined by adding the temperature increase and decease together.
Final temperature = increase in temperature - decrease in temperature
Final temperature = 32 - 14 = 18 degrees
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which of the following is not needed to determine the minimum sample size required to estimate a population proportion?
a. Standard Deviation
b. Margin of Error
c. α
d. z α/2
Answer:
Step-by-step explanation:
margin of error
(02.04 MC)
(Multiple Choice Worth 2 points)
For the function f(x) = -(x + 1)² + 4, identify the vertex, domain, and range.
O The vertex is (-1, 4), the domain is all real numbers, and the range is y ≥ 4.
O The vertex is (-1, 4), the domain is all real numbers, and the range is y ≤ 4.
O The vertex is (1, 4), the domain is all real numbers, and the range is y ≥ 4.
O The vertex is (1, 4), the domain is all real numbers, and the range is y ≤ 4.
The vertex is (-1, 4), the domain is all real numbers, and the range is y ≤ 4.
What are the domain and range of a function?
The range of values that we are permitted to enter into our function is known as the domain of a function. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.
if you use the foil method it will come out to -(x^2+2x+1)+4. then distribute the negative and simplify the equation (add the four) the equation comes out to be -x^2-2x+3.
The vertex is at -b/(2A).
The vertex is at x=2/(2*-1), which is -1. plug -1 into the original equation to find y, (y=-(-1)^2-2*(-1)+3) which is y=4. so the vertex is at (-1,4).
since the parabola opens down (negative a value) and has a maximum at 4, y is always less than or equal to 4. x is all real numbers as it goes on forever. so b is your answer.
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Can Someone Please Help Me? Thanks!
Find the opposite of the polynomial.
−5a²b⁴c
A. 10a²b⁴c
B. 5a²b⁴c
C. −2.5a²b⁴c
D. −5a²b⁴c
question a fair die with its faces numbered from 1 to 6 will be rolled. which of the following is the best interpretation of the probability that the number landing face up will be less than 3 ? responses for many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is 13. for many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is one third . for many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is 12. for many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is one half . for many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is 23. for many rolls of the die, the long-run relative frequency of a number less than 3 landing face up is two thirds . for three rolls of the die, a number less than 3 will land face up one time. for three rolls of the die, a number less than 3 will land face up one time. it will take three rolls of the die before a number less than 3 lands face up for the first time.
For many of the rolls die, the long run relative frequency of a number less than 3 landing face up is 1/3.
Given that,
Only two integers (1 and 2) are smaller than 3, hence their relative frequency will be 2/6=1/3.
The best way to interpret the data is thus,
For many rolls of the die, the long- run relative frequency of a number less than three landing face up is1/3.
Hence option A is correct which is for many of the rolls die, the long run relative frequency of a number less than 3 landing face up is 1/3.
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a painter leans a ladder against a vertical wall. the top of the ladder is 15 meters above the ground. when the bottom of the ladder is moved 3 meters farther away from the wall, the top of the ladder is 11 meters above the ground. what is the length of the ladder? round to the nearest hundredth of a meter.
From the ground the length of the ladder is 15 feet.
Step-by-step explanation:
From the Pythagorean Theorem, the situation described can be expressed mathematically as:
x² +9² = (x+3)²
or,
x² + 81 = x² + 6x + 9
Now, cancelling equal terms on either side of the equation and reducing gives:
x = 12
Since the ladder is defined to be 3 feet longer than the distance of its foot to the wall the ladder’s length must be:
12 feet + 3 feet
=15 feet
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2. Choose the correct answer.
Which theorem, term, or corollary is represented by the picture? The bold lines in the pictures represent the hypothesis of the theorem or corollary.
CPCTC
Corollary 1 to the Isosceles Triangle Theorem
Corollary 2 of the Isosceles Triangle Theorem
Isosceles Triangle Theorem
Converse to the Isosceles Triangle Theorem
The theorem (A) CPCTC represents the given condition of the triangle.
What is CPCTC?According to the formula CPCTC, which stands for "corresponding portions of congruent triangles are congruent," if two or more triangles are congruent, their corresponding angles and sides must also be congruent.
When demonstrating the congruence of triangles or other shapes, the term CPCT is employed.
When a student is asked to demonstrate that two angles or two sides are congruent, CPCTC is frequently employed at the end of the proof or close to it.
So, in the given triangle:
The angles are bold and the lines are not bold.
This represents that it is proved first that the angles are congruent.
And through CPCTC, we are concluding that the sides of the triangles are also congruent.
Therefore, the theorem (A) CPCTC represents the given condition of the triangle.
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Charlie is making copies of fliers to advertise his new club at school. The cost for 25 copies is $3.75. What is c, the total cost Charlie will pay for 40 copies?
The total cost for Charlie to make 40 copies of flyers is $6
Given the fact that 25 copies of flyers is costing him $3.75, we will then need to find the cost of each copy of the flyer. The figure is calculated using unit rates as follows:
25x = 3.75
x = 3.75/25
x = 0.15
so each copy of a flyer will cost him $0.15
To make 40 copies of flyers, Charlie will need to spend:
$0.15 × 40 = $6
So the amount of money Charlie will have to spend in order to make a copy of 40 flyers is $6
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Answer: Charlie will pay 6$.
Step-by-step explanation:
If I were to start with $50 and add $20 each week for 12 weeks, what is an equation that represents the relationship between the dollar amount and the number of weeks?
Answer:
This is a function y = mx + b:
You start with $50, so the y-intercept(b) is 50.Adding $20 a week means that the slope(m) is 20.So, the function would be y = 20x + 50, where y is the dollar amount after x weeks and x cannot be greater than 12.
The perimeter of a rectangle is 30 cm. Its width is 3 cm. Which equation can represent the perimeter of the rectangle if L= length? (please explain how you got the answer)
A.) 3 + L = 30
B.) 3L = 30
C.) 6 + 2L = 30
D.) 6L = 30
The equation that can represent the perimeter of the given rectangle is
6 + 2L = 30, option c is correct.
Given,
width of rectangle = 3 cm
length of rectangle = L
perimeter of rectangle = 30 cm
equation of perimeter of rectangle = 2 × (L + W)
By substituting the values of width and perimeter we can get the equation,
perimeter = 2 × (L + W)
=> 30 = 2 × (L + 3)
=> 30 = 2L + 6
=> 6 + 2L = 30
Therefore, the equation of the perimeter of a rectangle is 6 + 2L = 30.
What is the equation of the line that passes through the point (-4,5) and has a slope of 3/4
Answer:
y = 3/4 x + 8
Step-by-step explanation:
y-5 = 3/4 (x-(-4)
y - 5 = 3/4 (x+4)
y - 5 = 3/4 x + 3
Y = 3/4 x + 3 + 5
y = 3/4 x + 8
Answer:
(-4,5) x = -4 and y = 5
use y = mx + c formula
so 5 = 3/4 (-4) +c
5 = -3 + c
5 + 3 = c
so c = 8
y = 3/4x + 8
HELPPPP :Solve for x. (23x-3) degrees and 78 degrees
Arc & Angle measure formed by Chords, Secants, & Tangents
The value of x in the intersecting chords SP and PB is determined as 3.52.
What is the value x?The value of x is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.
Also this theory states that arc angles of intersecting secants at the center of the circle is equal to the angle formed at the center of the circle by the two intersecting chords.
arc SB = m∠SPB
From the diagram, we have arc SB = 78⁰
m∠JNK = 78 (interior angles of intersecting secants)
23x - 3 = 78
23x = 78 + 3
23x = 81
x = 81/23
x = 3.52
Thus, the value of x in the intersecting chords SP and PB is determined as 3.52.
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9.- Suma de fuerzas
4
45N + SON + 25N
4
4
127N 200N + 1250N
4
1
355N + 40N + 30N + 20N
Answer:
multiply
Step-by-step explanation:
2345567 in the subtract 578431111
Let f(x)=1/2x-3 Suppose you subtract 6 from the input of f to create a new function g, and then multiply the input of function g by 4 to create a function h. What equation represents h?
The value of h(x)= 2x- 36.
What is function?
In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.
Given:
f(x)=[tex]\frac{1}{2x}[/tex]-3
Now, subtract 6 from the input of f to create a new function g
g(x)= [tex]\frac{1}{2x}[/tex]-3 -6
g(x)= [tex]\frac{1}{2x}[/tex] -9
and, multiply the input of function g by 4
h(x)= 4([tex]\frac{1}{2x}[/tex] -9)
h(x) = 2x- 36
Hence, the value of h(x)= 2x- 36.
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