The series ∑(n=1 to infinity) M * n^(-1 - ε) converges by the p-series test, as ε > 0. Therefore, by the Weierstrass M-test, the original series ∑(n=1 to infinity) a_n n^(-z) converges uniformly for Re(z) ≥ 1 + ε.
To show that the series ∑n=1[infinity]ann−z converges uniformly for Rez≥1+ϵ, we need to use the Weierstrass M-test.
First, note that since an is a bounded sequence of complex numbers, there exists a positive constant M such that |an|≤M for all n.
Next, we need to find an expression for |ann−z| that will allow us to bound the series. Since we are choosing the principal branch of n−z, we have |n−z|=n−Rez for Rez≥1. Thus, we have
|ann−z|=|an||n−z|≤M|n−Rez|
Now, we need to find a series Mn such that Mn≥|ann−z| for all n and ∑n=1[infinity]Mn converges. One possible choice is Mn=M/n^2. Then we have
|Mn|=|M/n^2|=M/n^2 and
|Mn−ann−z|=|M/n^2−an(n−Rez)|≥M/n^2−|an||n−Rez|≥M/n^2−M|n−Rez|
Thus, if we choose ϵ>0 such that ϵ<1, then for Rez≥1+ϵ, we have
|Mn−ann−z|≥M/n^2−M(n−1)ϵ≥M/n^2−Mϵ
Now, we can use the Comparison Test to show that ∑n=1[infinity]Mn converges. Since ∑n=1[infinity]M/n^2 converges (p-series with p>1), it follows that ∑n=1[infinity]Mn converges as well.
Thus, by the Weierstrass M-test, we have shown that the series ∑n=1[infinity]ann−z converges uniformly for Rez≥1+ϵ.
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25% of N is 12. Solve for N. Just put the number.
Answer:
25% of 48 = 12
Step-by-step explanation:
12 ÷ 25% = 12 ÷ 0.25 = 48
Answer: Divide each term by 25 % and simplify.
N = 48
Step-by-step explanation:
Help pleaseee
The figure
Answer:
the 4th one pentagonal prism
Answer:
pentagonal prism
Step-by-step explanation:
it doesn't resemble a pyramid, so it could only be a prism, and it isn't a rectangular one, cause it has two pentagons, on top and bottom
Help!!!!!!!!!!!!! BRAINLIST WILL BE REWARDED
Answer:
135
Step-by-step explanation:
supplementary angles: either of two angles whose sum is 180°.
180 - 45 = 135
-4x + 8x - 6x
i don’t know what x is and that’s all i have. if anyone can help it would be helpful. the other questions are-
-3n/8 + 2n/8 - n/8
-4a - a/3
5b/8 + -2b/3
Answer:
The answer are
[tex]34 = - 2x \\ 35 = - \frac{1}{4} n \\ 36 = - \frac{13}{3} a \\ 37 = - \frac{1}{24} b[/tex]
simplify the expression
16+(-5)-2/5j-4/5j+6
Answer:
17 - 6j / 5
Step-by-step explanation:
Tamika is ordering a taxi from an online taxi service. The taxi charges $3.50 just for the pickup and then an additional $0.75 per mile driven. How much would a taxi ride cost if Tamika is riding for 5 miles? How much would a taxi ride cost that is m miles long?
Answer:
m= 7.50
Step-by-step explanation:
0.75x5=4.00
4.00+3.50=7.50
A taxi ride cost if Tamika is riding for 5 miles will be $7.25.
What is Linear function?A linear function in mathematics is one that has either one or two variables and no exponents. It is a function with a straight line as its graph.
Given, Tamika is ordering a taxi from an online taxi service. The taxi charges $3.50 just for the pickup and then an additional $0.75 per mile driven.
Let "m" be the miles Tamika is riding along.
Total additional charges = m *0.75
pick up charges = 3.50
So, Total charges Tamika has to pay for m miles = 0.75*m + 3.50
For m = 5 miles
Tamika has to pay for 5 miles = 0.75 * 5 + 3.50
Tamika has to pay for 5 miles = 7.25
Therefore, 7.25$ would a taxi ride cost if Tamika is riding for 5 miles.
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state true or false :every natural number is a whole number
Answer:
true , because natural number is starte on no.1 to infinity but whole no. is started on 0 to infinity so it is true .
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
The whole numbers are the numbers 0, 1, 2, 3, 4, and so on (the natural numbers and zero). Negative numbers are not considered "whole numbers." All natural numbers are whole numbers, but not all whole numbers are natural numbers since zero is a whole number but not a natural number.
The hypotenuse of a right triangle measures 15 cm and one of its legs
measures 5 cm. Find the measure of the other leg. If necessary, round to the
nearest tenth
Answer:
√200 or 14.1
Step-by-step explanation:
Pythagoras' Theorem: a²+b²=c²
Rearrange to get b² (one of the smaller sides): c²-a²=b²
225-25=200
√200 = 14.1
Answer:
14.1 I hope this helps! Brainliest please!
Step-by-step explanation:
So we use the Pythagorean theorem which is a squared + b squared = c squared. C is the hypotenuse. So we do:
15 squared - 5 sqaured = b squared
225 - 25 = b squared
200 = b squared
14.1 = b
H E L P pls and thank you :)
The estimate obtained from a sample of which size is likely to be closest to the actual parameter value of a population?
A. 84
B.112
C.12
D.184
Answer:
184 D
Step-by-step explanation:
A sample size of 184, is more likely to provide an estimate closest to the actual parameter value of the population.
Option D is the correct answer.
What is the population parameter?It is typically unknown and can only be estimated using sample data.
The goal of statistical inference is to use the information in a sample to make inferences or d
A population parameter is a numerical value that describes a characteristic of a population, such as the mean or standard deviation.
We have,
The estimate obtained from a larger sample size is likely to be closer to the actual parameter value of a population.
This is because a larger sample size reduces the effects of sampling variability and random errors, resulting in a more accurate estimate of the population parameter.
Thus,
A sample size of 184, is more likely to provide an estimate closest to the actual parameter value of the population.
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What is the y-intercept of the line shown?
−1
0
0.5
1
Answer:
-1
Step-by-step explanation:
It crosses the y axis at negative 1, the y axis is the vertical line
Suppose an ordered pair is not a solution of y > x + 10. Must it be a solution to y < x + 10? Explain. 50 points!!!!
Answer:
I think when u substitute the order pair for x and y Into the equation the y is gonna be les than the x + 10
Step-by-step explanation:
K so am confused abt ur question but here
example (2,5)
y < x + 10
substitute 2 for x and 5 for y
5 < 2 + 10
5 < 12
y is less than x + 10
1, 3, 9, 27, ... What's the pattern rule and the next three numbers?
Answer:
multiply by three
Step-by-step explanation:
Step-by-step explanation:
1 x 3 = 3 x 3 = 9 x 3 = 27
=> Pattern rule = [tex]3^{n-1}[/tex]
=> The next three numbers = 81 , 243 , 729
An expression is given
4x + 5y + 7x
Identify the coefficient(s) and constant.
Coefficient: 4,5 and Constant: 7
Coefficient: 4,5,7 and Constant: None
Coefficient: None and Constant: 4,5,7
Coefficient: 4,7 and Constant: 5
Step-by-step explanation:
The coefficients are 4, 5 and 7
There is no constant
The second one is right
Answer:
Coefficient: 4,5,7 and Constant: None
Step-by-step explanation:
A coefficient can be defined as the number next to the variable or unknown numbers
This would be 4, 5, and 7
However, there does not seem to be a constant, which is a value that should not be the coefficient of a variable.
PLEASE HELP ILL MARK BRAILIEST!!!
P.S please show how you figured it out
Answer:
I think that the answer is either B or C
Step-by-step explanation:
I concluded to this answer simply by looking at where the lines were placed.
Remember that if a line is not touching, but next to another line, they are parallel to each other? Well, that doesn't change here. since, {m angle 1} and {m angle 2} added together equal 180, I would believe that the answer is C, but I may be wrong.
Well, I hope that helps :)
Which properties were used to prove that the expressions 7x+4-x-2 and 6x+2 are equivalent?
Answer:
12
Step-by-step explanation:
12
What is the slope of the line
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
When finding the slope, pick two points on the linear line.
( -1.5, -1) (0.5, 0)
-1.5 is x1
-1 is y1
0.5 is x2
0 is y2
Place these numbers in a slop formula.
m = [tex]\frac{0 - (-1)}{0.5 - (-1.5)}[/tex] = [tex]\frac{1}{2}[/tex]
(m means slope)
Slope = [tex]\frac{1}{2}[/tex]
Answer:
1/2
Step-by-step explanation:
Solve for a
djəН
12
a =
✓ [?]
10
a
Pythagorean Theorem: a2 + b2 = c2
Enter
Answer:
a=[tex]\sqrt{44}[/tex]
Step-by-step explanation:
A^2+B^2=C^2
Substitute the values for what you know so:
a^2+10^2=12^2
Simplify:
a^2+100=144
-100 -100
------------------------
A^2=44
A=[tex]\sqrt{44}[/tex]
(7a^2 -a + 4) – (3a^2 - 4a - 3)
Step-by-step explanation:
Answer. in the attachment
Are the ratios 18:9 and 4:3 equivalent?
Answer:
No. (see below)
Step-by-step explanation:
If you match up the ratios like this:
18 : 9
4 : 3
Matching the two numbers (one on top of another, since they correspond to each other), you can see that these are not equivalent.
Here's why:
The top ratio is 18 to 9, which can be represented by 18 total people to 9 girls in the amount of total people.
We know that the number of boys will also be 9 because 9 is half of 18.
Let's look at the second ratio:
This can be represented by 4 total people to 3 girls in the amount of total people.
4 - 3 = 1
So there would be only 1 boy. Meaning that they're not equal because 1 is not half of 4. It would only be 1/4.
1/4 ≠ 1/2
If we make them similar denominators, you can really see it:
1/4 ≠ 2/4
Since my last question got reported ill give branliest + 20 points for like 2 mins of your time
Answer:
the diameter of the semi-circle is 5 in
the area of the shape is 79.63 in squared
Step-by-step explanation:
HELP HELP HELP HELP HELP HELP HELP HELP
Answer:
same to me HAHAHAawitawitThe cost of tickets to a school play are $10 for adults and $6 for children under 12. If there were a total of 100 tickets sold to the play on a certain night, what equation would you use to represent the total ticket sales, T, if the number of adult tickets can be represented by a. Show and explain each step to create the equation.
Answer:
10a+6b=T------------2
Step-by-step explanation:
Given data
Let the number of adults be a
and the number of children be b
we are told that the total tickets is 100
hence
x+y=100-------------1
The cost of adult ticket = $10
The cost of children ticket = $6
since the total cost is T
Hence
10a+6b=T------------2
what is the degree of the polynomial ? 6x^3y^5+8y^6
Answer:
degree 8
Step-by-step explanation:
The degree of a polynomial is determined by the largest exponent of the variable in the polynomial.
6x³[tex]y^{5}[/tex] ← has degree 3 + 5 = 8
8[tex]y^{6}[/tex] ← has degree 6
Thus the polynomial is of degree 8
The area of a rectangle is 735 in squared. The ratio of the length to the width is 5 : 3. Find the length and the width.
Answer: Length = 35
Width = 21
Step-by-step explanation:
From the question, we are informed that the area of a rectangle is 735 in squared and that the ratio of the length to the width is 5 : 3.
To find the length and the width of the rectangle goes thus. We should note that the area of a rectangle is the length multiplied by the width.
Therefore, 5x × 3x = 735
15x² = 735
x² = 735/15
x² = 49
x = ✓49
x = 7
Recall that length = 5x = 5 × 7 = 35
Width = 3x = 3 × 7 = 21
OK this is another question which I need help on please please help if you can. CAUSED ME MUCH DISTRESS
Answer:
15 = 2x - 3y
Step-by-step explanation:
We have the two points P1(3,-3) and P2(9,1).
First, calculate the slope between those points:
slope [tex]= \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - (-3)}{9 - 3} = \frac{4}{6} = \frac{2}{3}[/tex]
Now simply move 3 steps from (3,-3) towards the y-axis to get the intersection with the y-axis (each step reduces x by 1 and applies the slope to the y-value):
(3,-3)
---> (2, -3 - (2/3)) = (2,-3 2/3)
---> (1, (-3 2/3) - 2/3) = (1, -4 1/3)
---> (0, (-4 1/3) - 2/3) = (0,-5)
This tells us, that our line intersects the y-axis at (0,-5).
The general form of a line is f(x) = <SLOPE> * x + <Y-VALUEATXEQUALSZERO>.
In our case: f(x) = y = (2/3)x -5.
To get it into the correct form, we simply subtract y from both sides and get:
0 = (2/3)x - y - 5
To get only integers just multiply everything with 3 and add 15 and get:
15 = 2x - 3y, which fulfils the form asked for in the problem.
Solve the quadratic equation x2+8x−30=0 by completing the square.
What are the solutions to the quadratic equation, if any?
x=4±46−−√
This equation has no real solutions.
x=4±34−−√
x=±46−−√
Answer:
[tex]\bold{x=-4\pm\sqrt{46}}[/tex]
Step-by-step explanation:
[tex](a+b)^2=a^2+2ab+b^2\\\\\\x^2+8x-30=0\\\\\underbrace{x^2+2\cdot x\cdot 4+4^2}-4^2-30=0\\\\{}\qquad(x+4)^2\,-\,16-30=0\\\\{}\qquad\ \ (x+4)^2=46\\\\ {}\qquad\ \ x+4=\pm\sqrt{46}\\\\ {}\qquad\ \ x=-4\pm\sqrt{46}[/tex]
The solution to the quadratic equation by completing the square will be
x = -4 ± √46. The correct option is A.
What is a quadratic equation?It is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.
Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The given equation will be solved as below:-
x² + 8x − 30 = 0
Completing the square for the above equation.
( x + 4 )² - 16 - 30 = 0
( x + 4 )² = 46
x + 4 = ±√46
x = ±√46 - 4
Therefore, the solution to the quadratic equation by completing the square will be x = -4 ± √46. The correct option is A.
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How can you show that two figures are either congruent or similar to one another?
Answer:
By measuring the length of the sides and angles
Answer: If they are congruent, you'll see that they are exactly the same as one another. If there's measurements, they'll have the same numbers. If they are similar, they might be the same shape or just have similar measurements
Step-by-step explanation:
The 28 students in Mrs. Colby's class will share 98 slices of
pizza equally
How many slices will each student get?
Answer:
3 1/2 slices each
Step-by-step explanation:
98/28=3.5
Answer:
Every student will get 3 to 4 slices of pizza
Step-by-step explanation:
This is because you need to divided 98 with he 28 student, which you will get 3.5. That is the correct answer, but the question asked equally, so each student will get 3 to 4 slices of pizza.
Hope this helped
PLEASE HELP how do i solve (5-3i)^2
Answer:
16-30i
Step-by-step explanation:
This is what I got :)
Answer:
16−30i
Step-by-step explanation:
Use Square of Difference: {(a-b)}^{2}={a}^{2}-2ab+{b}^{2}(a−b)
2
=a
2
−2ab+b
2
.
{5}^{2}-2\times 5\times 3\imath +{(3\imath )}^{2}
5
2
−2×5×3+(3)
2
2 Simplify {5}^{2}5
2
to 2525.
25-2\times 5\times 3\imath +{(3\imath )}^{2}
25−2×5×3+(3)
2
3 Use Multiplication Distributive Property: {(xy)}^{a}={x}^{a}{y}^{a}(xy)
a
=x
a
y
a
.
25-2\times 5\times 3\imath +{3}^{2}{\imath }^{2}
25−2×5×3+3
2
2
4 Simplify {3}^{2}3
2
to 99.
25-2\times 5\times 3\imath +9{\imath }^{2}
25−2×5×3+9
2
5 Use Square Rule: {i}^{2}=-1i
2
=−1.
25-2\times 5\times 3\imath +9\times -1
25−2×5×3+9×−1
6 Simplify 2\times 5\times 3\imath2×5×3 to 30\imath30.
25-30\imath +9\times -1
25−30+9×−1
7 Simplify 9\times -19×−1 to -9−9.
25-30\imath -9
25−30−9
8 Collect like terms.
(25-9)-30\imath
(25−9)−30
9 Simplify.
16-30\imath
16−30
A triangle has side lengths of (6a-3b)(6a−3b) centimeters, (5a+5c)(5a+5c) centimeters, and (8c-b)(8c−b) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?
Answer:
P = a(61a - 36b + 50c) + 10b² + 89c² - 16bc
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsExpand by FOIL (First Outside Inside Last)FactoringGeometry
Perimeter Formula [Triangle]: P = L₁ + L₂ + L₃
L₁ is one sideL₂ is another sideL₃ is the 3rd sideStep-by-step explanation:
Step 1: Define
L₁ = (6a - 3b)(6a - 3b)
L₂ = (5a + 5c)(5a + 5c)
L₃ = (8c - b)(8c - b)
Step 2: Find Perimeter
Substitute in variables [Perimeter - Triangle]: P = (6a - 3b)² + (5a + 5c)² + (8c - b)²Expand [FOIL]: P = (36a² - 36ab + 9b²) + (25a² + 50ac + 25c²) + (b² - 16bc + 64c²)Combine like terms (a²): P = 61a² - 36ab + 9b² + 50ac + 25c² + b² - 16bc + 64c²Combine like terms (b²): P = 61a² + 10b² - 36ab + 50ac + 25c² - 16bc + 64c²Combine like terms (c²): P = 61a² + 10b² + 89c² - 36ab + 50ac - 16bcRearrange variables: P = 61a² - 36ab + 50ac + 10b² + 89c² - 16bcFactor: P = a(61a - 36b + 50c) + 10b² + 89c² - 16bc