Showing that this need not be true if f is continuous but not uniformly continuous.
Given :
let f be a uniformly continuous function on a set e. show that if {xn} is a cauchy sequence in e then {f(xn)} is a cauchy sequence in f(e).
( 1 )
If f is uniformly continuous on E, then given ε > 0 there is δ > 0 such that if x, y are in E and |x−y| < δ,
then |f(x) − f(y)| < ε. Let (xn) be a Cauchy sequence in E. Then given δ > 0 there is N such that if p, q > N,
then |xp − xq| < δ, and thus |f(xp) − f(xq)| < ε, implying that (f(xn)) is a Cauchy sequence.
( 2 )
Let E = {1, 1/2, 1/3, · · } and f(1/n) = 1 is n is odd, f(1/n) = −1 if
n is even. Then f is continuous but not uniformly continuous. The sequence (xn) = (1/n) in E is Cauchy but the
sequence (f(xn)) = (1, −1, 1, −1, · · ·) is not Cauchy.
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Business Information System (BIS)A combination of hardware, software, data, people, and procedures employed to pursue an organization's objective.
A system of hardware, software, information, people, and used to further an organization's goal is known as a business information system (BIS).
Given that,
What is Business Information System?Students can prepare for a range of positions in business, industry, government, and the military with a Bachelor of Business Administration with a major in Business Information Systems (BIS). Business information systems, often utilising computer systems and technology, provide information that firms utilise to govern themselves successfully and efficiently. Hardware, software, data, procedures (design, development, and documentation), and people make up the bulk of business information systems. Students majoring in BIS will learn how to use technology and information systems to enhance corporate processes and decision-making.
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Consider the following inequality:
−2(2z−3)≥2z+24
Step 1 of 2 : Write the solution using interval notation.
Answer:
z ∈ (-∞, -3]
Step-by-step explanation:
You want the solution to −2(2z−3)≥2z+24.
SolutionSimplify the inequality:
-4z +6 ≥ 2z +24
-18 ≥ 6z . . . . . . . . . add 4z -24
-3 ≥ z . . . . . . . . divide by 6
The solution is z ∈ (-∞, -3].
You are playing a game that involves tossing a single die. If you roll a one, you win $50.
If you roll a 2, you win $25. If you roll anything else, you lose $15. What are you expected winnings?
Answer:
the answer is: 01111001 01101111 01110101 00100000 01101000 01100001 01110110 01100101 00100000 01101000 01100001 01110110 01100101 00100000 00110011 00110000 00100101 00100000 01100011 01101000 01100001 01101110 01100011 01100101 00100000 01101111 01100110 00100000 01110111 01101001 01101110 01101110 01101001 01101110 01100111 00100000 01100001 01110011 01110011 01110101 01101101 01101001 01101110 01100111 00100000 01110100 01101000 01100101 00100000 01100100 01101001 01100011 01100101 00100000 01101000 01100001 01110011 00100000 00110110 00100000 01110011 01101001 01100100 01100101 01110011 00101110 . do a bit of work decoding it to get the right answer
Step-by-step explanation:
Prove that a line parallel to one side of a triangle divides the other two sides proportionally. Be sure to create and name the appropriate geometric figures.
A line parallel to one side of a triangle divides the other two sides proportionally.
What is triangle?
A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.
Let ΔADE and ΔABC are two triangles.
Given: DE∥BC
To prove: DB/AD = EC/AE
ΔADE and ΔAC share ∠A
∠A ≅∠A reflexive property
DE∥BC is given
∠ADE ≅ ∠B because they are corresponding angles when transversal
AB cuts parallel lines DE and BC
ΔADE ∽ ΔABC a pair of angles in each are congruent.
AB / AD = AC / AE
because corresponding sides of similar triangle's are proportional.
Now subtract 1 from each side
AB / AD - 1 = AC / AE - 1
Combining fractions,
(AB - AD) / AD = (AC - AE) / AE
⇒ DB / AD = EC / AE
Hence, a line parallel to one side of a triangle divides the other two sides proportionally.
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Geometric figure:
Select the correct answer.
Which equation has only one unique solution?
A. -4|x|+ 1 = -3
B. 9-|12x-1|=9
C. |x-2|-7= 7
D. |13-x|= 3
Answer:
9-|12x-1|=9
Step-by-step explanation:
Solve for x over the real numbers:
9 - abs(12 x - 1) = 9
Subtract 9 from both sides:
-abs(12 x - 1) = 0
Multiply both sides by -1:
abs(12 x - 1) = 0
Eliminate the absolute value:
12 x - 1 = 0
Add 1 to both sides:
12 x = 1
Divide both sides by 12:
Answer: x = 1/12
Answer:
Answer is B
Step-by-step explanation:
Match each linear system with one of the phase plane direction fields.
(The blue lines are the arrow shafts, and the black dots are the arrow tips.)
I need help. I don't know how to use the eigenvalues and take that information and put it on a graph. Please explain thoroughly! Thanks.
The correct match for each linear system with one of the phase plane direction fields will be:
1:B
2:C
3:D
4:A
What is plane?
In geometry, a plane is a surface made up of all the straight lines connecting any two locations on it. It is, in other words, a level or flat surface. A plane is uniquely defined in a Euclidean space of any number of dimensions by one of the following: three non-collinear points are used. Other names for it include a two-dimensional surface. A plane has an unlimited width, an endless length, zero thickness, and no curvature. The flat surfaces of a cube or cuboid, as well as the flat surface of paper, are all true instances of geometric planes, despite the fact that it is difficult to envision a plane in real life.
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Bob invested $2,500 in an account earning 3.4% annual interest that is compounded semi-annually. How long will it take the investment to triple?
(Round your answer to the nearest hundredth.)
We can conclude that it will take Bob 10 years and 10 months to triple his investment when the compounding is happening semi-annually.
What is compounding?Compounding is the method through which interest is added to both the principal balance already in place and the interest that has already been paid.
Thus, compounding can be thought of as interest on interest, with the result that returns on interest are magnified over time, or the so-called "magic of compounding."
So, the time that will be taken to make the investment triple is:
Amount invested: $2500
Interest rate: 3.4%
Compounding: Semiannually
Now, consider a period of 2 years:
3.4 * 6/12 = 1.7%
The interest rate that is effective will be 1.7%.
Currently, the future value of the compounded rate at 1.7% for a period of 65 factors equals 2.9913.
Consequently, the value will be $2,500 2.9913 = 7,478.25.
65 months divided by six years equals 10.833 years in total.
0.833 * 12 makes up 10 months a year.
Therefore, we can conclude that it will take Bob 10 years and 10 months to triple his investment when the compounding is happening semi-annually.
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help im in k12 thanks
The graph of the inequality is attached.
What is closed circle in inequality?
Open circles are used for numbers that are less than or greater than (< or >). Closed circles are used for numbers that are less than or equal to and greater than or equal to (≤ or ≥).
Given inequality is x > 3.2.
The inequality sign of the given inequality is grater than.
The graph of the inequality will starts with open circle.
Since x is greater than 3.2. Therefore the given inequality will represent all real numbers that are greater than 3.2.
Thus the inequality will represent all number that lie on right of 3.2 on the number line.
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When m of the original line is -3,m of the perpendicular line is ……..
slope(m) of the perpendicular line is 1/3.
What is meant by slope?Slope of a line in mathematics is defined as its steepness. It is calculated as rise(difference of y- coordinates) over run(differences of x- coordinates) .
What is meant by perpendicular lines?Two lines which intercept each other at an angle of 90 degree are known as perpendicular lines.
According to the given data and using the formula of perpendicular slope(m1*m2=-1);
Slope(m1) of original line =-3
Let the slope of perpendicular line be m2
m1*m2=-1
-3*m2=-1
m2=1/3
hence slope (m2) =1/3
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Are the triangles congruent, if so which triangles?
S
3 in
AD
Q
4 in
R
X
3 in
4 in
O Yes, A RSQ =A XÚC
O Yes, AUXC = AQRS
O Yes, A XCU A SRQ
O No, these triangles are not congruent
O Yes, AUXCAQSR
Answer:
Yes, [tex]\triangle UXC \cong \triangle QRS[/tex]
Step-by-step explanation:
The triangles are congruent by SAS.
In this activity, you will create a function from two points that satisfy it. A linear function passes through the points ( - 2 , 3 ) and ( - 3 , 5 ) . Complete the following tasks to find the equation of the function. Part A To find the equation, first find the rate of change. What is the rate of change for the linear function that passes through the two points?
The linear function would be y = -4x - 7 which passes through the points (- 2 , 3 ) and ( - 3 , 5 ).
Given that linear function passes through the points (- 2 , 3 ) and ( - 3 , 5 ).
Let the required line would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
x₁ = -2, y₁ = 3
x₂ = -3, y₂ = 5
⇒ y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
Substitute values in the equation, we get
⇒ y - 3 = (5 - 1)/(-3 - (-2))[x -(-2)]
⇒ y - 3 = (4)/(-1)[x +2]
⇒ y - 1 = -4(x +2)
⇒ y = -4x - 8 + 1
⇒ y = -4x - 7
Therefore, the linear function would be y = -4x - 7 which passes through the points (- 2 , 3 ) and ( - 3 , 5 ).
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2. Find the 72nd term in the arithmetic sequence 2,
-8, -18, -28, ..
Answer:
The 72nd term is -708
Step-by-step explanation:
According to a study done by a university student, the probability a randomiy selected individual will not cover his or her mouth when sneezing is 0.267. Suppose you sit on a bench in a mall and
obsorve people's habits as they sneeze.
What is the probability that among 10 randomly observed individuals fewer than 5 do not cover their mouth when sneezing?
Answer:
the total number of random sample n 10
probability of is 0.267
Determine the probability: It will definitely turn dark tonight.
a. 0.5
b. 1
c. 0.30
d. 0.67
The probability of 'It will definitely turn dark tonight' would be 1.
So option (B) is correct.
What is a probabilty?
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.
If by "likelihood" probability, the word definitely implies the probability would be 1, certainty.
Because definitely after daylight, the light will turn dark at the night.
So the probability would be 100% or 1.
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What is the equation of the line that passes
through the point (-3, 4) and has a slope of
2/3?
what is the area of a circle with a radius of 2 cm anda circle with a radius of 4 cm
Answer:
Step-by-step explanation:
area = pi * r^2
area = pi * 2^2
area = 4pi
area = pi * 4^2
area = 16pi
Fill in the blanks below in order to justify whether or not the mapping shown represents a function.
The mapping diagram above a function since
in where there
Answer:
This is a function
Step-by-step explanation:
For every input there is only one output.
a recipe calls for 5 teaspoons of seasoning for every 6 batches of chilli if you have 102 batches of chilli how many teaspoons of seasoning will you need
For 102 batches of chilli, 85 number of teaspoons of seasoning needed.
What do you mean by fraction?
Fraction represents a part of a whole, or more generally, any number of equal parts. In everyday English, fractions represent how many parts of a particular size are there.
For positive common divisors, the numerator and denominator are natural numbers. The numerator represents the number of equal parts and the denominator shows the number of parts that make up the unit or whole. A zero part can never make up a whole, so the denominator is never zero.
It is given that a recipe calls for 5 teaspoons of seasoning for every 6 batches of chilli.
For 6 batches of chilli, number of teaspoons of seasoning needed = 5
For 1 batch of chilli, number of teaspoons of seasoning needed = 5/6
For 102 batches of chilli, number of teaspoons of seasoning needed = [tex]\frac{5}{6}\times 102[/tex] = 85
Therefore, For 102 batches of chilli, 85 number of teaspoons of seasoning needed.
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Select the correct answer.
What is the y-intercept of f(x) = 3x+2?
Ο Α.
OB.
O C.
OD.
(9, 0)
(0, 9)
(0, -9)
(9,-9)
4
Answer:
C, (0, 9)
Step-by-step explanation:
The y-intercept is when the x-value is 0. We pug in 0 for x, getting f(0) = 3^2=9. The x-coordinate must be 0, and the y-value is 3^2, or 9. The correct answer is (0, 9)
A hypothesis test was used to test the hypothesis that men drive faster on average than women. The p-value was 0.16 and the level of significance used was 0.1. Then there is sufficient evidence to conclude that, on average, men drive faster then women O false O true
On average, men drive faster then women
The statement is true.
What is p-value?
The p-value, used in null-hypothesis significance testing, represents the likelihood that the test findings will be at least as extreme as the result actually observed, assuming that the null hypothesis is true.
We are given a statement that,
A hypothesis test was used to test the hypothesis that men drive faster on average than women.
The p-value in that case was 0.16 and the level of significance used was 0.1
As the p value is greater than level of significance we can say that the null hypothesis is correct
Hence we can say that on average men drive faster than women
The statement is correct
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find the volume of the composite figure 2 3 2 3 1 1 1 5 8
The total volume is given as 195.36 m³.
What is volume?Volume can be defined as the capacity of any object. It can be calculated by multiplying the base area to the height.
The composite figure consists of three cuboids and two right circular cylinders.
The volume of a cuboid is the product of its length, breadth and height.
And, the volume of cylinder is given as πr²h
As per the figure given in the question the total volume is given as,
3(1 × 5 × 8) + 2 (π × 2² × 3)
= 40 × 3 + 12π × 2
= 120 + 24 × 3.14
= 195.36
Hence, the volume of composite figure is given as 195.36 m³.
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The size of a wolf population in a national park increases according to the formula y=y₀ e^{0.027 t}, where t is time in years and y₀ is the initial population at time 0 . If the size of the current population is 58 wolves, find how many wolves there will be in 5 years.
In 5 years, there will be ? wolves.
(Round to the nearest whole number as needed.)
Answer:
66
Step-by-step explanation:
y = 58 e^(0.027 * 5)
y = 58 e^(0.135)
y = 58 * 1.144537
y = 66.383133
y = 66
Find how long it takes a person to drive 260 miles on a highway if she merges onto a highway at 7 p.m. and drives nonstop with her cruise control set on 80 mph.
When time is also known, distance—the measurement of how far something has travelled in a straight line—can be used to determine speed.
Step-by-step explanation:Speed can be calculated using distance—the amount of distance something has travelled in a straight line—when time is also known.Distance, D = 260 miles
Velocity, V = 80 miles/hour
Time taken, t = distance/velocity
= D/V
= 260/80
= 3.25 hours
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I need help completing the proving Statement
This looks like a fill-in the blanks question for a two column proof :]
3. CPCTC
The reasoning for this is that because triangle ABC and EDC are congruent, their corresponding parts are also congruent, (CPCTC; Corresponding Parts of Congruent Triangle are Congruent) or AC = EC
4. ACE
Because AC = EC, triangle ACE is isosceles
5. Base Angles Theorem
The base angles of a isosceles triangle are congruent
:]
What is the range of this absolute value function?
The range of this absolute value function is -∞ < y ≤ 7
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.
Consider the vertical extent of the graph along y axis.
It starts from +7 extends till -∞
So, the range is -∞ < y ≤ 7
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40% of the treats in a bag of Bark Bites are peanut butter. If there are 12 peanut butter treats, how many treats are in a bag of Bark Bites? Pick the model that represents the problem.
Answer:
30
Step-by-step explanation:
40% of what number is 12?
.4n = 12 Divide both sides by .4
n = 30
Answer:
30
Based on the given conditions, formulate: 12/40%
Multiply both the numerator and denominator with the same integer: 120/40
Cross out the common factor:30
Answer: 30
If a sum of $500 were shared among a group of people in the following ratios, how much would each person receive?
a. 6:4
b. 1:4:5
c. 1:8:1
d. 8:9:8
e. 10:5:4:1
Jonah ran 1 Taps on Monday, 21 laps on Tuesday, and 6 laps on Wednesday.
How much farther did he run on Wednesday than on the other two days
combined? Show your work.
Jonah runs 2 (19/20) laps more than the remaining two days
Adding Fractions:The fractions that have the same denominator are like fractions, to add like fractions directly, But if the denominators are not the same then we need to change their denominators to the same then we can add the fractions.
To make denominators as same we need to take the LCM of denominators of two fractions.
Here we have
Jonah ran 1(3)/(4) laps on Monday
=> 1 3/4 = 7/4 laps
On Tuesday he ran 2(3)/(10) laps
=> 2 3/10 = 23/10 laps
On Wednesday he ran 6(1)/(5) laps
=> 6 1/5 = 31/5 laps
The total number of laps ran combining Monday and Tuesday
= 7/4 laps + 23/10 laps
= (35 + 46)/20 [ take Lcm of 4, 10 i.e 20 ]
= 81/20
From the above calculations,
Jonah ran 81/20 laps on combining Monday and Tuesdays
The difference between Wednesday's counted laps and Monday, and Tuesday's counted laps
= 31/5 - 81/20
= (140 - 81)/20 [ Take Lcm of 5, 20 i.e 20 ]
= 59/20
= 2 (19/20)
Therefore,
Jonah runs 2 (19/20) laps more than the remaining two days
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Complete Question:
Jonah ran 1(3)/(4) laps on Monday, 2(3)/(10) laps on Tuesday, and 6(1)/(5) laps on Wednesday. How much farther did he run on Wednesday than on the other two days combined? Show your work.
Simplify the expression below. Leave your expression in an exact form with coefficient a and radicand b so we have: a\sqrt[]{b} . Keep in mind that the coefficient a can be a product of a number and a variable. 2\sqrt[]{x^2y} Simplifies to a\sqrt[]{b} where: our coefficient a = and our radicand b =
The simplified expression of 2√x²y is 2x√y
How to simplify the expressionFrom the question, we have the following parameters that can be used in our computation:
2\sqrt[]{x^2y}
Rewrite properly
So, we have the following representation
2√x²y
Take the square root of x²
So, we have
2x√y
Hence, the solution is 2x√y
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wright a function that relates the distance traveled,d , to the time,t,
The function that relates the distance traveled to the time is given as follows:
d = vt.
In which v is the average velocity during the time traveled.
What is the relation between velocity, distance and time?The average velocity is calculated as the division of the total distance by the total time, hence the following equation is built to model the proportional relationship between these variables:
v = d/t.
In this problem, we want to relate the distance traveled to the time, hence we have to solve the expression for d, as follows:
d = v x t
d = vt.
(applying cross multiplication to isolate the variable d).
Then it is a proportional relationship in which the average velocity acts as the constant of proportionality.
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