Suppose {xn} is increasing and has a subsequence {xnk} which converges to L. We will prove that {xn} itself converges to L.
For any ϵ>0, we want to find an integer Nϵ such that |xn−L|≤ϵ for any n≥Nϵ.
Since {xnk} is increasing and converges to L, we can find kϵ such that for any k≥kϵ, −ϵ<xnk−L<0.
Take Nϵ=nkϵ, then for any n≥Nϵ, xnkϵ≤xn≤L, so −ϵ≤xnkϵ−L≤xn−L≤0.
Similarly, we can prove when {xn} is decreasing
A rectangular poster has a area of 504 centimeters. The width of the poster is 14 centimeters. How long is the poster?
Answer:
36 cm
Step-by-step explanation:
504/14=36
Mr Harrison is 9 months old. How old is Mr Harrison daughter in days
Answer:
273.75 days
Step-by-step explanation:
what is one third the product of 2 numbers a and b.
Answer:
1/3 (a+b)
Step-by-step explanation:
The required solution is 1/3ab.
It is required to find the solution.
What is arithmetic?Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.
Given:
Let the 2 numbers be a and b.
According to given question we have,
Product =a× b=ab
1/3 of product =1/3ab
Therefore, the required solution is 1/3ab.
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Please take a look at the picture
Answer: C
Step-by-step explanation:
Please take a look at the picture
Answer:
I think it'
is A and B
Step-by-step explanation:
hope hwlps
The brand manager for a brand of toothpaste must plan a campaign designed to increase brand recognition. He wants to first determine the percentage of adults who have heard of the brand. How many adults must he survey in order to be % confident that his estimate is within percentage points of the true population percentage
Using the margin of error, it is found that he must survey 601 adults in order to be 95% confidence that his estimate is within 4 percentage points of the true population percentage.
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]\frac{1+\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
95% confident, hence:
[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so [tex]z = 1.96[/tex].
We have no estimate, hence, [tex]\pi = 0.5[/tex] is used.
Within 4%, hence, it is needed to find n for which M = 0.04.
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.04 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]
[tex]0.04\sqrt{n} = 1.96(0.5)[/tex]
[tex]\sqrt{n} = \frac{1.96(0.5)}{0.04}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96(0.5)}{0.04}\right)^2[/tex]
[tex]n = 600.25[/tex]
Rounding up, 601 adults must be sampled.
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A line that passes through the points (12,12) and (20,6)
Answer:
8,48 I think
Step-by-step explanation:
I subtracted them from each other
The required equation of the line is given as y = -6x / 8 + 21.
Given that,
A line that passes through points (12,12) and (20,6)
The slope of the line is a tangent angle made by line with horizontal. i.e. m = tanx where x in degrees.
here,
Standard equation of the line,
y -y₁ =(y₂ - y₁) / (x₂ - x₁) (x - x₁)
Substitute the point in the above equation,
y - 12 = (6-12)/(20 - 12)[x - 12]
y = -6/8[x - 12] + 12
y = -6x/8 +9 + 12
y = -6x / 8 + 21
Thus, the required equation of the line is given as y = -6x / 8 + 21.
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a coin is flipped 3 times and lands on heads each time. What is the probability of it landing on tails on the fourth flip?
Answer:
1/4
Step-by-step explanation:
since the dice would be rolled 4 times, and the dice rolled heads 3 times, the probability of the coin land8ng of tail on the 4th flip is 1/4
The probability of it landing on tails on the fourth flip will be 1/4.
What is probability?
Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favorable outcomes / Number of sample
Given that a coin is flipped 3 times and lands on heads each time. The probability of getting head on the fourth flip will be:-
Probability = Number of favorable outcomes / Number of sample
Number of favorable outcomes = tails = 1
Number of samples = 4
Probability = 1 / 4
Therefore, the probability of it landing on tails on the fourth flip will be 1/4.
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What's the kinetic energy of an object that has a mass of 12 kilograms and moves with a velocity of 10 m/s?
Answer:
Step-by-step explanation:
Assuming it has no spin
KE = ½mv²
KE = ½(12)10²
KE = 600 J
9.
Identify the point corresponding to Q.
IT'S NOT A. Q' (-3, -4)
A. Q′ (−3, −4)
B. Q′ (−4, 1)
C. Q′ (−1, −4)
D. Q′ (−4, −3)
Answer:
C(-1, -4)
Step-by-step explanation:
see the point reflected over the line through the vertex point
Answer:
D. Q′ (−4, −3)
Step-by-step explanation:
From looking at the graph it looks like the answer would be
Q= (3, -4) if the X-axis goes first
Q= (-4, 3) if the Y-axis goes first
23 x 5 + 6 x 50 -7 = ?
Answer: Your anwser would be 408 please mark brainliest thank you
Step-by-step explanation:
Answer:408
Step-by-step explanation:
To find the answer, we can use the order of operations ( PEMDAS)
23*5=115
6*50=300
so simplified
115+300-7
add
415-7
subtract
408
so 23*5+6*50-7=408
п
What is the end behavior of the polynomial function?
1
8
B
4
2
6
2
2
8
B
X
-4
6
o As X->-co, then Y---
As X-→-00, then y0
As X-0, then y →-00
ne X -> then V -> 0
Answer:
The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity
Step-by-step explanation:
hope this help
dont know if this is correct
The end behavior of the polynomial function is as x -> ∞, y -> -∞
How to determine the end behavior?From the graph of the polynomial, we have the following highlight:
As x approached infinityThe function approaches negative infinityThe above highlights mean that:
As x -> ∞, y -> -∞
Hence, the end behavior of the polynomial function is as x -> ∞, y -> -∞
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Two sides of a triangle measure 27 inches and 32 inches.
Which could represent the length of the third side?
Answer options:
5 in
59 in
7 in
62 in
Answer:
62 in
Step-by-step explanation:
the Hypotenuse of a triangle is always longer than the two other sides, 27 + 32 is larger than all but one of the options, 62. Making 62 the answer by process of elimination.
Which table could be a partial set of values for a linear function?
(Had to repost cuz of spamming)
For homework, Tina is asked to write down the opposite value for each number listed. Which comparison did Tina write incorrectly?
Answer:
x
Step-by-step explanation:
It still would be a negative.
The comparison that Tina wrote incorrectly is X. Then the correct option is B.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The table is given below.
Comparison Number Opposite value
W -3 3
X -(-9) 9
Y 0 0
Z 4 - 4
The number -(-9) is also written as 9 and the opposite number of 9 is negative 9. Then the comparison that Tina wrote incorrectly is X. Then the correct option is B.
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Gven: f(x) = 4x +1 and (x)= x^2 + 1.
find (fog)(x)
Answer:
Step-by-step explanation:
27836?+_68_729+_8978
Hello Please help me.
Answer:
Step-by-step explanation:
1) D
2) B
3) no solution
y ≤ 0.5x - 4 is area C including the red line
y ≥ 0.5x + 5 is area A including the blue line
A 52-centimeter-long board is cut into 3 pieces. The longest piece is twice as long as the shortest piece. The other piece is 4 cm longer that the shortest piece. How long is each piece?
Answer:
4c 6th fastest 9.I gghiii
One snowy day, the snow was falling at a rate of 3 inches per hour.
If it kept snowing at the same rate, now many inches would
accumulate in 24 hours
artice
соо
Answer:
72 inches
Step-by-step explanation:
You would multiply the 3 inches per hour times the 24 hours to get 72 inches of snow.
Answer:
72 Inches
Step-by-step explanation:
24x3=72
A jet is flying in a direction N 70° E with a speed of 600 mi/h. Find the north and east components of the velocity. Round to two decimal places.
Using vector concepts, it is found that the components of the velocity are given as follows:
North: 205.21 mi/h.East: 563.82 mi/h.How can a vector be represented in i and j notation?Given a magnitude M and angle [tex]\theta[/tex], the a vector V can be represented as follows:
[tex]V = M\sin{\theta}i + M\cos{\theta}j[/tex]
In which:
i is the horizontal(east/west) component.j is the vertical(north/south) component.In this problem, we have that the magnitude and the angle are given as follows:
[tex]M = 600, \theta = 70^{\circ}[/tex]
Hence the north component is:
[tex]600\cos{70^{\circ}} = 205.21[/tex]
And the east component is:
[tex]600\sin{70^{\circ}} = 563.82[/tex]
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Which symbol correctly compares the numbers?
-0.64 0-0.5
O>
O <
O I don't know.
Answer:
<
Step-by-step explanation:
-0.5 is greater than -0.64
We need to find the symbol -0.64 ,0-0.5. -0.64<0-0.5.
What is Number system?A number system is defined as a system of writing to express numbers.
We need to find which symbol is used between Minus zero point six four and minus zero point five.
-0.64 and -0.5
As we know that the integers are number with positive, Negative and zero.
-0.64<-0.5
On the number line the integer -0.64 lies on left of -0.5.
So -0.64 is less than -0.5.
Hence -0.64 is less than -0.5.
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Find the missing side of the triangle. Round to the nearest tenth where necessary find qr
Answer:
QR = 4.9 ft
Step-by-step explanation:
Since the triangle is a right triangle, use the Pythagorean Theorem (a² + b² = c²).
[tex]a^2+b^2=c^2\\\\a^2+1^2=5^2\\\\a^2+1=25\\\\a^2=24\\\\\sqrt{a^2}=\sqrt{24}\\\\a=4.9[/tex]
Please take a look at the picture
Answer:
B) -g/-h
Step-by-step explanation:
-g/-h=g/h
Rewrite the fraction.
-(-g/h) = g/h
Hope this helps :)
The scatter plot shows a regression line of advertising dollars spent and sales. If the company were to spend $6,500 on advertising, what would be the predicted sales?
A) $110,000
B) $114,000
C) $118,000
D) $122,000
HELPPP PLEASE IM GIVING OUT BRAINLIEST
Answer:
C
Step-by-step explanation:
what is this simplified as a fraction
Step-by-step explanation:
35/48
this cannot be simplified any further
HELP IF CORRECT WILL GIVE BRAINLIEST (if you are trying to play around i will report u u-u)
Answer:
synthetic.
Step-by-step explanation:
I don't know how to give a step by step.
Answer:
Well I don't have the previous reading stated in the question obviously, but fossil fuels are natural resources. They form from decomposing plants and animals and are mainly found in the Earth's crust. These fuels are made of hydrogen and carbon which can be burned for energy.
the length of a rectangle in (3+√7) and it's with is (1+2√7). what is the area of the rectangle? what is the perimeter of the rectangle
Answer:
Area: (3+√7) x (1+2√7) = 17+7√7 = 35.52
Perimeter: 2(3+√7) + 2(1+2√7) = 8+6√7 = 23.87
Write the expression that represents the sum of
double a number and triple a number.
Answer: let x = the "number"
2x + 3x is the expression
Step-by-step explanation:
Find the surface area of this cuboid
Answer:
62
Step-by-step explanation:
SA=2(5x2)+2(5x3)+2(3x2)
SA=20+30+12
SA=62
f(x)=2x^2 + x - 6/ x-1
Answer:
See below
Step-by-step explanation:
Zeroes:
[tex]f(x)=\frac{2x^2+x-6}{x-1}[/tex]
[tex]0=\frac{2x^2+x-6}{x-1}[/tex]
[tex]0=2x^2+x-6[/tex]
[tex]0=(2x-3)(x+2)[/tex]
[tex]x=\frac{3}{2},-2[/tex]
Vertical and Horizontal Asymptotes:
[tex]x\neq 1[/tex] is excluded from the domain, therefore, there's a vertical asymptote at [tex]x=1[/tex]
No horizontal asymptotes as the degree of the numerator is greater than the degree of the denominator by 1.
Oblique (Slant) Asymptote:
[tex]f(x)=\frac{2x^2+x-6}{x-1}=2x+3,R(-3)[/tex], so the oblique/slant asymptote is [tex]y=2x+3[/tex]