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 new hotel was built with r rooms. The first weekend it was open, 3/5 of them were reserved. Which of the following expressions represents the number of rooms which were reserved?
A r-3/5
B r x 3/5
C r+3/5
D ÷3/5
PLEASE HELP ITS STUDY ISLAND
Answer:
c r/ 3/5
Step-by-step explanation:
i think
1. Write the equation of a horizontal line that passes through the point (–2, 2). x = –2 y = –2 y = 2 x = 2
Answer:
x = 2
Step-by-step explanation:
The given point is (-2, 2). A horizontal line passing through this point is x = 2.
Howards baseball team won 7/10 of its game. Jeremys team won 2/5 of its game. They both played the same number of games. Whose team won more games, or did they win the same amount?
Answer:
Jeremy's team won more games
Step-by-step explanation:
Let's transform these fractions into ratios:
[tex]\frac{7}{10} =7:10\\\\\frac{2}{5} =7:10[/tex]
Then, simplify:
[tex]7:10[/tex] ≈ [tex]1:1.4[/tex]
[tex]2:5=1:2.5[/tex]
Finally, compare:
[tex]1:1.4\neq 1:2.5[/tex]
Result:
Jeremy's team won more games since [tex]1:2.5>1:1.4[/tex]
Note:
The way I simplify the ratios may be confusing so here is a quick explanation;
Make the smaller of the two numbers in the ratio into one then divide the larger number by the smaller number for the other part of the ratio
Example:
5:10
5 turns into 1
10 divided by 5 equals 2
Simplified Ratio: 1:2
Jeremy won more games than Howard.
What is Fraction?The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.
The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.Given:
Howard Team won = 7/10
Jeremy team won = 2/5
Now, taking LCM (5, 10)= 10
So, Jeremy team won = 2/5
= 4/10
So, Jeremy won more games than Howard.
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I WILL GIVE BRAINLIST IF ALL ANSWERED CORRECTLY
Injured runners train on a special track at a rehabilitation center. The track is a square with a half circle on its left and right sides. The area of the square is 128 square feet. What is the length of the track? Use the table to help you answer the questions.
Square 11.02 11.12 11.22 11.32 11.42 11.52
Value 121.0 123.2 125.4 127.7 130.0 132.3
Square 11.62 11.72 11.82 11.92 12.02
Value 134.6 136.9 139.2 141.6 144.0
1. Fill in the blanks to complete the description of the track. (2 points)
The track has ____ sides of the square and the distance around ____ complete circle(s).
2. The length of one side of the square is the square root of its area. Use the table to find the approximate length of one side of the square. Explain how you used the table to find this information. (2 points)
3. Use your answers above to find the total length of the part of the track that is made up of sides of the square. (2 points)
4. The circumference of (distance around) a circle is π times the diameter, or C = πd. A side of the square is the diameter of each half circle.
In your answer to question 1, you gave the number of complete circles included in the track. Use this answer and C = πd to find the approximate length of the circular part of the track to the nearest tenth of a foot. Use 3.14 for π and show your work. (2 points)
5. Find the approximate length of the track, including the straight and circular sections. (2 points)
Answer:
The length of the track is approximately 51.7 ft
The track has three sides of the square and the distance round a half of a complete circle
Step-by-step explanation:
The given track shape and measurements are;
The shape on the left side of the track = Square
The shape on the right side of the track = Half circle
The area of the square on the the left side of the track = 128 square feet
Therefore, from the area, A, of a square of side length, s, which is s × s, and letting the side length of the square = s, we have;
Area of the square portion of the track = s × s = s² = 128 ft²
Therefore, s = √(128 ft²) = 8·√(2) ft.
Whereby the side length of the square is bounded by the diameter of the half circle, we have;
Length of the diameter of the half circle = s = 8·√(2) ft.
The length of the perimeter of the half circle = π·D/2 = π × 8·√(2)/2 = π × 4·√(2) ≈ 17.77 ft.
The perimeter of the track, which is the length of the track is made up of the three sides of the square opposite to the half circle and the circumference of the half circle.
Therefore;
The length of the track = 3 × 8·√(2) ft + π × 4·√(2) ft. = 4·√2×(π+6) ≈ 51.7 ft
The length of the track ≈ 51.7 ft
Which gives;
The track has three sides of the square and the distance round a half of a complete circle.
Jeremy can row 2/3 of a mile in 1/2 hour how long will it take him to row 1 mile?
Answer:
It takes 3/4 of an hour to go 1 mile
Step-by-step explanation:
You can do this by setting up a proportion and by using decimals for some fractions
2/3 = 0.66667 Miles
1/2 = 0.5 hours
0.66667/0.5 = 1/x Cross multiply
0.66667 * x = 0.5 * 1 Simplify
0.66667 * x = 0.5 Divide both sides by 0.66667
x = 0.5 / 0.66667
x = 0.74999625 Notice when rounded this is 0.75
x = 0.75 Now notice that 0.75 as a fraction is 3/4
x = 3/4
Jeremy can row 2/3 of a mile in 1/2 hour then it will take him 3/4 hour to row 1 mile.
If Jeremy can row 2/3 of a mile in 1/2 hour, then the time it takes him to row 1 mile can be found by setting up a proportion:
(2/3 mile) / (1/2 hour) = 1 mile / (x hours)
Cross-multiply:
(2/3) × x = 1 × (1/2)
Now solve for x:
x = (1/2) / (2/3)
x = 3/4
So, it will take Jeremy 3/4 of an hour (or 45 minutes) to row 1 mile.
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What is the midline of the function y=19cos(9x+3)+34 ?
plss help mee
The midline of the function is y = 34.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
The midline of a periodic function is the horizontal line that divides the graph of the function into two equal parts.
For a cosine function of the form y = A cos(Bx - C) + D, the midline is given by the equation y = D.
In this case, the function is y = 19cos(9x+3)+34, so the midline is given by the constant term, which is D = 34.
Therefore,
The midline of the function is y = 34.
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What are the solutions to the quadratic function. f(x) = x^2+4x-12
Answer:
2, -6
Step-by-step explanation:
x^2 + 4x - 12
A = 1
B = 4
C = -12
i used the "X" method to solve for the solutions. i think it's easier than using the quadratic formula but it doesn't always work
for the "X" method you have to multiply your A value and your C value together so 1 x (-12) = -12. that is going to be the top part of the X
the bottom part of the x will be your B value which is 4
we have to find multiples of -12 that will also add to 4
so -2 and 6 multiply to -12 but also add to 4 so we know these numbers will work
i added added two drawings to show how i found the solutions using the "X" method and the quadratic formula
Given that X varies directly as Y³ and X = 54, Y = 3. find X 10 Y = 5 what is the relationship between X and Y?
Answer:
x=6y3
Step-by-step explanation:
we first find the constant of proportionality where by we say; x= ky3
we're given x = 54
and y = 3
so
54=k(3cubed)
therefore
54= 9k
divide be 9 both sides to get k which is the constant
k=6
now rewrite the equation replacing k with 6
it will be...
X=6Y3
the following points lies in the solution set of the system of inequalities shown graphed below?
A. (1, 0)
B. (2, 2)
C. (-4, 0)
D. (2, -4)
A man flies a kite 354 feet in the air when he runs out of string, what is the angle of elevation if he had 200 yards of string to begin with
Answer:
Step-by-step explanation:
Assuming the string is straight (it will not be so due to gravity and wind load)
θ arcsin(354 / (200(3)) = 36°
Plotting points in the four quadrants
Point S has the coordinates (6, -4)
Which point on the graph shows the reflection of point s across the y axis
Answer:
it's -4 is the answer by the way
How much force is required to accelerate a 4 kg mass at 6 m/s2
Answer:
is it 24 N?
as we know ....
force=mass * acceleration
force=4kg*6m/s2
hence force is 24N
The required Force = 24 N
What is Force?The push or pull on an object with mass causes it to change its velocity.
Given that a body of 4 kg mass is accelerated at 6 m/s²
Force = ma
where m = mass and a = acceleration
F = 6*4 = 24 N
Hence, the Force required = 24 N
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55. H(x) = – 3x² + 6x
=
Answer:
Well this is a function/ quadratic question.
So using this info we can make this into a standard form for quadratics which is
ax^2+bx+c=0
In this case c is 0 and we cna just make everything else equal to zero so.
-3x^2+6x=0
Now with this we can use the quadratic formula
-b±√(b²-4ac)/(2a)
So pluggin everything in
X=-6±√(6²-4(-3)0)/(2(-3))
Now we solve
36/-6
or -6
Now we just do
-6±-6
x= -12
x= 0
These are your answers
x=-12
x=0
Plsssss help me! Brainlist! I’m so confused!
david has x nickels and y dimes
Which is the best estimate of the product 3,780 × 2?
Answer:
8000
Step-by-step explanation:
According to the food label on a box cookies, each box has 16
servings and each sering contains 4 cookies. The weight of the
ba of cookies is Kilogroms. What is the weight of each
cooke?
I cant help you but I can give you the equation: 16 x 4 x weight per cookie = answer
Step-by-step explanation:
did you forget to write the whole question?
expand 6(7+11x)
,,,,
Answer:
It would be 41+66x
Step-by-step explanation:
A person is running a distance race at a constant rate. What time will they finish the race what information would you need to be able to solve the problem?
Answer:
you need the distance they're running and the pace they are running at.
Simpson office furniture pays Tom Russell a $2490 monthly salary plus a 9% commission on merchandise he sells each month .Assume Tom's sales were $88,000 for last month.
Answer:
Amount Tom was paid for his sales last month 88,000 x9%= $7920.00
Step-by-step explanation:
A vendor sells burgers and cookies. A customer buys 2 burgersand 2 cookies for $7.50. Another customer buys 4 burgers and 3 cookies for $13.75. Find the cost of each item.
Answer:
The burgers cost $2.50 and the cookies cost $1.25.
Step-by-step explanation:
Let b represent burgers and c represent cookies.
2b + 2c = 7.50
4b + 3c = 13.75
Step 1: Use one of the two equations and isolate one of the variables.
2b + 2c = 7.50
- 2c -2c
[tex]\frac{2}{2}[/tex]b = [tex]\frac{7.50}{2}[/tex] - [tex]\frac{2}{2}[/tex]c
b = 3.75 - c
Step 2: Plug what you get for b into the second equation.
4(3.75 - c) + 3c = 13.75
15 - 4c + 3c = 13.75
15 - 1c = 13.75
Step 3: Isolate the variable and solve for c.
15 - 1c = 13.75
-15 -15
[tex]-\frac{1}{1}[/tex]c = [tex]\frac{-1.25}{-1}[/tex]
c = 1.25 ← price for cookies
Step 4: Plug in what you have for c into one of the previous equations and solve for b.
2b + 2(1.25) = 7.50
2b + 2.50 = 7.50
- 2.50 -2.50
[tex]\frac{2}{2}[/tex]b = [tex]\frac{5}{2}[/tex]
b = 2.50 ← price for burgers
Now you know the cost of each item:
The burgers cost $2.50 and the cookies cost $1.25.
Does anyone know this?
Answer:
I think 7.6 i remember i had something like this
Step-by-step explanation:
NEED HELP ASAP! TYSM IF YOU DO
Which of the following equations represents the greatest value of x?
Equation 1
x^2 = 17
Equation 2
x^2 = 26
Equation 3
x^3 = 64
Equation 4
x^3 = 27
Answer:
Equation 2 represents the greatest value of x!
Step-by-step explanation:
Let's solve each equation for x.
Equation 1; x = 4.1 (about)
Equation 2: x = 5 (about)
Equation 3: x = 4 (exact)
Equation 4: x = 3 (exact)
Hope this helps. :)
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.
What is the slope of the function?
O-6
O 4
O 4
O 6
Answer:
12/2 = 6
Step-by-step explanation:
2 ways to do it, graph it, or do the slop finding formula y2-y1/x2-x1
answer:
Step-by-step explanation:
I hope she is correct answer
A Gardner has 1 1/4 cubic feet of soil available for filling pots. Each pot will need 2/5 cubic foot to be filled. What is the greatest number of pots that the gardener fill
The greatest number of pots that can be filled is 3.
In order to determine the greatest number of pots that can be filled, the quantity of soil available would be divided by the capacity of each pot.
Number of pots that can be filled = 1 1/4 ÷ 2/5
= 5/4 ÷ 2/5
= 5/4 x 5/2 = 25/8 = 3 1/8
Thus, the greatest number of pots that can be filled is 3.
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Eddie's overtime is figured on a 40-
hour work week. Last week he
worked the following hours:
Monday = 9.7
Tuesday = 8.3
Wednesday = 8
Thursday = 9.1
Friday = 8.6
=
He is paid time and a half for
overtime and makes $14.40 for
regular hours. What is Eddie's gross
pay?
Answer:
597.6 Dollars
Step-by-step explanation:
Answer:
$655.92Step-by-step explanation:
Total number of hours worked:
9.7 + 8.3 + 8 + 9.1 + 8.6 = 43.7Overtime hours:
43.7 - 40 = 3.7Gross payment:
40*14.4 + 3.7*14.4*1.5 = 655.92Suppose you roll a pair of six-sided dice and add their totals, What is the probability that the sum of the numbers on your dice is a number other than 11
Answer:
17/18
Step-by-step explanation:
total number of outcomes=6×6=36
favorable outcomes for a total of 11=56,65
number of favorable items for a total of 11=2
P(a total of 11)=2/36=1/18
P(for a total other than 11=1-1/18=(18-1)/(18)=17/18
how do i do 3 5/6 - 2 7/15?
Answer:
don't know don't know don't know don't know don't know don't know don't know
Step-by-step explanation:
don't know don't know don't know don't know don't know don't know don't know don't
Write a story that can be representd by the equation y=x+1/5x
Answer:
I sorry but I don't get this question
