The statement lim infn sₙ > lim infn tₙ and lim sup sₙ ≤ lim sup tₙ is proved such that sₙ ≤ tₙ for all n≥n₀.
What do you mean by inf and sup?The biggest element in P, if one exists, that is less than or equal to each element of S is known as the infimum of a subset S of a partially ordered set P. As a result, the phrase largest lower bound is also frequently employed. A set's infimum is its highest upper bound, while its supremum is its lowest upper bound. The supremum is the smallest upper bound of a set, whereas the maximum is the largest member of a set. The largest number in one column that is less than or equal to the target value in the other column is found using the greatest lower bound (glb) operator. The smallest number that is larger than or equal to the target number is discovered using the least upper bound (lub) operator.
Let us suppose that sₙ ≤ tₙ if n≥N, but that
lim infn sₙ > lim infn tₙ.
Let [tex]E_{s}[/tex] denote the set of all subsequential limits of {sₙ}, and let [tex]E_{t}[/tex] denote the set of all subsequential limits of {tₙ}. Then
inf [tex]E_{s}[/tex] >inf [tex]E_{t}[/tex].
This implies that there exists some x∈[tex]E_{t}[/tex] such that inf [tex]E_{s}[/tex] >x>inf [tex]E_{t}[/tex]., since otherwise inf [tex]E_{t}[/tex]. would not be the greatest lower bound of [tex]E_{t}[/tex]. Hence some subsequence of {tₙ}, say {tₙ}, converges to x< inf [tex]E_{s}[/tex].
lim sup sₙ ≤ lim sup tₙ.
Let [tex]E_{s}[/tex] denote the set of all subsequential limits of {sₙ}, and let [tex]E_{t}[/tex] denote the set of all subsequential limits of {tₙ}. Then
sup [tex]E_{s}[/tex] ≤ sup [tex]E_{t}[/tex].
This implies that there exists some x∈[tex]E_{t}[/tex] such that sup [tex]E_{s}[/tex] ≤ x ≤ sup [tex]E_{t}[/tex]., since otherwise sup [tex]E_{t}[/tex]. would be the greatest lower bound of [tex]E_{t}[/tex]. Hence some subsequence of {tₙ}, say {tₙ}, converges to x< sup [tex]E_{s}[/tex].
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Hana has some blue paint. She wants to lighten the shade, so she mixes in 1 cup of white paint. The color is still too dark, so Hana keeps mixing in 1 cup of white paint at a time. After adding 4 cups, she decides the color is too light.
A. Explain in words how much paint Hana should have added initially to get the shade she wants.
Enter your answer.
B. Model With Mathematics Represent your answer to part A with one or more inequalities.
Enter your answer.
C. Hana decides that she likes the shades of blue that appear in between adding 1 cup and 4 cups of white paint. How can you represent the number of cups of white paint that yield the shades Hana prefers?
Enter your answer.
Answer:
e, so she mixes in 1 cup of white paint. The color is still too dark, so Hana keeps mixing in 1 cup of white paint at a time. After adding 4 cups, she decides the color is too light.
A. Explain in words how much paint Hana should have added initially to get the shade she wants.
Enter your answer.
B. Mod
Step-by-step explanation:
verbal expression for 7 to the third power
The answer is " 7 to the power 3rd ".
We translate the algebraic expression 7³ into a verbal expression. The given expression has a base number of 7 raised to the power of 3 . This means is that 7 is multiplied by itself 3 times. So we should write " 7 to the power 3rd "
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Are the ratios 1:2 and 8:16 equivalent?
Answer:
Yes, the ratios are equivalent.
Step-by-step explanation:
Suppose that the relationship between price, P, and quantity, Q, is given by the equation Q = 140-4P.
Which of the following equations correctly represents solving Q = 140-4P for P?
OP=140-Q
OP=35-4Q
OP=140-4Q
OP=140+Q
OP=35-10
Answer:
In 1864, Sherman succeeded Grant as the Union commander in the Western Theater. He led the capture of the strategic city of Atlanta, a military success that contributed to the re-election of President Abraham Lincoln.
Step-by-step explanation:
I really need help, I might get a grade detention
Answer:
Step-by-step explanatio
from up to down
12
30
10
What percent is represented by the diagram below?
Alternative text
A. 13%
B. 65%
C. 130%
D. 650%
Answer:
I think it's will be C
Step-by-step explanation:
C I psomes
Answer: C 130%
Step-by-step explanation:
find the LCM of 2 and 3
Answer:
6
Step-by-step explanation:
If you multiply both together once that will be the lowest it gets
Answer: 6
Step-by-step explanation: compare the multiplication tables ig
Emma has $12.60 worth of nickels and quarters. She has 4 times as many quarters as
nickels. How many quarters does she have?
On solving linear equation 1.05x=12.60, we get that Emma has 48 quarters.
What is linear equation in one variable?Let x be any variable then ax + b = c b is an linear equation in one variable.
where a, b, c are constants then we get solution for x as
x=(b-c)/a
Given as Emma has 4 times as many as quarters as nickels
Let the no of nickels be x
Then as there are 4 times as many as quarters as nickels
then no quarters be = 4x
Value of one nickel = 5 cents= $0.05
Value of one quarter = 25 cents = $0.25
Therefore x nickels and 4x quarters worth is = x(.05)+4x(.25)
Total worth of given nickels and quarters = $12.60
Then 0.05x+x = 12.60
This is an linear equation in one variable
1.05x=12.60
x= 12.60/1.05
x=12
Therefore ,Emma has 12 nickels
and 4(12)= 48 quarters
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Which choice correctly explains the expression?
5 × 9
Responses
5 groups with 9 items per group
5 groups with 9 items per group
5 groups with 5 items per group
5 groups with 5 items per group
9 groups with 9 items per group
9 groups with 9 items per group
Skip to navigation
Answer:
The first choice
Step-by-step explanation:
Since we're looking at 5 × 9, we'd need to group them into 5 groups of 9, or 9 groups of 5. In this case, the first choice is the correct answer.
Mark the other guy with brainliest
Gabriel started training with the track team five weeks ago. During the first week, he ran 0.5 mile at each practice. The next three weeks he ran 0.75 mile, 1 mile, and 1.25 miles at each practice. If he continues this pattern, how many miles will he be running at each practice during the 7 th week?
If Gabriel continues the pattern of running that he has done on the past four weeks, the miles he will run on the 7th week is 2 miles.
How many miles will Gabriel run?Gabriel's pattern of running is such that he increases the number of miles by 0.25 miles every week.
This is why he ran 0.5 miles, and then 0.75 miles and then 1 mile.
If he keeps going like this, one the 7th week, he will run:
5th week = 1.5 miles
6th week = 1.75 miles
7th week = 2 miles
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seventy-four thousand,
ninety-nine
Answer:
I think you're looking for 74,099
for each integer $n$ greater than $1$, let $f(n)$ be the number of solutions of the equation $\sin x
The value [tex]\displaystyle \sum^{2007}_{n = 2} F(n)[/tex] is 2016532.
What is an integer?The collection of positive and negative integers is known as an integer. Integers, like whole numbers, do not include the fractional portion. Integers can therefore be defined as numbers that can be positive, negative, or zero but not as fractions. On integers, we can carry out all arithmetic operations, including addition, subtraction, multiplication, and division. Integer examples include 1, 2, 5, 8, -9, -12, etc. "Z" stands for an integer. The Latin term "Integer," which implies entire or intact, is where the word "integer" first appeared. Zero, positive numbers, and negative numbers make up the particular set of numbers known as integers.
Integer examples include: -1, -12, 6, and 15.
Zero is not an integer that can be positive or negative. There is no (+ or -) sign on zero, making it a neutral number.
F(2) = 3
We learn that for the majority of the graphs by examining different graphs.
F(n) = n+1
3+4+5+5+7+8+9+9+··········+2008
= (1+2+3+4+5+·····+2008)-3-501
= [tex]\frac{(2008) \times( 2009)}{2} -504[/tex]
= 2016532
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Hannah can spend up to $40 on snacks and drinks at the movie theater. A snack costs $5 and a drink costs $3.50.
Use for the number of snacks
Use for the number of drinks
Which inequality represents this situation?
Answer:
5s + 3.50d < 40
Step-by-step explanation:
if you were to total up the costs of a snack and drink together you'll end up with $8.50
-multiply $8.50 until you reach $40 mark
i.e 8.50×2(means 2 of each item) = $17
8.50×3 = $25.5
8.50×4 = $34
8.50×5= $42.5
-if you look at it, the calculation for 5, the pricing is now over the budget therefore the answer is then 5s + 3.50d < 40 because she can only spend up to $34 at most
Solve the equation below for y:
6x – 3y = 36
A. y = 2x − 12
B. y = 12 - 2x
C. y = 1/2x + 6
D. y = 6 - 1/2x
tyy<3
Write a declaration for a variable hits that can hold the number of times a baseball player has hit the ball in a baseball game.
A declaration of a hits variable that can store how many times a baseball player has hit the ball during a game of baseball int hits;
How do you declare a variable value?
A programme declares a variable whenever it states that it requires one. Place declaration statements for our brief programmes in-between the main method's two curly braces. The variable's name and data type are provided in the declaration. It could also provide a specific value that has to be entered into the variable.
When a variable is given a value for the first time, it is said to be initialized. The symbol = stands in for the assignment operator. Instead of writing int I and then 9, you can establish a variable for addition and then give it a value in the same line by writing int I = 9.
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simplify each expression 9(7k-2)+6k
Answer:
= 69k - 18
Step-by-step explanation:
9(7k-2) + 6k
= (9*7k + 9*-2) + 6k
= (63k - 18) + 6k
= 63k + 6k - 18
= 69k - 18
Marshall pours 1/2 gallon of lemonade into 8 glasses. He pours the same amount of lemonade into each glass. How much lemonade, in gallons, does Marshall pour into each glass?
the distribution of iq (intelligence quotient) is approximately normal in shape with a mean of 100 and a standard deviation of 15.according to the standard deviation rule, % of people have an iq between 55 and 145. do not round.
According to the standard deviation rule, 99.7% of people have an IQ between 55 and 145.
How to use the Empirical Rule in statistics?The standard deviation rule which is the empirical rule in statistics tells us that for distributions that have the normal shape, approximately 99.7% of the observations will fall within 3 standard deviations of the mean.
Now, In this question the mean is 100, and the standard deviation is 15. Thus, we can say that approximately 99.7% of the observations (IQ scores) fall between 100 − (3 * 15) and 100 + (3 * 15) or between 55 and 145.
Now, approximately 100% − 99.7% = 0.3% of the observations fall outside this interval. Since the normal shape is symmetric, approximately 0.15% of the observations fall above 145.
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A box of mass 20 kg is being pushed up a slope of 15 m long with a
constant speed of 30 m/s as shown in the figure below. What is the
gravitational potential energy? (g= 9.8m/s²)
The gravitational potential energy is 2940 Joules
What is potential energy?The formula for gravitational potential energy is expressed as;
Gravitational Potential energy = m g h
Where;
m is the massg is the acceleration due to gravityh is the height of the objectSubstitute the values into the formula;
⇒ 20 × 9. 8 × 15
Multiply through
⇒ 2940 Joules
Thus, the gravitational potential energy is 2940 Joules
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What is the remainder when 17^77 is divided by 35?
The remainder when 17^(77) is divided by 35 is 12
How can the remainder of dividing a large number be found?The number being divided = 17^(77)
The number by which 17^(77) is divided = 35
Using a graphing calculator as follows, we have;
Enter the value 17^(77) in the calculatorEnter the value 35 in the calculatorPress the divide by '÷' buttonUse the 'Display as proper fraction' button on the calculator, to display the result as proper fraction, [tex] a \frac{b}{c} [/tex]Use the left arrow button to move to the fraction part of the result displayed as proper fraction The remainder is the numerator of the fraction part of the proper fraction, which is 12[tex] \frac{17^{77}}{35} = V+ \frac{12}{35} [/tex]
Where V is a very large number quotient
From the above fraction, we have;
17⁷⁷ ÷ 35 = V + 12/35Expressing the above result using long division gives;
__V___ (Quotient)
35 (17⁷⁷)
____
12 (Remainder)
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Find the point equidistant from the points (0, 0, 0), (0, 4, 0), (3, 0, 0), and (2, 2, -3).
the point equidistant from the points (0, 0, 0), (0, 4, 0), (3, 0, 0), and (2, 2, -3) are (1/2, 1, 3/2).
What do you understand by equidistant points?Equidistant is a synonym for "equally distant," which is the state of two points being at the same distance from one another. Equidistant implies at the same distance from a location. The term "equidistant" is commonly used in reference to circles, perpendicular bisectors, parallel lines, and other geometrical concepts .Equidistant refers to the relationship between two or more objects or points that are situated at the same distance from one another. A point is considered to be equidistant from two other points when they are both located at the same distance from it. In the middle of the two starting points is a midway. The distance formula or the halfway formula can be used to demonstrate this.
Equation of sphere passes through origin is given by
x2 + y2 + z2 + ax + by+ cz =0
Given, it also passes through (1,0,0), (0,2,0),(0,0,3)
1+ a = 0, a = -1
4+2b =0, b=-2
And, 9+3c = 0, c= -3
The equation of the sphere becomes x2 +y2+ z2 -x -2y -3z = 0
Comparing with x2 +y2+ z2+ 2gx +2fy +2kz +C =0
Therefore the point that is equidistant from all the given points will be the centre of the sphere passing through all these points.
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Which expression is equivalent to (a^8)^4
Answer:
Brainliest pls
Step-by-step explanation:
a^32
Simplify. 9 + 18 ÷ 3
is |-10| greater than
|6|?
Answer:
Yes
Step-by-step explanation:
The value of |-10| is,
→ |-10| = 10
The value of |6| is,
→ |6| = 6
Now the greater value is,
→ 10 > 6
→ |-10| > |6|
Yeah, |-10| greater than |6|.
Answer:
No, it's not
Step-by-step explanation:
Hope it helps you
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One diagonal of a rhombus is three times as long as the other diagonal. If the area of the rhombus is 54 square millimeters, what are the lengths of the diagonals?
Answer:
Assume one diagonal of 2x and other of x inches. and sides of length =L inches.
Area of rhombus = 2*2x*x/2=2x^2 = 81 x=9/sqrt.2 and 2x=9*sqrt 2.
Diagonals are x=6.365 inch 2x=12.73 inch check area =12.73*6.365= 81.026 sq.inch.
Step-by-step explanation:
Use a calculator to approximate cot(5) to two decimal places. (Enter a number.)
The approximation of the trigonometry ratio cot(5) is 11.43
How to approximate the trigonometry ratio?The trigonometry ratio expression is given as
cot(5)
In trigonometry ratio, we have the following equation
cot(x) = 1/tan(x)
This means that x = 5
Substitute 15 for x in the equation cot(x) = 1/tan(x)
So, we have
cot(5) = 1/tan(5)
Using a calculator, we have:
cot(5) = 1/0.0875
Evaluate the quotient
So, we have
cot(5) = 11.4286
Approximate the above result
So, we have
cot(5) = 11.43
Hence, the approximation of the trigonometry ratio cot(5) is 11.43
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Module 2: Lesson 1
Spark Your Learning: Which is the Better Deal/
1. Which best describes the difference between a rebate and a discount, and how is the tax
rate used to find the total cost? (Fill in the oval)
O For a rebate the tax, the tax is calculated on the full price, and the customer receives the
rebate later. For a discount, the tax is calculated on the reduced price after the discount is
applied.
O For a rebate the tax, the tax is calculated on the reduced price after the discount is
applied. For a discount, the tax is calculated on the full price, and the customer receives the
rebate later.
The difference between a tax rebate and a discount is For a rebate the tax, the tax is calculated on the full price, and the customer receives the rebate later. For a discount, the tax is calculated on the reduced price after the discount is applied.
How do tax rebates and discounts differ?A tax rebate is also known as a tax refund and the purpose of it is to pay back a tax payer when they paid more taxes than they were meant to pay. It is therefore calculated on the full amount of tax.
This is different from a tax discount which works by using the discount to reduce the amount of tax owed and then you can pay off the discounted amount as tax.
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how do I solve this?
Jordan knits a square blanket that has an area of 1,500 square inches. What is the approximate length of each side of the blanket?
O 16 inches
O 27 inches
O 39 inches
O 42 inches
What is 6(3x-17) + 2x -18 = 9(4x+7) -9 + !7
The Simplification of the expression 6(3x-17) + 2x -18 = 9(4x+7) -9 + 17 and value for the unknown x, is approximately 11.94
Simplification6(3x-17) + 2x -18 = 9(4x+7) -9 + 17
open parenthesis18x - 102 + 2x - 18 = 36x + 63 - 9 + 17
collect like terms18x + 2x - 36x = 63 - 9 + 17 + 102 + 18
- 16x = 191
divide both sides by - 16x = 191 / - 16
x = 11.9375
Approximately,
x = 11.94
Therefore, the Simplification of the expression 6(3x-17) + 2x -18 = 9(4x+7) -9 + 17 and value for the unknown x, is approximately 11.94
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