we colored all points of r2 with integer coordinates by one of six colors. prove that there is a rectangle whose vertices are monochro- matic. can we make the statement stronger by limiting the size of the purported monochromatic rectangle?

Answers

Answer 1

Yes, we can make the rectangle has sides of length n and n, and all four vertices have the same color

A rectangle is a two-dimensional shape with four sides, two of which are parallel and equal in length, and the other two sides are also parallel and equal in length.

In this case, the objects are the points in the plane with integer coordinates, and the available spaces are the six colors.

Since there are an infinite number of points with integer coordinates and only six colors, it follows that there must be a color that appears at the vertices of a rectangle.

In other words, we can color the points in a manner such that there will be a rectangle in which all four vertices are the same color. This is because, if we divide the points into six different regions, there must be at least one region that contains more points than the others.

When we look for a rectangle, we look for two points in this region that are the farthest apart from each other. The rectangle that connects these two points will have all four vertices the same color.

In conclusion, we can make the statement stronger by limiting the size of the purported monochromatic rectangle.

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Related Questions

mabel owes $374 on her credit card and is about to make a repayment of $155.What will be the new balance on her credit card

Answers

The new credit card balance on her credit card is $219 if no interest is added on balance.

What Is a Credit Card Balance?

The total sum of money owing by a cardholder to their credit card company is known as their credit card balance. Balances fluctuate depending on when and how they are used; they rise when purchases are made and fall when payments are made by cardholders. Any sum that is left over at the end of the billing cycle is added to the bill for the following month and is subject to interest. The balances on a person's credit cards play a significant role in determining their credit score. Future lenders will evaluate them to assess the risk (and price) of extending further credit to their clients.

Given that Mabel owes $374 and make a repayment of $155.

Then the new credit card balance is, if no interest is added on balance

= $374 - $155

= $219

So, The new credit card balance on her credit card is $219

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1 kg of wheat costs $10 how much does 260g cost

Answers

2.6

260 g is equivalent to 0.26 kg
0.26 x 10 = 2.6

Help me y'all plss I need help help​

Answers

Answer:

Step-by-step explanation:

19?

Step-by-step explanation:

a row n adds the number n to the sum (= the first number from the right in row n-1), and therefore also n to the 3rd number from the right of row n-1.

in any case, the first number from the right is the result of

1 + 2 + 3 + 4 + 5 + ... + n-1 + n

that sum is

n(n+1)/2

for the row 20 that is

20×21/2 = 10×21 = 210

the 3rd number from the right in row 20 is then

210 - 2 = 208

18. Suppose A (red, blue, yellow), B = (Red, yellow, green), and C= (green, red, purple). Which set is equivalent to (AUB)NC? (a) (purple) (b) (red) (c) {red, green) (d) {yellow, purple)​

Answers

Based on the information from the sets, it can be inferred that the correct answer is: red, green (option C).

How to identify the correct answer?

To identify the correct answer we must take into account the elements that are in each set. Once we identify this information, we must analyze the elements in common between the sets. In accordance with the above, we must take into account this:

∪= Union of sets, refers to all the elements of the operands.  ∩ = Intersection of sets, refers to the common elements between the operands.

Based on the above, the correct answer is red and green because these are the elements that have the sets A, B, and C.

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Test (Spring 2023)
Solve the equation. Check your solution.
2x-4-18x + 4

Answers

Answer:

bring -18x to 2x

2x-18x

then bring -4 to +4

2x-18x+4-4

Answer:
16x

Can’t really explain how I got it

X and Z are endpoints of a segment, and point T is on the segment. If XZ = 3x, XT = x + 3, and TZ = 13, then x = and XZ =

Answers

We can then plug this value into the given for XZ, which is 3x, to solve for the length of XZ. This comes out to be 18. Therefore, the value of x is 6, and the length of XZ is 18.

x = 6, XZ = 18

To solve for x, we can use the formula for the midpoint of a segment, which is (x + z)/2.

Plugging in the given values, we get (x + 13)/2 = 6.

Simplifying, we get x = 6.

To solve for XZ, we can simply plug in the given value for x, which is 6.

Therefore, XZ = 3(6) = 18.

Given three values related to a line segment, XZ, XT, and TZ, we can solve for both the value of x and the length of XZ. To do this, we can use the formula for the midpoint of a segment, which is (x + z)/2. Plugging in the given values for XT and TZ, we can solve for x, which comes out to be 6. We can then plug this value into the given for XZ, which is 3x, to solve for the length of XZ. This comes out to be 18. Therefore, the value of x is 6, and the length of XZ is 18.

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Unemployment rose from January to March a year from 2.5% to 2.9%. How big was the increase in percentage points and in percent?​

Answers

Answer:

0.4% increase although I don't know what a percentage point is sorry.

Step-by-step explanation:

Answer:

The increase in percentage points was 0.4

The increase in percent was 16%

Step-by-step explanation:

To find the increase in percent, divide the increase in percentage points by the initial unemployment rate and multiply by 100: (0.4 / 2.5) * 100 = 16%.

the maximum weight, w, that a stepladder can hold is 250 pounds. which inequality represents this situation?

Answers

w ≤ 250

This inequality can be used to represent the maximum weight that a stepladder can hold, which is 250 pounds. In other words, the weight, w, must be less than or equal to 250 pounds.

The weight, w, must be less than or equal to 250 pounds. This inequality can be used to represent the maximum weight that a stepladder can hold, which is 250 pounds. In other words, if the weight of the object being placed on the stepladder is greater than 250 pounds, it is not safe to use the stepladder. This inequality helps to ensure the safety of the person using the stepladder, as it limits the amount of weight that can be placed upon it. Furthermore, it also helps to protect the stepladder itself, as it prevents it from being overloaded with too much weight, which could cause it to break or malfunction. In conclusion, the inequality w ≤ 250 represents the maximum weight that a stepladder can safely hold.

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solve the following systems of linear equations by graphing

y=2/3x+4 and y=/x-1

Answers

Answer:

The solution to the system is (1.8, 7.6)

Step-by-step explanation:

To solve the system of linear equations by graphing, we need to plot the two lines on the same coordinate plane and find the point where they intersect, which will be the solution of the system.

Plot the lines:

y = 2/3x + 4 can be written as y = (2/3)x + 4, where the slope is 2/3 and the y-intercept is 4.

y = -x + 1 can be written as y = -x + 1, where the slope is -1 and the y-intercept is 1.

Find the intersection point:

To find the intersection point, we can substitute the x-value from one equation into the other equation. Let's use y = 2/3x + 4.

Substitute x from y = 2/3x + 4 into y = -x + 1:

-x + 1 = 2/3x + 4

Multiplying both sides by -3, we get:

3x - 3 = -2x - 12

Adding 2x to both sides, we get:

5x - 3 = -12

Adding 12 to both sides, we get:

5x = 9

Dividing both sides by 5, we get:

x = 1.8

Now that we have x, we can substitute it back into either equation to find the corresponding y-value. Let's use y = 2/3x + 4:

y = 2/3x + 4

y = 2/3 * 1.8 + 4

y = 3.6 + 4

y = 7.6

So the solution to the system is (1.8, 7.6), which is the point where the two lines intersect.

3
For the polynomial function f, when f (x) is divided by x-9, the remainder is 7. Which of the
following must be true about the graph of y = f (x) in the xy-plane?
It passes through the point (7,-9).
It passes through the point (-9,7).
It passes through the point (7,9).
It passes through the point (9,7).

Answers

3rd option is correct.

In the very center of the Irenic Sea lie the beautiful Nisos Isles. In 1998 the number of people on these islands was only 200, but the population triples every 25 years. Queen Irene has decreed that there must be at least 1.5 square miles for every person living in the Isles. The total area of the Nisos Isles is 24,900 square miles. c In how many years, approximately, from 1998 will the population of Nisos be as large as Queen Irene has proclaimed that the islands can support?

Answers

The population of Nisos be as large as Queen Irene has proclaimed that the islands can support is 16600.

What is the unitary method?

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given that, Queen Irene has decreed that there must be at least 1.5 square miles for every person living in the Isles.

The total area of the Nisos Isles is 24,900 square miles.

Here, 24,900/1.5

= 16600

Therefore, the population of Nisos be as large as Queen Irene has proclaimed that the islands can support is 16600.

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I need help with answering this image

Answers

The value of the missing internal angle in the irregular polygon is equal to 125°.

How to determine the missing measure of the remaining internal angle

The sum of internal angles (S), in degrees, in any convex polygon is determined by the following formula:

S = 180 · (n - 2)

Where n is the number of sides in the polygon.

According to the image seen beside, we find an irregular pentagon, that is, a polygon with five sides. First, determine the sum of internal angles:

S = 180 · (5 - 2)

S = 180 · 3

S = 540°

Second, find the value of the missing internal angles:

y = 540° - 86° - 142° - 72° - 115°

y = 125°

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∠A and ∠B are vertical angles. If m∠A = (7x+4) and m∠B = (8x - 20) then find the measure of ∠B

Answers

Since ∠A and ∠B are vertical angles, they have equal measures, so m∠A = m∠B. We can set the two expressions equal to each other:

7x + 4 = 8x - 20

Solving for x:

-x = -24

x = 24

So, m∠A = 7x + 4 = 7 * 24 + 4 = 188, and m∠B = 8x - 20 = 8 * 24 - 20 = 188.

Therefore, the measure of ∠B is 188 degrees.

K
M 3 J
Mark this and return
What is the length of line segment KJ?
O 2√3 units
O 3√2 units
O 3√3 units
O 3√5 units
Save and Exit
Next
Submit

Answers

The length of line segment KJ is D. 3√5 units

What is a Line Segment?

A line segment in geometry is a section of a straight line that is enclosed by two clearly defined endpoints and contains all of the points on the line that lie inside those endpoints. The Euclidean distance between two ends of a line segment determines its length.

∠KMJ = 180° - 90° (adjacent angles on a straight line)

= 90°

Using Pythagorean Theorem,

KJ² = 6² + 3²

KJ² = 45

KJ = √45

= √9√5

= 3√5

The answer is D. The length of line segment KJ is 3√5 units.

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As part of their opening day celebration, Benny’s Bakery made 150 cupcakes. The cupcakes all looked identical on the outside, but 6 of them had caramel inside. Customers who bought a cupcake with a caramel inside won a free cake. The cupcakes were randomly arranged and customers were allowed to choose their own cupcakes. Zoe was the first customer in line and bought three cupcakes. What is the probability that exactly one of Zoe’s cupcakes had caramel inside?

Answers

The probability that exactly one of Zoe's cupcakes had caramel inside after the cupcakes were randomly arranged and customers were allowed to choose their own cupcakes is 1/3266.

The probability that exactly one of Zoe's cupcakes had caramel inside can be calculated as follows:

P(exactly one cupcake with caramel) = (number of ways to choose one cupcake with caramel) / (total number of combinations of three cupcakes)

There are 6 cupcakes with caramel, so there are 6 ways to choose one cupcake with caramel.

Out of 150 cupcakes, there are 150 choose 3 = 19,600 ways to choose three cupcakes.

So, the probability that exactly one of Zoe's cupcakes had caramel inside is:

P(exactly one cupcake with caramel) = 6 / 19,600 = 1/3,266

Therefore, the probability that exactly one of Zoe's cupcakes had caramel inside is 1/3,266.

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A rectangle has an area if 82 feet exponent 3
what is the length if the width is 10 feet

Answers

The length of the rectangle is 8.2 feet.

Given area of the rectangle is 82 feet and width is 10 feet

let variable : length of rectangle

then the equation is 10x=82

x=82/10

x=8.2

x=length=8.2

Therefore the length of the rectangle is 8.2 feet.

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which expression fails to compute the area of a triangle having base b and height h (area is one-half base time height)?

Answers

The expression fails to compute the area of a triangle having base b and height h is (1.0 /2.0)*b*h.

Therefore the answer is A.

The correct expression to compute the area of a triangle having base b and height h is (1/2) * b * h, or equivalently, 0.5 * b * h.

Expression A is incorrect because it uses floating-point division, which may result in round-off errors or inaccuracies in the computation.

Expression B is the correct expression because it uses integer division and the division by 2 is clear.

Expression C is also correct because it uses floating-point division and the division by 2.0 is clear.

Therefore, both expressions B and C are correct, and expression D is a correct equivalent form of B and C.

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--The question is incomplete, answering to the question below--

"which expression fails to compute the area of a triangle having base b and height h (area is one-half base time height)?

A. (1.0 /2.0)*b*h

B. (1 /2)*b*h

C. (b*h)/2.0

D. 0.5*b*h"

What is the product of the expression, 4x(x2)? (1 point)
1. 4x3
2. 16x2
3. 4x2
4. 8x

Answers

The product of the given expression; 4x (x²) as required to be determined is; Choice 1; 4x³.

Which expression represents the product as required?

It follows from the task content that the product of 4x (x²) is to be determined as required.

Since the given expression is; 4x (x²); we have that;

4 • x • x²

It therefore follows from the product of powers law of indices that we have;

4•x³

= 4x³.

Ultimately, the product of the expression is; 4x³.

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A jar contains only pennis, nickels, dimes, and quarters. there are 24 pennies, 23 dimes, and 22 quarters. There are 80 coins in all. How many of the coins are not nickels? if n represents the number of nickels in the jar what equation could you use to find n?

Answers

Answer:

Step-by-step explanation:

m

how much commission would a salesperson earn for selling a $25.000. car? he receives an 18% commission

Answers

The commission earned by the salesperson for selling a $25,000 car with an 18% commission rate can be calculated by multiplying the price of the car by the commission rate:

Commission = 0.18 * $25,000

Commission = $4,500

Therefore, the salesperson would earn a commission of $4,500 for selling the car.

largest possible value of x

Answers

Answer:

i) 9

ii) 11

Step-by-step explanation:

First off, what is a "mode"?

The mode in a set of data is simply the most common answer/outcome;

Next, we need to understand the data;

In this case, families were asked about the number of cats they have;

The children answered 0, 1, 2 or 3;

8 families have 0 cats,

6 have 1,

10 have 2,

x have 3

So, the mode will be the most common answer to how many cats a family has;

As we can see from the data, the most common response was 2, i.e. 10 families have 2 cats, compared to only 8 with 0 cats and 6 with 1 cat;

If we know the mode is 2, the value of x has to be less than 10 as it is not the most common response;

The largest possible value will be 9.

If the mode is 3, then that means the x has to be the greatest number of responses;

Since the greatest number of responses to the other options is 10, then the number of responses to having 3 cats has to be at least 11;

The smallest possible value of x, if the mode is 3, will be 11.

can someone please help me show my work?

i have the answers!

brainly please help this due in 8 mins!

Answers

Answer: Check the numbers that are already there.

Step-by-step explanation:

Example, what times 6 equals 24? then divided 24 by that number. Do this for all the numbers

There were 84 runners to start a race in the first half of the race 1/3 of them dropped out in the second half of the race 2/7 of the remaining runners dropped out how many runners finish the race 

Answers

Answer:

40

Step-by-step explanation:

84 runners to start a race

in the first half of the race 1/3 of them dropped out = 84/3 = 28 dropped out

so 56 left

in the second half of the race 2/7 of the remaining runners dropped out

2/7 *56 =16 dropped out

so 56-16 = 40 left

how many runners finish

40

Courtney’s Bookstore is having a clearance sale. All paperbacks are one price and all hard covers are another price. Abigail buys 5 paperback books and 2 hardcover books for $29. Rodney buys 2 paperback books and 1 hardcover books for 13 dollars. What is the price of each type of book? Use a system of equations to solve.

Answers

Answer: Total price: $28.67

Step-by-step explanation:  From Courtney Summers, the author of Cracked Up To Be, comes a dark new tale of high school rivalry in which vicious rumors and nasty tricks are the currency that buys you popularity or seals your fate at the bottom of the food chain.

The general election is today, and volunteers are organizing the ballots. Depending on the part of the city in which a citizen lives, he or she receives a different ballot. The types of ballots consist of RED ballots numbered 1, 2, 3, 4 and BLUE ballots numbered 1, 2, 3, 4 Let R be the event of drawing a red ballot, B the event of drawing a blue ballot, the event of drawing an even numbered ballot, and the event of drawing an odd ballot

Answers

Event R: Drawing a Red Ballot, Event B: Drawing a Blue Ballot, Event Even: Drawing an Even Numbered Ballot, Event Odd: Drawing an Odd Numbered Ballot.

The general election is today, and volunteers are organizing the ballots. Depending on the part of the city in which a citizen lives, he or she receives a different ballot. The types of ballots consist of RED ballots numbered 1, 2, 3, 4 and BLUE ballots numbered 1, 2, 3, 4. First, the volunteers need to define the events of drawing a red ballot and drawing a blue ballot. This can be done by defining the events R and B, respectively. Next, the volunteers need to define the event of drawing an even numbered ballot and the event of drawing an odd numbered ballot. This can be done by defining events Even and Odd, respectively. The volunteers can then use these events to determine which ballots are being drawn by the citizens. For example, they can use the events R and Even to determine which citizens are drawing a red even numbered ballot.

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What is the sum of 17.25 and 1.725 , to the nearest integer?

Answers

take 17.25 and turn it into 17.250 to make the equation easier to solve.

then add:
17.250
+ 1.725
————
18.975

rounded to the nearest integer would mean the sum is 19.

The number of bees in a large garden is decreasing by 2.5% every year. If this year it has 8 million bees, how many millions of bees will be there in 6 years? Round to the nearest hundredth. million bees​

Answers

Answer:

I have solved it and attached in the explanation.

Step-by-step explanation:

A Nelson le piden trasladar agua para llenar un contenedor en forma de prisma hexagonal con las siguientes medidas: Lado del polígono= 4m y Altura= 10m. Ayúdale a calcular el área de la figura y después el volumen. Y suponiendo que tenemos otro prisma del triple de espacio, ¿cuál sería su volumen?
ayudaa jajaja

Answers

The area and volume based on the information will be area 144 √3 square meters and 240√3 cubic meters

How to calculate the area

To calculate the area of the hexagonal prism, you need to calculate the area of each face and add them up. To calculate the area of one face of the hexagon, you can use the following formula:

Area of a regular hexagon = (3 * √3) / 2 * side^2

Plug in the side length of 4m:

Area of a face = (3 * √3) / 2 * 4^2 = (3 * √3) / 2 * 16 = 24 * √3

So the area of one face is 24 * √3 square meters. There are a total of 6 faces, 3 of which are hexagons, so the total area of the hexagonal prism is:

Total area = 6 * (24 * √3) = 144 * √3 square meters

To calculate the volume of the hexagonal prism, multiply the area of one face by the height:

Volume = (24 * √3) * 10 = 240 * √3 cubic meters

So the volume of the hexagonal prism is 240 * √3 cubic meters

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Nelson is asked to move water to fill a container in the shape of a hexagonal prism with the following measurements: Side of the polygon= 4m and Height= 10m. Help him calculate the area of the figure and then the volume. And assuming that we have another prism three times the space, what would its volume be?

If you flip a coin 12 times, what is the best prediction possible for the number of times it will land on heads?

Answers

If a coin is tossed 12 times, the maximum probability of getting heads is 12

Mr.White is renting a van for one week and a few additional days d he does not have to pay a per mile fee evaluate the expression 260+70d to find how much he will pay for a 10-day rental

Answers

Answer:

For a 10-day rental, d = 10 - 7 = 3 days.

Step-by-step explanation:

So, the total amount Mr. White has to pay is 260 + 70d = 260 + 70 * 3 = 260 + 210 = 470 dollars.

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bob has a high-volume virtual private network (vpn). he would like to use a device that would best handle the required processing power. what type of device should he use? Graph the line through (2,0) withm = -2. This sentence is properly punctuated:My grannys houses windows got smashed last night.True or false! Help ______ is the use of a different material, method or technique than what was specified, usually by request of the contractor with approval of the designer. Figure B is what type of transformation of figure A? If $3000 is invested for 5 years with an interest rate of 10%per annum, calculate the final balance, rounded to thenearest cent, if:Simple interest was used. Function f is represented by this table of values.If f(x) is vertically stretched by a factor of 2 to obtain g(x), which table of values represents function g? PLEASE HELP ME OUT WITH THIS QUEATION The city of McLean is doing construction on their local baseball stadium to increase guest capacity. When the stadium was built in 1971, it had 2000 seats. Several years ago, they increased the number of seats by 40%. Now, this renovation is taking the current size of the stadium and upping the capacity by 45%.After this renovation, what is the guest capacity of McLean's baseball stadium? A particular brand of toilet paper is offered at two stores ANWSER ASAP!!!100 pointsAt a national park, a trail rises no more than 3 feet above sea level. The inequality shown represents x , the height in feet of the trail. x3 Which number line shows the possible values of x ? 2.if a material is defined at both a distribution center and a production plant, what will be the procurement type in the mrp2 data view for each? write an essay that dscusses how the colonies came to believe they should declare independence What would happen If I explored two oceanic plates at a convergent boundary?earthquakesfaultsocean formationmountainsvolcanoesisland chainsseafloor spreading The Haverstown theater club is selling tickets for dinner and a show. They already have props and costumes, but they spend $142.50 on food. If they charge $9.50 for each ticket, how many tickets do they need to sell to cover their costs? PLEASE HELP ME!!!!(Will get points) A toy company is designing a new cylindrical container for their interlocking block product. The height h (in inches) and the radius r (in inches) are related by the inequality h> 0.3r ^2. The toy company has the following additional constraints. The height must be no more than 15 inches greater than the radius. The area of the base must be at least 36pi square inches. Which of the following is a possible set of dimensions for the container?A) radius., height 21 inchesB) radius 8 in., height 21 in C) Radius., 7 inches., height 23 inD) radius., 9 inches., height 18 inches I NEED THIS IN LIKE 30 MINUTES PLEASE Write a C++ program to find and print the first perfect square (i*i) whose last two digits are both odd. please try to explain every step by writing comments. the internet has had an enormous impact on business strategies. among these impacts, the internet has decreased which of the following? When we ask why a particular decision was made by a court, we are expressing which of the following?A. Respect for the courtB. FactsC. Statutory lawD. Legal positivism Pls help, my head is spinning in circles