How many numbers must be selected from the set left curly bracket 1 comma 2 comma 3 comma 4 comma 5 comma 6 comma 7 comma 8 comma 9 comma 10 right curly bracket in order to guarantee that at least one pair adds up to 11

Answers

Answer 1

Answer:

6 numbers

Step-by-step explanation:

Given

[tex]x = \{1,2,3,4,5,6,7,8,9,10\}[/tex]

Required

Pairs that add up to 11

The pairs are:

[tex]x = \{\{1,10\},\{2,9\},\{3,8\},\{4,7\},\{5,6\}\}[/tex]

In the above set, we have:

[tex]n(x) =5[/tex]

Using pigeonhole principle

This principle implies that, there is at least 1 more pair.

Hence, the numbers that must be selected to guarantee the required sum of 11 is:

[tex]n= 5+1[/tex] --- The 1 represents (at least 1 more)

[tex]n=6[/tex]


Related Questions

help me please i will give 50 pts and a brainiest

Answers

Answer:

14 Feet

Step-by-step explanation:

Answer:

14 is the answer

140/10=14

hope this helps

have a good day  :)

Step-by-step explanation:

What do I need to do

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Step-by-step explanation:

.....

Answer:

The answer is 4.

Step-by-step explanation:

All you have to do is count the dots between the library and Gabes house.

Please answer, what is x?

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Answer:

ths is the real answer 您同性恋您同性恋您同性恋您同性恋您同性恋

您同性恋您同性恋

Step-by-step explanation:

Please help me!!!! Will give the brainliest!

Answers

Answer: 1 graph A

2 graph B

3 graph C

4 the number of sales a month

Step-by-step explanation:

Choose a method you prefer to solve for a system of linear equations.
x+y=0
x-y= -16

Answers

Answer:

Eliminating

Step-by-step explanation:

The given equations are ,

x+y=0x-y= -16

Here I would prefer to use Elimination Method. Since there is negative y and positive y in the equations . So we can eliminate y easily and then we can find x. Also , let's solve ,

On addition :-

→ 2x = -16

→ x = -16/2

x = -8

Hence the most preferred method is " Elimination Method ".

reduce to hours and minutes 66000 seconds​

Answers

Answer:

18.333333 hours

Step-by-step explanation:

1099.99998 mintunes

Help help help I need help ASAP

Answers

Answer: 54.4

Step-by-step explanation:

Letter G is plotted in which Quadrant?
A . Quadrant IV
B.Quadrant II
c. Quadrant III
D. Quadrant I

Answers

Answer:

please send the picture of the question plz!

Step-by-step explanation:

-7 2/3 + (-5 1/2) + 8 3/4

in faction

Answers

Answer:

= -4.41666666667

Step-by-step explanation:

Answer:

    [tex]-7\frac{2}{3} + -5\frac{1}{2} +8\frac{3}{4}\\\\\frac{-23}{3} -\frac{11}{2} + \frac{35}{4}\\\\[/tex]

LCM (3, 2 ,4) = 12

   [tex]\frac{(-23*4) -(11*6)+(35*3)}{12} = \frac{-92-66+105}{12} =\frac{-53}{12} = -4\frac{5}{12}[/tex]

1/2x + 3/2 (x + 1) - 1/4 = 5

Answers

The answer to your problem is x= 15/8 as decimal form it’s 1.875

Use proportions to solve the following problem. A recipe calls for 4 eggs and 3 cups of milk. To prepare for a larger number of guests, a cook uses 22 eggs. How many cups of milk are needed?

Answers

Answer:

16.5 cups of milk are needed.

Step-by-step explanation:

i hate you for reporting my answer.

Rationalize the denominator and simplify

Answers

The answer is number A

Simplify the following radical expression square root of 20

Answers

Answer:

2 radical 5

Step-by-step explanation:

i am smart

Answer:

[tex]\sqrt{20} =2\sqrt{5}[/tex]

Step-by-step explanation:

Given:

[tex]\sqrt{20}[/tex]

Step 1: Factor out the biggest square number:

[tex]\sqrt{4}\sqrt{5}[/tex]

Step 2: Simplify:

[tex]2\sqrt{5}[/tex]

Therefore, [tex]\sqrt{20} =2\sqrt{5}[/tex]

PLEASE HELP, I WILL GOVE BRAINLIEST. Katrina's cat weighed 12 3/4 pounds at its last visit to the veterinarianSince that visit, the cat has gained 5/8 pound. How much does Katrina's cat weigh now? Show your work

Answers

Answer

13 1/2 pounds

Step-by-step explanation:

welcome ;)

Answer:

the cat now weighs 13 3/8 LBS

Step-by-step explanation:

convert the fractions so you can add them together,  

mult 3/4 by two to get common denominators

6/8 + 5/8

the cat gained 11/8 pounds. (1 3/8)

since the numerator is larger we add the mixed number to the 12 pounds.

13 3/8 pounds.

Question- A bakery sells 5 apple muffin for every 2 brand muffins sold. Which table shows this ratio?
No links or you get reported
is my answer correct?​

Answers

Answer:

The one on the bottom left corner. I'm not sure what letter that is!  

Hope this helped :)

Step-by-step explanation:

Choose all the numbers that make 5 × □ < 5 true.
A- 1 1/4 B-3/8 C-10/11 D-4 4/5 E- 4/3 F- 1/4

Answers

Answer:

B, C, F

Step-by-step explanation:

It's asking 5 x (what?) is less than 5.

It has to be less than one to be a correct answer then.

What is the volume of this composite solid?
4 m
2 m
7 m
2 m
2 m
O A. 58 cubic meters
O B. 64 cubic meters
O C. 78 cubic meters
O D. 62 cubic meters

Answers

Answer:

64

Step-by-step explanation:

A P E X

Kathy is building a bed for her dollhouse. She used her real bed as a guide for how to create the dollhouse bed. Her bed is 36 inches wide and 60 inches long. If she wants to scale this down by 1/10, what would be the dimensions of the dollhouse bed? Explain how you got your answer.
*Use the term SCALE FACTOR in your explanation.

Answers

The dimensions of the dollhouse bed are 3.6 inches × 6 inches. By dividing 10 by each dimension, the dollhouse bed's dimensions may be found.

What exactly is dilation?

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

The dimension of real bad;

a = 36 inches

L = 60 inches

Down scale factor = 1/10

The dimensions of the dollhouse bed are obtained by dividing 10 in each dimension;

a'=36/10

a'=3.6 inches

L'=60/10

L'=6 inches

Hence the dimensions of the dollhouse bed are 3.6 inches × 6 inches.

To learn more about dilation, refer to

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A factory employs 18 women to sew 540 dresses. The women take 6 weeks to do the job. If 12
women had been employed instead, how many weeks would it have taken them to sew the 540
dresses?

Answers

9514 1404 393

Answer:

  9 weeks

Step-by-step explanation:

In problems of this nature, the usual assumption is that the time required is proportional to the work product and inversely proportional to the number of people doing the job. Here, there is no change in the amount of work, but the number of people is reduced by a factor of 12/18 = 2/3.

So, the amount of time required is expected to increase by a factor of 1/(2/3) = 3/2.

  (6 weeks)×(3/2) = 9 weeks

It would have taken 9 weeks to sew the 540 dresses.

The new candy store packed 3 ponds of bubblegum in each of their bags. How many bags would Sam need to bu if he wanted 288 ounces of bubblegum?

Answers

Answer:

NYS Math Module 3 Grade 4 Lesson 32 Concept Development

Problem 1

We all know there are 7 days in a week. How many weeks are in 259 days?

Problem 2

Everyone is given the same number of colored pencils in art class. If there are 249 colored pencils and 8 students, how many pencils does each student receive?

Problem 3

Mr. Hughes has 155 meters of volleyball netting. How many nets can he make if each court requires 9 meters of netting?

Step-by-step explanation:

Answer:

6 bags

Step-by-step explanation:

228 ounces = 18 pounds

18 pounds ÷ 3 pounds

6 bags

-------------------------------------------------------------------------------------------------------------

We all know there are 7 days in a week. How many weeks are in 259 days?

37 weeks

[tex]\frac{1}{7} :\frac{y}{259}[/tex]

y · 7 = 1 · 259

7y = 259

7y ÷ 7 = 259 ÷ 7

y = 37

Everyone is given the same number of colored pencils in art class. If there are 249 colored pencils and 8 students, how many pencils does each student receive?

31 color pencils each and 1 extra pencil

249 ÷ 8 =

31.125 colored pencils each

This rounds to 31 color pencils and 1 extra pencil.

Mr. Hughes has 155 meters of volleyball netting. How many nets can he make if each court requires 9 meters of netting?

7 courts and he will be left with 2 meters of netting

155 ÷ 9

17 and 2/9 volleyball courts

17 courts and he is left with 2 meters of netting.

Two people meet in the purple room on the fourth floor of a building. On departure, one person travels West 20 feet, South 12 feet, and Down 12 feet. The other person travels North 20 feet, East 10 feet, and Up 12 feet. How far apart are the two people? Round to the nearest tenth.

Answers

Answer:

50 feet

Step-by-step explanation:

Set up a 3-dimensional coordinate system (see the attached image).

This setup shows an axis that runs North-South (South is negative, North is positive), an axis that runs East-West (East is positive, West is negative), and an axis that runs Up-Down (Up is positive, Down is negative).

The two points in question are then:

First person's location (12, -20, -12), and the second person's location is (-20, 10, 12).

The distance between two points  [tex]\left( x_1,\,y_1,\,z_1\right)[/tex]  and  [tex]\left( x_2,\,y_2,\,z_2\right)[/tex] is

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2[/tex]

[tex]d=\sqrt{(-20-12)^2+(10-(-20))^2+(12-(-12))^2}\\\\d=\sqrt{(-32)^2+30^2+24^2}\\\\d=\sqrt{2500}\\\\d=50[/tex]

A company sells cereal in two different-sized boxes: a 17-ounce box for $2.89, and a 24-ounce box for $3.29. How do the unit prices of the two boxes compare?

Answers

the 17 ounce cereal is $0.17 per ounce and the 24 ounce cereal is $0.13 per ounce.

Which value for x makes the sentence true?

Answers

D!

One clue to this (if you don’t just multiply 0.22 by 2.95) Is that this is the only value above 1. since the ending equation has a number larger than the original, this is a give away! Hope this helps :)

PLEASE HELP BRO IM FAILING MATH

Answers

Answer:

Step-by-step explanation:

we have several angles that have the same vertex and so they are congruent

1) e = 35 degrees because the opp angle has this measure

2) d = 109 degrees for the reason above

3) for find f we have to notice that the sum of the three angles (if you look at the vertical line you can notice that it is a straight line, so describes two angles whose measures are 180 degrees)

f = 180 - (35 + 109)

f = 180 - 144 = 36 degrees

A company is making aid badges with personal ID codes on them for each employee. The ID code will consist of two letters followed by 2 digits. Using this scenario, how many possible ID codes are there?

Answers

Answer:

67, 600

Step-by-step explanation:

There are 26 alphabet and 10 digits then the number of the possible ID codes will be 67600.

What are permutation and combination?

A permutation is an act of arranging the objects or elements in order. Combinations are the way of selecting objects or elements from a group of objects or collections, in such a way the order of the objects does not matter.

A company is making aid badges with personal ID codes on them for each employee.

The ID code will consist of two letters followed by 2 digits.

Then the number of ways ID codes are there will be

[tex]\rightarrow 26 \times 26\times 10\times 10\\\\\rightarrow 67600[/tex]

More about the permutation and the combination link is given below.

https://brainly.com/question/11732255

Find the missing angle.

Answers

Answer:

V=51, U=90 W= 39

Step-by-step explanation:

V= 51 Degrees (has told in the question)

U= 90 Degrees (Its A Right Angel Triangle, And Right Angle Is Always 90 Degrees)

W= 39 Degrees (Sum Of All Sides Of A Triangle = 180 Degrees

                           51 + 90 + W = 180

                           141 + W = 180

                           W = 180 - 141

                           W = 39 )

Hope It Helps,

Thanks

Start with 180 degrees and subtract the angles you are given
180-90-51
39

A study of women’s weights found that a randomly selected sample of 234 women had a mean weight of 157.3 lb. Assuming that the population standard deviation is 15.6 lb., construct a 95% confidence interval estimate of the mean weight of all women.

Answers

Answer:

(155.301 ; 159.299)

Step-by-step explanation:

Xbar = 157.3

Sample size, n = 234

Population standard deviation, σ = 15.6

The confidence interval :

Xbar ± standard Error

Standard Error = Zcritical * σ/√n

Zcritical at 95% = 1.96

Standard Error = 1.96 * (15.6/√234) = 1.999

Lower boundary : 157.3 - 1.999 = 155.301

Upper boundary : 157.3 + 1.999 = 159.299

(155.301 ; 159.299)

A guy wire connects the top of an antenna to a point on level ground at 15ft from the base of the antenna. The angle of elevation formed by this wire is 79. What is the length of the wire and the height of the antenna?

Answers

Answer:

VEFG4KLKB

Step-by-step explanation:

BLB

The length of the guy wire is approximately 74.7 feet, and the height of the antenna is approximately 72.2 feet.

Here, we have,

To find the length of the guy wire and the height of the antenna, we can use trigonometry and the concept of right triangles.

In this scenario, the guy wire represents the hypotenuse of a right triangle, and the height of the antenna represents one of the legs of the triangle.

The angle of elevation formed by the guy wire is given as 79 degrees.

Let's denote the length of the guy wire as h and the height of the antenna as a.

Using the trigonometric function sine (sin), we can relate the angle of elevation and the sides of the triangle:

sin(angle) = opposite/hypotenuse.

In this case, the opposite side is the height of the antenna (a), and the hypotenuse is the length of the guy wire (h).

sin(79°) = a/h.

To solve for h, we can rearrange the equation as:

h = a / sin(79°).

We also have another relationship between the sides of the triangle.

The base of the right triangle is given as 15 feet, and the height of the antenna is a.

Therefore, using the Pythagorean theorem, we have:

h² = a² + 15².

Now we can substitute the expression for h from the first equation into the second equation:

(a / sin(79°))² = a² + 15².

Expanding and simplifying, we get:

a² / sin²(79°) = a² + 225.

Multiplying both sides of the equation by sin²(79°), we have:

a² = sin²(79°) * (a² + 225).

Expanding again, we get:

a² = sin²(79°) * a² + 225 * sin²(79°).

Rearranging the equation, we have:

a² - sin²(79°) * a² = 225 * sin²(79°).

Factoring out a², we get:

(1 - sin²(79°)) * a² = 225 * sin²(79°).

Using the trigonometric identity sin²(θ) + cos²(θ) = 1,

we know that cos²(θ) = 1 - sin²(θ).

Therefore:

cos²(79°) * a² = 225 * sin²(79°).

Taking the square root of both sides, we have:

cos(79°) * a = 15 * sin(79°).

Simplifying, we get:

a = (15 * sin(79°)) / cos(79°).

Using a calculator or software, we find:

a ≈ 72.2 feet (rounded to one decimal place).

Now, to find the length of the guy wire (h), we can substitute the value of a into the first equation:

h = a / sin(79°).

Using a calculator or software, we find:

h ≈ 74.7 feet (rounded to one decimal place).

Therefore, the length of the guy wire is approximately 74.7 feet, and the height of the antenna is approximately 72.2 feet.

To learn more trigonometry click:

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HELP ME PLEASE LAWS OF SINES !! IXL !!

Answers

Answer:

f = 19.0

Step-by-step explanation:

By applying sine rule in the triangle given in the figure,

By applying triangle sum theorem,

m∠F + m∠G + m∠H = 180°

110° + m∠G + 40° = 180°

m∠G + 150° = 180°

m∠G = 30°

[tex]\frac{sin(\angle F)}{GH}= \frac{sin(\angle G)}{HF}=\frac{sin(\angle H)}{FG}[/tex]

[tex]\frac{sin(\angle 110^0)}{f}= \frac{sin(\angle 30^0)}{g}=\frac{sin(\angle 40^0)}{13}[/tex]

[tex]\frac{sin(\angle 110^0)}{f}= \frac{sin(\angle 40^0)}{13}[/tex]

[tex]\frac{0.9397}{f}= \frac{0.6428}{13}[/tex]

f = [tex]\frac{13\times 0.9397}{0.6428}[/tex]

f = 19.0

In ΔEFG, f = 37 inches, g = 92 inches and ∠E=97°. Find the area of ΔEFG, to the nearest square inch.

Answers

Answer:1689

Step-by-step explanation:

Delta Math

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