10. Suppose that we have 50 balls labeled 0 through 49 in a bucket. What is the minimum number of balls that we need to draw to ensure that we get at least 3 balls which end with the same digit

Answers

Answer 1

Answer:

21 drawings

Step-by-step explanation:

The number labelings are 0 - 49

The minimum set that could be the same number is the labeling 0, 10 , 20

It could also be 1, 11, 21 or even 2,12,22

In all the cases, we can be sure that we might have three labelings ending with the same number when we pull our ball labeled 20

That makes a total of 21 drawings

Answer 2

Following are the response to the given question:

Pigeon Hole's Principle can also be used to tackle this problem. Assuming that we already have labels ranging from [tex]0\ to\ 49.[/tex]

We possess five balls which conclude with the number 0 [tex]\text{(ball \ 0, ball\ 10, ball\ 20, ball\ 30, and\ ball\ 40)}.[/tex] We possess five balls which conclude with the digit 1[tex]\bold{(ball\ 1, ball\ 11, ball\ 21, ball\ 31, ball\ 41)}.[/tex] .....I have five balls that end in the number 9 [tex]\text{(ball\ 9, ball\ 19, ball\ 29, ball\ 39, and ball\ 49)}.[/tex]

Each digit ending is represented by five balls.

In the pigeonhole principle, it [tex]kn+1[/tex] objects [tex](k \geq 1)[/tex] are distributed among n boxes, one of the boxes will contain at least [tex]k+1[/tex] objects. Assume that you draw a ball and place it in a box labeled with its last digit. So there will be n = 10 boxes.

Box 0: we place balls that end in the digit 0. Box 1: we place balls that end in the digit 1. .....Box 9 is where we put balls that end in the number 9.

According to the pigeon hole concept, you need to draw [tex]kn+1[/tex] balls to assure that at least one of the boxes includes [tex]k+1[/tex] objects. Because [tex]k+1 = 3,[/tex] we require three objects in at least one box (we need three balls ending with the same digit).

[tex]k + 1 = 3 \\\\k =2[/tex]

Therefore, we have to draw [tex]kn+1[/tex] balls, [tex]k = 2, n = 10[/tex], at least[tex]21\ balls[/tex] must be drawn to ensure that at least three of them have the same 1 digit.

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Related Questions

Which of the following lists the numbers shown below in order from least to
greatest? Please hurry

Answers

-63/8, -7.8, 4 √5, √51

9(r) = -1 - 77
Evaluate function

Answers

it would be 9(r) = -78

Which measurement statement is correct?

Answers

Answer:

What do you need help with?

!!!!HELPPPPPPPP ASAP!!!!

Answers

Answer:

first one is -1

second one is 0

third one is  6

last one is 2

Step-by-step explanation:

Can someone explain the snake method, I don't understand how to do it

Answers

Answer:

x ∈ [−2; 1] ∪ 3.5

Step-by-step explanation:

Given

Inequality: (x-1)(x+2)(2x-7)≤0

Solution:

If we solve the corresponding equation (x-1)(x+2)(2x-7)²= 0, we get roots

x =  -2, 1, 3.5

We need to consider the following 4 intervals:

(−∞; −2), [−2; 1], (1; 3.5), (3.5; ∞)

1st interval (−∞; −2)

The expression (x-1)(x+2)(2x-7)² is positive as two of the multiples are negative and one is always positive (square number), and therefore  does not satisfy the inequality.

2nd interval  [−2; 1]

The expression is negative as only one of the multiples is negative, and therefore the interval (−1; 2) satisfies the inequality.

3rd interval (1; 3.5)

The expression is positive as all the multiples are positive. Therefore, the interval (1; 3.5) also does not satisfy the inequality.

4th interval

The expression is positive as above, and therefore also does not satisfy the inequality.  

So, the answer to the inequality is:

x ∈ [−2; 1] ∪ 3.5

Answer the question below, and then fill in the blanks if necessary.
Can the distributive property be used to rewrite
8 X (10 – 3)?
Yes
No
If yes, fill in the blanks below.
8 x (10 - 3) = ( , ) - ( , )

Answers

Answer:

Yes

80-24

Step-by-step explanation:

Using distributive property, multiply 8 by 10 and 8 by negative 3.

Marking Braniest!!! What is 100÷4÷4÷4

Answers

Answer:

1.5625

Step-by-step explanation:

100 divided by 4 is 25. 25 divided by 4 is 6.25 and 6.25 divided by 4 is 1.5625

Answer:

1.5625

This is what I think is the answer

What is the midpoint between 10,-3 and -4,-9

Answers

Answer:

(3,3)

Step-by-step explanation:

Use the midpoint formula to find your answer. The formula is [tex](x_{1} +x_{2} /2; y_{1} +y_{2} /2)[/tex].

If that equation looks funny then let me explain. You need to add 10 and -4 together, then divide it by 2. You also need to add -3 and -9, then divide that by 2.

pwease help!! i need help to put the answers in the box c:

Answers

Answer:

6 months is: 15675

2 months is: 5172.75

1 month is: 2586.37

15 months is: 38795.62

the missing number is: 12 months

Step-by-step explanation:

Why does the series not exist?

Answers

Step-by-step explanation:

(7n − 5) / (2n + 5) approaches 7/2 as n approaches infinity.  However, this is an alternating series.  So the function is fluctuating between -7/2 and +7/2.  So the limit does not exist.

A student states that the constant of proportionality is 2.5 since 10 - 7.5 = 2.5.

I NEED HELP FOR MY TEST!

Answers

I cannot see the table. But if I could that would be helpful.

But, if you were to look at the table see if the numbers are increasing or decreasing for the y column. Once you figure this out, find out how much the numbers are increasing/decreasing by and that should be the answer for the constant of proportionality. If it is decreasing, it would be a negative number. If it is increasing, it would be a positive number.

Imagining that she’s taking a summer job working at a local entertainment complex your hourly wage is six dollars you will work 40 hours per week and be paid every other week for a total of 16 weeks use the figure provided estimate your gross pay for the summer and each pay period

Answers

6*40 for how much u make a week then divide 16 by 2 for every other week. Then multiply your sum for 6*40 by 16/2

So you would make $1,920

Solve the problem by entering and solving an equation.
A rectangular picture frame has a perimeter of 52 inches. The height of the frame is 12 inches. What is the width of the frame?

Answers

Given : A rectangular picture frame has a perimeter of 52 inches. The height of the frame is 12 inches.

To Find : The width of the frame .

Solution : Let us take the width of the frame be x . So , we know the formula to find the perimeter of rectangle as ;

[tex]\boxed{\red{\bf Perimeter_{rectangle}=2(l+b)}}[/tex]

Where , l is the length of the rectangle and b is the breadth of the rectangle .

⇒ Perimeter = 2 ( l + b ) .

⇒ 52 in. = 2 ( 12 + x ) in.

⇒ 52 in.= 24in. + 2x .

⇒ 2x =( 52 - 24 ) in

⇒ 2x = 28 in.

⇒ x = 28/2 in.

⇒ x = 14 in.

Hence the width of the rectangle is 14 inches.


Look at the number below.
6642
How is the value of the digit in the thousands place related to the value of the digit in the hundreds place?
A It is six times greater.
B
It is ten times greater.
С
It is one hundred times greater
The values of the digits are the same.

Answers

Answer:

Option (B)

Step-by-step explanation:

Given number is 6642.

Number at ones place = 2

Number at tens place = 4

Number at hundredth place = 6

Number at thousand place = 6

Value of the number at tens place = 4 × 10 = 40

Value of the number at hundreds place = 6 × 100 = 600

Value of the number at thousand place = 6 × 1000 = 6000

Number at thousand place = 10 × (Number at hundreds place)

Therefore, Option (B) will be the answer.

HELP ME ASAP!!! I WILL MARK BRAINLIEST!!

Answers

Its the last one Brand A is more expensive and is 2$ and Brand B is $1.5

Answer:

Brand A ($2) is more expensive than Brand B ($1.50)  (see below)

Step-by-step explanation:

First, you will have to find the slopes of both lines. Slope is y/x, which is the cost/meter or cost per meter.

Using the slope formula:

          y2 — y1

m  =   ---------------

           x2 — x1

Plug in any two points from both lines:

          y2 — y1

m  =   ---------------  = graph 1 (0, 0), (1,2)

           x2 — x1

            2 — 0

m  =   ---------------

             1 — 0

                2

m  =   ---------------  = $2/m

                1

_______graph 2_______

          y2 — y1

m  =   ---------------  = graph 2 (0, 0), (4, 6)

           x2 — x1

            6 — 0

m  =   ---------------

            4 — 0

                6                  3

m  =   ---------------  = -----------  = $3/2 m

                4                  2

Because you are unable to have an exact cost per meter of Brand B, you can use a ratio:

$3  =  $x

2m =  1m

Cross multiply:

3 (1) = 2x

3 = 2x

x = (3 ÷ 2)

x = 1.5

So Brand B is $1.50 per meter while Brand A is $2.00 per meter. Brand B is cheaper.

Which order pairs are solutions to the equation 4x+2y=4

Answers

Answer:

Slope=2.000/4.000

​ −2.000x−intercept= 22

​  =1y−intercept= 12

=2.00000

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    4*x+2*y-(4)=0

 Pull out like factors :

  4x + 2y - 4  =   2 • (2x + y - 2)

Solve :    2   =  0

This equation has no solution.

A non-zero constant never equals zero.

 Solve   2x+y-2  = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  2x+y-2  = 0 and calculate its properties

Notice that when x = 0 the value of y is 2/1 so this line "cuts" the y axis at y= 2.00000

 y-intercept = 2/1  =  2.00000

When y = 0 the value of x is 1/1 Our line therefore "cuts" the x axis at x= 1.00000

 x-intercept = 2/2  =  1

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 2.000 and for x=2.000, the value of y is -2.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -2.000 - 2.000 = -4.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

   Slope     = -4.000/2.000 = -2.000

y=5x-7
-3-2x=12 for x

Answers

Answer:

4 2/3

lmk if this is correct or not

Step-by-step explanation:

5x-7-3-2x=12

5x-4-2x=12

3x-2=12

3x=14

14/3

x=4.666 or 4 and 2/3

I NEED HELP HERE ASAP, I’m giving brainliest to the right one. I forgot how to solve this:/

Answers

Answer:

28 weeks

Step-by-step explanation:

It says that $42 was 1/3 of her total. So you multiply $42 by 3 and you get $126. You now divide $126 by her weekly allowance, $4.5, and the answer is 28.

1. $42 x 3 = $126

2. $126/$4.5 = 28

3. The answer is Sharon has been saving her allowance for 28 weeks.

Hope this helps!

-Jerc

Answer:

She has been saving her money up for 28 weeks.

Step-by-step explanation:

1. If 42 is 1/3 of her money, then you would multiply 42 by 3 to get the full 3/3 so: 423=126

2. Next, you would divide $126 by $4.50 because that is the total amount of money divided by how much she saved up each week, so: 126/4.5=28 and that gives us the answer which is 28.

The product of the number g and the opposite of 7 is equal to k.
Change to an algebraic expression

Answers

answer: -7g = k

explanation: -7 is the opposite of 7
g(-7) = k. Hope this helps. You don’t need brackets by the way you can just say -7g or g times -7 if you want. Hope this helps and a Brainliest would be appreciated

It is well known that generally a female's growth spurt occurs before a male's; therefore the
female's height data will likely be higher than the male's data.
Discuss this idea in a well-structured paragraph. Use your calculations of the mean, median, mode
and range of the data to support your decision.

Answers

Answer:

Most girls start their sexual development between the ages of 8 and 13 (the average age is 12), and have a growth spurt between the ages of 10 and 14.

Most boys start developing sexually between the ages of 10 and 13, and continue to grow until they're around 16.

this my help

1/2 times 4 /please answer for me :)

Answers

Answer:

2

Step-by-step explanation:

1/2*4 = 2

hope this helps

The various steps of a food chain or web are known as ______. These explain where an organism sits on an ecological pyramid.

Answers

Answer:

Trophic Level

Step-by-step explanation:

The first trophic level is of producers (green plants). The second trophic level is of primary consumers also known as herbivores, third of carnivores, or secondary consumers, fourth is of tertiary consumers also known as top carnivores.

**100** The given data represent the total compensation for 10 randomly selected CEOs and their​ company's stock performance in 2009. Analysis of this data reveals a correlation coefficient of r = 0.1887. What would be the predicted stock return for a company whose CEO made​ $15 million? What would be the predicted stock return for a company whose CEO made​ $25 million?

Answers

Answer:

Your answer is: Look Below

Step-by-step explanation:

Hope this helped : )

The equation P = 6s represents the perimeter P of a regular hexagon with side length s. What is the perimeter of a regular hexagon with side length 7 m?​

Answers

Answer: 42

Step-by-step explanation:

The required perimeter of the regular hexagon is 42 m.

Given that,
The equation P = 6s represents the perimeter P of a regular hexagon with side length s. What is the perimeter of a regular hexagon with side length 7 m is to be determined.

What is the perimeter?

Perimeter is the measure of the figure on its circumference.

here,
the perimeter of the regular hexagon is given,
P = 6s
Put s = 7
P = 6(7)
p = 42

Thus, the required perimeter of the regular hexagon is 42 m.

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find the slope (5,4) (5,9)

Answers

Answer:

undefined

Step-by-step explanation:

To find the slope between two points, we can use the slope formula. The slope formula is:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

where m is the slope and (x₁, y₁) and (x₂, y₂) are two points.

By plugging in (5, 4) and (5, 9) for (x₁, y₁) and (x₂, y₂) respectively, we get:

[tex]m=\frac{9-4}{5-5}=\frac{5}{0}[/tex]

Note, we cannot divide by zero. By using the slope formula, we get that the slope is undefined.

I hope this helps. Happy studying.

I don’t understand what this means

Answers

Answer:

This means that if you have that amount of those and you do whatever the rest of the question is.

Step-by-step explanation:

Answer:

120 different ways

Step-by-step explanation:

So Fundamental Counting Principle helps understand probability. So for this question, they are asking how many different ways there are.

To do that, we have to split into sets.

Set A: 4 Theme Parks

Set B: 6 Passes

Set C: 5 Food Options

Now we have to multiply the sets.

4 x 6 x 5 = 120

Therefore, the answer is 120 different ways.

Given the function h(x) = x2 – 7x + 8, determine the average rate of change of
the function over the interval 2 < x < 10.

Answers

The average rate of change of the function over the interval 2 < x < 10 is 5

How to determine the average rate?

The function is given as:

h(x) = x^2 - 7x + 8

Calculate h(2) and h(10)

h(2) = 2^2 - 7 * 2 + 8

h(2) = -2

h(10) = 10^2 - 7 * 10 + 8

h(10) = 38

The average rate is then calculated as:

Rate = (h(10) - h(2))/(10 - 2)

This gives

Rate = (38 + 2)/(10 - 2)

Evaluate

Rate = 5

Hence, the average rate of change of the function over the interval 2 < x < 10 is 5

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12-14 plzzz if u see the picture

Answers

Answer:

I can't see it very well sorry

MO bisects ∠LMN, m∠NMO =6x-20,and 2x+36. Solve for x and find m∠LMO

Answers

Answer:

fwe

Step-by-step explanation:

HELP PLEASE PLEASE 50 PTS
The polynomial is missing the coefficient of the third and last terms.
729x3 – 1,458x2y + ____xy2 – ____y3
If the polynomial is factorable using the binomial theorem, what is the coefficient of xy2?
324
648
972
1,944

Answers

Answer:

C

Step-by-step explanation:

Ed2021

The missing coefficient of xy² is 972, option C is correct.

What is Polynomial?

Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables

The given polynomial is 729x³ – 1,458x²y + ____xy² – ____y³

To find the missing coefficients, we can use the fact that the polynomial is factorable using the binomial theorem.

According to the binomial theorem, the expansion of (a + b)^3 is:

(a + b)³ = a³ + 3a²b + 3ab² + b³

Comparing this with the given polynomial, we can see that a = 9x and b = -2y.

Substituting these values in the binomial theorem, we get:

(9x - 2y)³ = (9x)³ + 3(9x)²(-2y) + 3(9x)(-2y)² + (-2y)³

Simplifying this expression, we get:

729x³ - 1,458x²y + 972xy² - 8y³

Therefore, the missing coefficient of xy² is 972, option C is correct.

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