Two containers hold several balls. Once a second, one of the balls is chosen at random and switched to the other container. After a long time has passed, you record the number of balls in each container every second. In 10,000 s, you find 80 times when all the balls were in one container (either one) and the other container was empty.

Required:
a. How many balls are there?
b. What is the most likely number of balls to be found in one of the containers?

Answers

Answer 1

Answer:

(a) 8 balls

(b) 4 balls

Step-by-step explanation:

Let

[tex]N \to[/tex] Number of balls

For a box, the probability that there are N balls in it is:

[tex]Pr = 0.5^N[/tex]

For 2 boxes, it is:

[tex]Pr = 2 * 0.5^N[/tex]

From the question, we have:

[tex]\frac{80}{10000} \to[/tex] Favorable outcome

To solve for N, we have:

[tex]2 * 0.5^N = \frac{80}{10000}[/tex]

[tex]2 * 0.5^N = 0.008[/tex]

Divide both sides by 2

[tex]0.5^N = 0.004[/tex]

Take log of both sides

[tex]\log(0.5^N) = \log(0.004)[/tex]

Apply law of logarithm

[tex]N\log(0.5) = \log(0.004)[/tex]

Make N the subject

[tex]N = \frac{\log(0.004)}{\log(0.5)}[/tex]

[tex]N =7.966[/tex]

Approximate

[tex]N = 8[/tex]

Solving (b): Balls in one of the two boxes.

Here, we assume that each ball will have almost the same number of balls at a given instance;

Hence, we have:

[tex]Balls \approx \frac{N}{2}[/tex]

[tex]Balls \approx \frac{8}{2}[/tex]

[tex]Balls \approx 4[/tex]

4 balls in each box


Related Questions

A recipe for oatmeal raisin cookies requires 2 eggs for every dozen cookies . Which equation shows the relationship between eggs ( e ) and dozen cookies ( c ) ?

Answers

Answer:

2e = c

Step-by-step explanation:

Let :

Egg = e

Cookies = c

2 eggs for every 1 dozen of cookies

This gives the Mathematical expression :

2 eggs = 1 c

2e = c

Answer this question please ASAP!!

Answers

A or the first answer shown

Answer:

No it is not close to half of the data below the mean and half the data above the mean

50 POINTS !!


PLEASE HELP !! ILL GIVE BRAINLIEST TO THE RIGHT ANSWERS.

Answers

Answer:

20?

Step-by-step explanation:

Answer: 8.9

Step-by-step explanation:

To find the hypotenuse, use the formula [tex]a^2 + b^2 = c^2[/tex]

The two "legs" are a and b (it doesn't matter which leg is a and which leg is b), but the most important thing is that the hypotenuse is c.

So, we now know that we have to solve for c. To solve for c, substitute the values shown in the image for a and b.

[tex]a^2 + b^2 = c^2[/tex]

[tex]8^2+4^2=c^2[/tex]

[tex]16 + 64 = c^2[/tex]

[tex]80 = c^2[/tex]

[tex]\sqrt{80}[/tex] = c

Use a calculator, and after rounding, you get 8.9

Simplify 3x^(1/2)*5x^(2/5)

Answers

Answer:

= 15x^9/10

Step-by-step explanation:

Multiply the numbers: 3 . 5 = 15

= 15x^1/2x2/5

Apply exponent rule: a^b . A^c = a^b + c

= 15x^1/2+2/5

1/2 + 2/5 = 9/10

= 15x^9/10

In each of the​ following, find all real numbers x that satisfy the given equation. If none satisfy the​ equation, then state the answer as​ "None."

(25/4)^3x = 32/3125​

Answers

Answer:

The solution is [tex]x = -\frac{5}{6}[/tex]

Step-by-step explanation:

We solve this question using exponential properties.

We have that:

[tex](\frac{25}{4})^{3x} = \frac{32}{3125}[/tex]

Simplifying:

[tex](\frac{5^2}{2^2})^{3x} = \frac{2^5}{5^5}[/tex]

[tex]([\frac{5}{2}]^{2})^{3x} = (\frac{2}{5})^{5}[/tex]

[tex](\frac{5}{2})^{6x} = (\frac{2}{5})^{5}[/tex]

Changing the numerator and denominator in the right side:

[tex](\frac{5}{2})^{6x} = (\frac{5}{2})^{-5}[/tex]

Since both bases are equal:

[tex]6x = -5[/tex]

[tex]x = -\frac{5}{6}[/tex]

The solution is [tex]x = -\frac{5}{6}[/tex]






"I think of a number, take away 1 and multiply the result by 3."​

Answers

Answer:

I got 6.

Step-by-step explanation:

I picked my number to be 3. I took away 1 to make it 2. I then multiplied 2 by 3, to get 6.

I thinks it 6
I took it before I got a good grade on it it was a 6 for me

What is the answer?

Answers

Answer:

x^2(x-5)

Step-by-step explanation:

f(x)=x-5

g(x)=x^2

g(f(x)=?

x^2(f(x)=?

x^2(x-5)

If this helps please mark as brainliest

9514 1404 393

Answer:

  D.  (x -5)²

Step-by-step explanation:

Replace the variable with the function argument.

  G(F(x)) = G(x -5) = (x -5)² . . . . . matches choice D

Which correctly describes a cross section of the square pyramid? Select three options. A square pyramid with 2 foot sides. A cross section parallel to the base is a square with side lengths of 2 ft. A cross section parallel to the base is a square with side lengths of less than 2 ft. A cross section perpendicular to the base through the top vertex is a triangle with the same dimensions as the triangular sides of the pyramid. A cross section perpendicular to the base through the top vertex is a triangle with different dimensions than the triangular sides of the pyramid. A cross section that is perpendicular to the base that does not pass through the top vertex of the pyramid is a trapezoid.

Answers

Answer:

Step-by-step explanation:

A cross section perpendicular to the base through the top vertex is a triangle with the same dimensions as the triangular sides of the pyramid.

A cross section perpendicular to the base through the top vertex is a triangle with different dimensions than the triangular sides of the pyramid.

its C and D i think good luck people

<3

Use OZ with VW – XY
What is XY ?

A 30
B. 35
C. 40
D 50

Answers

Answer:

40

Step-by-step explanation:

From the diagram;

VW = 2(20)

VW = 40

Simce VW is similar to XY, hence VW = XY = 40

Hence the length of XY is 40

solve for y: -4y + 5 > -15​

Answers

Step-by-step explanation:

-4y+5>-15

-4y>-15-5

-4y>-20

divide both (-)

4y>20

divide through by 4

y>20/4

y>5

Point D has coordinates (8,3). Point G has coordinates (-4,3). What is the length of segment DG?

Answers

Answer:

0

Step-by-step explanation:

Coolin

two congruent squares are shown in figures 1 and 2 below

Answers

Answer:

Equal to, c^2, a^2+b^2, a^2 + b^2 = c^2

Answer:

The combined area of the shaded triangles in Figure one is equal to the combined area of the shadead triangles in figure 2. The area of the unshaded square in Figure 1 can be represented by c^2. The combined area of the two unshaded squares in Figure 2 can be represented by a^2+b^2. The areas of the squares in Figure 1 and Figure 2 who that a^2+b^2=c^2.

Step-by-step explanation:

I'm right and if you think I'm wrong then you're wrong

A pitcher contains 2 liters of liquid. Jin pours 368 milliliters of this liquid into a test tube.


How much liquid is left in the pitcher?


Enter your answer in the box.

Answers

Answer:

1,632 liters of liquid remain in the pitcher.

Step-by-step explanation:

Given that a pitcher contains 2 liters of liquid, and Jin pours 368 milliliters of this liquid into a test tube, to determine how much liquid is left in the pitcher the following calculation must be performed:

368 milliliters = 0.368 liters

2 - 0.368 = X

1.632 = X

Therefore, 1,632 liters of liquid remain in the pitcher.

In the xy-plane, the graph of function f(x) has zeros at −5, −2, and 2. Write the polynomial function.

Answers

Answer:

[tex]f(x) = x^3 +5x^2-4x-20[/tex]

Step-by-step explanation:

Given

[tex]Zeros: -5,-2,2[/tex]

Required

The polynomial function

If a function has a, b and c as its zeros, the function is:

[tex]f(x) = (x - a)(x - b)(x - c)[/tex]

So, we have:

[tex]Zeros: -5,-2,2[/tex]

[tex]f(x) = (x - (-5))(x - (-2))(x - 2)[/tex]

Open the inner brackets

[tex]f(x) = (x +5)(x +2)(x - 2)[/tex]

Expand the difference of two squares

[tex]f(x) = (x +5)(x^2 - 4)[/tex]

Expand

[tex]f(x) = x^3 +5x^2-4x-20[/tex]

Question 6
What is the missing value of the following synthetic division?

Answers

Answer:

Hello!

16

Step-by-step explanation:

Because

-5+16=11

What is the area of the regular trapezoid below?
- 6 cm
T
8 cm
10 cm

Answers

Answer:

Area = 64 cm²

Step-by-step explanation:

To find the area, we have to follow some steps:

=> Step 1: Make the bases similar:

Since we have 2 bases given 6 and 10 we have to come up with a third base by finding their average:

(6 + 10) / 2

(16) / 2

8

So now that we know our base,

=> Our second step is to multiply the base we found by the height of the trapezoid:

Area = common base * height

Area = 8 * 8

Area = 64 cm²

Hope this helps!

Question 3 of 10
On a piece of paper, graph this system of inequalities. Then determine which
region contains the solution to the system.

Answers

Answer:

Step-by-step explanation:

SEVEN

Find the median of these numbers ? 2,7,5,4,3

Answers

Answer:

4

Step-by-step explanation:

MARK AS BRAINLIST!!

Answer:

4.

Step-by-step explanation:

The median is the 'middle number.'

In order to find the median of a data set, you must first put the numbers in numerical order.

2, 7, 5, 4, 3

       ↓

2, 3, 4, 5, 7

The 'middle number' in this data set is 4.

Therefore, the median is 4.

Angles and are supplementary. Find the measure of angle C

Answers

Answer:

Angle C = 106 degrees

Step-by-step explanation:

I'm thinking the question should read "Angles a and C are supplementary" (software error, not yours)

Supplementary angles add up to 180 degrees

180 - 74 = 106 degrees

How many solutions would the following system of equations have? y=3x+2, and y=3x-4 is it 0, 1 or infinite ?

Answers

There are no solutions

The average credit card debt for a recent year was $8,776. Five years earlier the average credit card debt was $8,189. Assume sample sizes of 32 were used and the population standard deviations of both samples were $690. Is there evidence to cónclude that the average credit card debt has increased? Use a- 0.05
a. State the hypotheses
b. Find the critical value.
c. Compute the test statistic
d. Make the decision.
e. Summarize the results

Answers

Answer:

We reject H₀.  We support that the new average credit card debt is bigger than the previous average

Step-by-step explanation:

Five years earlier

μ   = 8189

σ  =  690

Sample size   n  = 32

Recent year debt

x  =  8776

Sample size   n  = 32

a) Hypothesis Test:

Null Hypothesis                        H₀            x  =  μ   = 8189

Alternative Hypothesis           Hₐ             x >  μ

b) z(c)  Alternative Hypothesis establishes that the test is a one tail-test to the right.

z(c)   for significance level  α = 0.05    is  from z-table      z(c) = 1,64

c) z(s)  =  (  x  -   μ ) / σ /√n

z(s)  =  ( 8776  - 8189 ) / 690 /√32

z(s)  =  587 *5,66/ 690

z(s) = 4,81

d) Comparing   z(c)    and z(s)

z(s)  >  z(c)   Then z(c) is in the rejection region and we reject H₀

e) We have evidence that at 95 % of confidence the new value for the debt in credit card is now bigger than the average

m and p are complementary angles m/M = 56, and m/P = 2x + 4. Write and solve an equation to find the value of x.

Answers

This equilibrium of the brain cells can transfer deeply throughout earth core

Angle measure labeled a
The arc mesure labeled c

Answers

Step-by-step explanation:

angle measure a =48/2=24°

the arc measure =360°-48°=312°

stay safe healthy and happy.

Identify the parts of a sphere,
a is the
bis the
c is the center
d is the radius
diameter
great circle
HELP 50points

Answers

Answer:

Hello, it appears you did not provide an image that was supposed to be included in order to help answer your question, so I'm afraid I cannot assist you without seeing it. If you supply the necessary photo, I would be more than happy to help you.

Select the correct answer from each drop-down menu.
The area of a rectangle is 91 square inches. If the length of the rectangle is 1 less than twice its width, write an equation that could be used to find the width, w, of the rectangle.

Answers

Answer:

(2w^2) + (-1w) + (-91)

Step-by-step explanation:

The equation that can be used to find the width, w, of the rectangle with the given area is: 2w² - w - 91 = 0.

What is the Area of a Rectangle?

Area pf a rectangle = length × width

Given the following:

Area of rectangle = 91 in.²Width = wLength of the rectangle = 2w - 1

Equation for finding w, using the area formula, would be:

(2w - 1)(w) = 91

2w² - w - 91 = 0

Therefore, the equation that can be used to find the width, w, of the rectangle with the given area is: 2w² - w - 91 = 0.

Learn more about area of rectangle on:

https://brainly.com/question/25292087

Write the word sentence as an inequality a number b is less than 15​

Answers

I’m sure the answer is B < 15

PLEASE HELP!! Click the picture

Answers

Answer:

If y - 4 = 5 then:

y = 5 + 4

y = 9

WILL


GIVE BRAINLIST FOR MATH



....

Answers

9 am.

When the line on the graph is at the lowest for x value it is the lowest temperature.

50 POINTS !!


PLEASE HELP !! ILL GIVE BRAINLIEST TO THE RIGHT ANSWERS.

Answers

Answer:

sorry to burst your bubble but thats 5 ponits

Step-by-step explanation:

Let a and b be real numbers were a≠ b ≠ 0. Which of the following functions could represent the graph below?

Answers

Answer:

A

Step-by-step explanation:

where the graph

WHERE THE GRAPH???

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