1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Monica [59]
3 years ago
13

Two containers hold several balls. Once a second, one of the balls is chosen at random and switched to the other container. Afte

r 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?
Mathematics
1 answer:
natka813 [3]3 years ago
6 0

Answer:

(a) 8 balls

(b) 4 balls

Step-by-step explanation:

Let

N \to Number of balls

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

Pr = 0.5^N

For 2 boxes, it is:

Pr = 2 * 0.5^N

From the question, we have:

\frac{80}{10000} \to Favorable outcome

To solve for N, we have:

2 * 0.5^N = \frac{80}{10000}

2 * 0.5^N = 0.008

Divide both sides by 2

0.5^N = 0.004

Take log of both sides

\log(0.5^N) = \log(0.004)

Apply law of logarithm

N\log(0.5) = \log(0.004)

Make N the subject

N = \frac{\log(0.004)}{\log(0.5)}

N =7.966

Approximate

N = 8

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:

Balls \approx \frac{N}{2}

Balls \approx \frac{8}{2}

Balls \approx 4

<em>4 balls in each box</em>

You might be interested in
Erik sees 42 stars in the sky on Tuesday
Sophie [7]

Answer:

Well, 7 * 6 is 42...

So that would mean Erik saw 6 stars?

Idk

Hope this helps!

Stay safe

3 0
3 years ago
The weight of a person on or above the surface of the earth varies inversely as the square of the distance the person is from th
AleksandrR [38]
If you do this with a complex set of fractions and let
K = G Me m_space be the same in both parts, there should be some cancellation.

W_earth = 180 lbs

W_earth = K /3900 miles^2
W_space =K  /(3900 + 850)^2

180 / W_space = k/3900^2
x = k / (4750)^2

\frac{180}{Wspace} =  \frac{ \frac{k}{3900^{2} } }{ \frac{k}{4750^{2}} /[tex]\\Now you need to invert and multiply the bottom fraction on the left.\\[tex] \frac{180}{x} {=} \frac{k}{3900^{2}} {*} \frac{4750^{2}}{k} 

The ks cancel out.

You are left with 180/x = 4750^2 / 3900^2 Now cross multiply
180 * 3900^2 = 4750^2  = x
180 * 3900^2 / 4750^2 = x 
180 * 0.67413 = x
x = 121 pounds. Weight is a force, but because all the units on one side are equivalent to the units on the other, the conversions become part of k. Normally you would have to do the conversions, but not in this particular case.

4 0
3 years ago
Read 2 more answers
Identify the constant of<br> proportionality (k)<br> 8Y = 16x<br> k=
RUDIKE [14]

Answer:

JUST WRITE THIS AS YOUR ANSWER

Step-by-step explanation:

Step 1: Put together the general equation.

Step 2: Solve for the constant of proportionality.

Step 3: Plugging the constant into the equation, solve for the unknown variable.

Let's solve a few problems to see how this works, shall we?

Example 1: Y is directly proportional to x. When x = 5, y = 8. What does y equal when x = 9?

First, we set up our general equation. Because y is directly proportional to x, we have:

y = cx

where c is the constant of proportionality. In other words, when x goes up, y goes up, and when x goes down, y goes down.

The next thing we do is plug our values for x and y into the equation so we can solve for c:

8 = (c)(5)

Solving for c, we get c = 8/5 = 1.6 and we plug this into our equation:

y = 1.6x

Now, we can plug x = 9 into the equation to find out what y equals:

y = (1.6)(9)

y = 14.4

So, our answer is 14.4

Example 2: Y is directly proportional to the square of x. When x = 2, y = 32. What does y equal when x = 5?

This time, our general equation is slightly more complicated because x is squared:

y = cx2

Like before, we solve for our constant:

32 = (c)(22)

32 = (c)(4)

We get c = 8:

y = 8x2

Solving for y when x = 5, we get y = (8)(52) = (8)(25) = 200

Example 3: Y is inversely proportional to x. When x = 2, y = 8. What does y equal when x = 24?

This time, because y is inversely proportional to x, our general equation is different:

xy = c

so when x goes up, y goes down, and vise versa. But, other than that, we solve these kinds of problems the same way as direct proportion problems. Solving for the constant, we get:

(2)(8) = c

So c = 16 and our equation is now:

xy = 16

Solving for y when x = 24 we get y = 16/24 = 2/3

Example 4: Y is inversely proportional to the square root of x. When x = 36, y = 2. What does y equal when x = 64?

As before, we set up our equation:

eq001

Since the square root of 36 is 6, it is easy to solve for c:

(6)(2) = c

We get c = 12 and our equation is now:

eq002

Solving for y when x = 64 we get 8y = 12 or y = 12/8 = 1.5 because the square root of 64 is 8.

6 0
3 years ago
Evaluate each function.<br> h(x) = 2x + 2; Find h(10)<br> O 22<br> O 18<br> O 8<br> O -8
Vladimir79 [104]

Answer:22

Step-by-step explanation:

Substitute and solve

8 0
3 years ago
Which equation represents the line of reflection for this graph?
tino4ka555 [31]

Answer:

x= 0

Step-by-step explanation:

Because it scale factor

7 1
3 years ago
Other questions:
  • Sophie and Simon are peeling a pile of potatoes for lunch in the cafeteria. Sophie can peel all the potatoes by herself in 45 mi
    9·2 answers
  • You will be administratively suspended if you have a breath or blood alcohol level of ____ or above or refuse to submit to a che
    13·2 answers
  • you open a cafe. the function f(x)=4000x represents your expected net income(in dollars) after being open x weeks. before you op
    8·1 answer
  • What is 25 percent out of 500.00?
    11·2 answers
  • A customer's monthly trash collection bill was $24.74. Due to a rate increase, her monthly bill is now $26.86. To the nearest te
    5·1 answer
  • Please, I really need help on this problems!!
    6·1 answer
  • Please help me answer this question!
    14·1 answer
  • A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 3 large boxes and 5 small boxes has a t
    13·1 answer
  • Can somebody help me please?
    6·1 answer
  • The coordinates of the vertices of △GHI are G(−7,2), H(−2,2), and I(−2,8). Find the side lengths to the nearest hundredth and th
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!