Two ants walk on a line in a random fashion. they begin 10cm apart. at each time step, each ant has a probability of 1/2 to move 1cm to the left, and probability 1/2 to move 1cm to the right. what is the probability that after 7 time steps, the ants have met one another (i.e., passed through the same point)?

Answers

Answer 1

121/16384 exactly, or approximately 0.739% Each time step, there are 4 possibilities that will happen. They are a1 a2 -1 -1 = Ants move to left, distance remains the same. -1 1 = Ants move away from each other, distance = distance + 2 1 -1 = Ants move to each other, distance = distance - 2 1 1 = Ants move to right, distance remains the same. For the rest of the discussion, I'll call the possible moves advance, retreat, and idle (and there's 2 ways idle can happen). If you consider the possible moves, the ants can reach each other only at time steps 5, 6, or 7. Let's consider each of those values separately. 5 time steps. This can only happen if all 5 moves are advances. And after they reach each other we don't care what happens for the remaining 2 steps so there is 1 * 4 * 4 = 16 possible sequences where the ant reach each other on the 5th step. 6 time steps. The only way this can happen is with 5 advances and 1 idle, with the idle happening during one of the 1st 5 steps. So there's 5 ways for that to happen. And since there's 2 different actions that are an idle, we multiply that 5 by 2 to get 10. And finally, we don't care what happens with the 7th step, so we multiply once again by 4, getting 40. 7 time steps. This can happen 2 ways. If the 1st 6 steps are 4 advances and 2 idles with the idles happening during any step, then we have 6!/(2!4!) = 15 different arrangements. Since we have 2 different types of idles, we need to multiply by 2 for each idle, so we have 15 * 2 * 2 = 60 possible ways to do this. It can also happen if during the 1st 6 steps we have 5 advances and 1 retreat with the retreat happening during one of the 1st 5 moves. So there's 5 ways to get the ants to meet if the sequence has a retreat. So with a sequence of 7 time steps, there are 16 + 40 + 60 + 5 = 121 possible sequences that have the ants at the same point at the same time. Now since there are 4 possibilities for each step, there are 4^7 = 16384 possible sequences that can be done. So the probability of the 2 ants meeting each other is 121/16384 = 0.007385254 = 0.7385254%

Related Questions

Suppose you are going to make a sandwich. You have mayonnaise and mustard to spread on the bread. You have white, wheat, and rye bread. You have ham, turkey, and pastrami. How many different sandwiches can you make using one spread, one type of bread, and one type of meat?

Answers

18 samiches
m8 thats alot of samiches

2 spreads

3 breads

3 meats

2 * 3 *3 = 18

18 different sandwiches....now I'm hungry

Ive been super sick so im a little behind. Help please .

1. A line goes through the points (8,9) and (-2,4)
(a) What is the slope of the line? Show your work
(b) Write the equation of the line in point-slope form. Show your work
(c) Write the equation of the line in slope-intercept form. Show your work.

Answers

(a) formula: (y2-y1)/(x2-x1)
(4-9)/(-2-8) = (-5)/(-10) = 0.5

(b) formula: y-y0 = m(x-x0) where x0,y0 is a point on the line and m is the slope
y - 9 = 0.5 ( x - 8 )

(c) formula: y=mx + b
Start with formula from (b)
y -9 = 0.5x - 4
Add 9 to both sides
y = 0.5x +5

Hope this helps.
The answers are in the top right corner.

3(b-4)=5b-2 plz help I'm confused

Answers

3( b-4) = 5b - 2

3b - 12 = 5b - 2

3b - 5b = 12 - 2

-2b = 10

b = -5

hope this helps

3b-12=5b-2
-12=2b-2
-10=2b
b=-5

ALGEBRA 2- Which equation has the solutions x = 1 ± √5 ?

A. x2 + 2x + 4 = 0
B. x2 – 2x + 4 = 0
C. x2 + 2x – 4 = 0
D. x2 – 2x – 4 = 0

Answers

A. But you can also read a book and not rely on this

D. x^2 - 2x - 4 = 0

You can solve this problem 2 different ways.
1. Plug in a value of x = 1 ± √5 into each of the possible equations and see if the result is 0.
or
2. Use the Quadratic formula to solve each of the equations and see which comes up with the correct answer.

For this case, I'll use the 2nd option.
A. x^2 + 2x + 4 = 0
a = 1, b = 2, c = 4
Upon attempting this, you'll quickly discover that you're going to try to get the square root of -12. Since there's no imaginary terms in the desired root, this equation can't be it.

B. x^2 – 2x + 4 = 0
Same issue here, trying to get the square root of a negative number. So this one doesn't work either.

C. x^2 + 2x – 4 = 0
Getting closer. Have (-2 ± sqrt(20)) / 2 = -1 ± √5
Still not it, but closer. At least not trying to get the square root of a negative number.

D. x^2 – 2x – 4 = 0
Since the other 3 are wrong, this must be right. But let's do the math anyway.
a = 1, b = -2, c = -4
The quadratic formula gets (2 ± sqrt(20)) / 2 = (2 ± 2√5)/2 = 1 ± √5
And it works out. So this is the answer.

How do I graph this equation?

Answers

just plot some points

for example when x = 0 y = 0-9 = -9

do the same with values of x from -3 to + 3 in steps of 1.

Answer is below...................

Find four consecutive integers with the sum of 54

Answers

54/4 = 13.5

take the 2 whole numbers below 13.5 and the 2 whole numbers above 13.5

12 + 13 + 14 + 15 = 54

The hypotenuse of a right triangle measures 10 inches and the side opposite to <0 one of the non right angles is 5 inches long

The measure of <0 is
30
45
60
90
?

Answers

Final answer:

The measure of angle <0 in the right triangle is approximately 30 degrees.

Explanation:

To find the measure of angle <0 in the right triangle, we can use trigonometry. The side opposite to angle <0 is given as 5 inches. The hypotenuse is given as 10 inches. We can use the sine ratio to find the angle:

sin(<0) = opposite/hypotenuse

substituting the given values:

sin(<0) = 5/10 = 0.5

Now, to find the measure of angle <0, we can use the inverse sine function:

<0 = arcsin(0.5)

Using a calculator, we find that the measure of angle <0 is approximately 30 degrees.

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Suppose you go shopping for a new futon bed for your apartment/home. The model you really like happens to be on sale for $1100. It's original price is $1200. What percent of the original price will you save if you purchase it? Write your answer to the nearest tenth of a percent, but in decimal form.

Answers

If a model of a bed is on sale for $1100 out of $1200, you determine the percentage off with 1100/1200, which simplifies to 11/12. 11/12 is 91.7%. We then subtract that from 100%, so we get 100-91.7, leading us to a percentage saved of 8.3%.

When the factors ofa trinomial are (x+ p) and (x + q) then the coefﬁcient ofthe x- term in the trinomial is:?

Answers

the sum of p and q for apex

What is the square root of 83 to the nearest tenth?

Answers

Knowing the squareroot of 81 is 9, we can easily know that square root of 83 is close to 9.

9 to the closest tenth is 10.

Hope I helped :)

Based on the information given the square root of 83 to the nearest tenth is 9.1.

Square root:

To determine the square root to the nearest tenth we will have to find the square root of the given number which is 83.

Hence,

Square root=√83

Square root= 9.1104335791443

Square root=9.1 nearest tenth

Inconclusion the square root of 83 to the nearest tenth is 9.1.

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Brainliest reward math question

Answers

dude you are puuting up so many questions today.
hard questions im trying. too hard

1. A
To do find the deduction, you do 978 x.05.
2. I don't understand the question at all, I'm very sorry.

Lisa purchased a prepaid phone card for $25 . Long distance calls cost 12 cents a minute using this card. Lisa used her card only once to make a long distance call. If the remaining credit on her card is $19.96 , how many minutes did her call last?

Answers

Her call lasted 42 minutes.
Find the difference between 25 and 19.96 and divide the difference by 12.

It costs $6 per pound for peanuts at Blessed Food Market. Which of the following represents the range of the function in terms of cost per pound?

A. $6
B. Amount of Peanuts
C. Cost of Peanuts Purchased
D. Peanuts Purchased

Answers

Hey there :) Great Question
The answer is C.Cost of peanuts purchased.
The reason being is that the cost of peanuts purchased will be equal to how much it costed per pound, and will show you how many pounds were purchased.

D and B wouldnt be the answer because you cant know how much every single peanut weighs each one is a different weight.

Answer:

Step-by-step explanation:

I did it and got it right!

a boat salesperson earns a 2.5% commission on the sale of each boat Find the commision earned on a boat that sells for 18,500

Answers

100% = 1.0
2.5% = 0.025

So now we know the decimal that corresponds to 2.5%, so all we have to do is multiply the price of the boat by this value in order to find the commission earned:

18 500 x 0.025 = $462.50

Whenever you need to find the percentage OF a number (often money), you just convert that percentage to a decimal (just move the decimal to the left twice so 40% becomes 0.40, 10.5% becomes 0.105, 2% becomes 0.02, etc) and MULTIPLY that decimal by the amount/number you need to find the percentage of.

For example, find the 20% commission of a $10,000 car sale
Calculation:
0.20x$10000 = $2000
Answer:
the commission would be $2000

That’s how you do it. I hope that helps. You should be able to solve it on your own now.

The larger of two numbers is one more than four times the smaller number. if the sum of the numbers is 106, find the numbers.

Answers

Call the numbers x and y. According to the first sentence, x = 4y + 1. According to the second sentence, x + y = 106. You can combine these two equations to find the values of these variables:

x + y = 106
4y + 1 + y = 106
5y = 105
y = 21

We have y, so now we can solve for x using either original equation:

x + y = 106
x + 21 = 106
x = 85

Final answer:

To solve the problem, create two equations based on the information given, then solve these equations step-by-step. After calculation, the two numbers are 21 and 85.

Explanation:

Given the problem, we can translate and create two equations which are:

The larger number is one more than four times the smaller number. We can express this as: L = 4S + 1 The sum of the numbers is 106. We can express this as: L + S = 106

Step 1: From the first equation, we know that L = 4S + 1. We can substitute this into the second equation in place of L, giving us 4S + 1 + S = 106.

Step 2: Add up, and we get 5S + 1 = 106. Subtract 1 from both sides and we get 5S = 105.

Step 3: Divide both sides by 5 to solve for S, we get S = 21.

Step 4: Substitute S = 21 into the equation L = 4S + 1, you can calculate and find L = 85.

Therefore, the two numbers are 21 and 85.

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At a toy factory, toy cars are produced on an assembly line. It takes 8.216 seconds to attach the wheels. It takes 3.652 seconds to attach the hood. How long does it take to attach the wheels and hoods on 42 toy cars

Answers

the answer is 11.868 hopes this helps

At a toy factory, it takes 498.456 seconds to attach the wheels and hoods on 42 toy cars.

We have been given that toy cars are manufactured on an assembly line in a toy factory. Attaching the wheels takes 8.216 seconds. Attaching the hood takes 3.652 seconds.

What are Arithmetic operations?

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.

* Multiplication operation: Multiplies values on either side of the operator

For example 12×2 = 24

To determine the time it takes to attach the wheels and hoods on 42 toy cars

According to the given condition, the arithmetic form would be as

⇒ 42 × (8.216 + 3.652)

Calculate the sum of the difference to get,

⇒ 42 × (11.868)

Apply the multiplication operation, and we get

⇒ 498.456

Therefore, it takes 498.456 seconds to attach the wheels and hoods on 42 toy cars.

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What is the first step in the construction of a line parallel to ab through point p? answers?

Answers

find slope
parallel line have same slope

Answer:

option b

Step-by-step explanation:

I’m confused on how you would find what triangle is.

Answers

First find x. The interior angles must add to 180.
(x+20)+(2x-10)+(3x+20)= 180
6x+30=180
6x=150
x=25

Now plug in the value of x to find each angle measure.
x+20
25+20
45

2x-10
2(25)-10
40

3x+20
3(25)+20
95

Because all angles are different measures, the triangle must be scalene. There is one angle greater than 90 degrees so it is obtuse.

Final answer: Scale and obtuse

50 POINTS formula plus solution.
A regular pentagonal pyramid has a base area of 300 m2 and a lateral area
is 70 m2. What is the surface area of the regular pyramid?

A. 370 m2
B. 185 m2
C. 670 m2
D. 118 m2

Answers

To get the surface area, add all areas together

IN this case 300 and 70

your answer is A

hope this helps

Assume that lines that appear to be parallel are parallel. Find the value of x and the measure of angle y

Answers

What information have we been given here? From the diagram, we can see that (9x+1)° and (14x-34)° degrees are supplementary, meaning:

(9x+1)+(14x-34)=180

There, we have an equation we can fairly easily solve for x. What about y?

If we take a look at the line y° occupies, we can see that it shares a straight angle with our (14x-34)° term and - as implied by the right angle on the bottom line - a 90° angle.

All three of these should add up to 180°, so we have:

(14x-34) + y + 90 = 180

Another think to note is that, upon inspection, (14x-34)° and y° are complementary - they add up to 90° - and subtracting the 90 from both sides of our equation confirms that fact:

(14x-34) + y = 90

If you've solved for x prior to this, solving for y should be pretty straightforward.

Answer:

The answer would be (14x-34) + y = 90.

Step-by-step explanation:

How do you write 100, in an exponential form

How do write 100,000, in an exponential form

And how do you write 10,000 ,in an exponential form

Answers

1. 10^2

2. 10^5

3. 10^4

Hope this helped!

Nate

Final answer:

Numbers can be written in exponential form with a base of 10. For example, 100 is written as 10^2, 100,000 as 10^5, and 10,000 as 10^4.

Explanation:

To write numbers in exponential form, you need to understand the concept of exponential notation which is a way to express a number as a base raised to a power. In each of the given cases, the base is 10.

For 100, there are two zeros following the 1. This means that 100 can be written as 10 to the power of 2, or 10^2.

Similarly, for 100,000, there are five zeros following the 1. This would be written as 10 to the power 5, or 10^5.

Lastly, 10,000, has four zeros following the 1. This would be written as 10 to the power of 4, or 10^4.

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To have an inverse function, a function f must be

Answers

To have an inverse function, a function f must be onto the function,

What are functions?

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

What are inverse functions?

Inverse function of function is defined as the, that modified and derived function from parent function that has domain[range of parent function] and range [domain of parebt function].

here,
To have an inverse function, a function f must be onto function, because it is neccessary that the function gives one distinct image for the distinct pre-image.

Thus, To have an inverse function, a function f must be onto function,

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Final answer:

To have an inverse function, a function must be bijective, meaning it is both one-to-one (injective) and onto (surjective). An example is shown with the function f(x) = x^2 which is not injective, hence doesn't have an inverse function.

Explanation:

In mathematics, to have an inverse function, the original function, represented as f, must be both injective (one-to-one) and surjective (onto). This dual property is called being bijective. This means every element of the function's domain maps to one distinct element in the function's range (injective) and that every element in the range has a pre-image in the domain (surjective).

For example, consider the function f(x) = x^2. This function is not injective, as both f(-2) and f(2) give the same output, hence it does not have a true inverse function across all real numbers.

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What is 4,080,499 rounded to the nearest thousand?

Answers

4,080,499 rounded to the nearest thousand is 4,080,000.

The length of a rectangle is two thirds its width. the area is 12 square meters. find its width. round your answer to two decimal places.

Answers

L = [tex]( \frac{2}{3} )[/tex]w
a = 12
Length times width = area
L · w = a
[tex]( \frac{2}{3} )[/tex]w · w = 12
[tex]( \frac{2}{3} )[/tex] [tex] w^{2} [/tex] = 12
Divide both sides by [tex] \frac{2}{3} [/tex] or mulitply both sides by [tex] \frac{3}{2} [/tex] (either one is fine)
[tex]( \frac{2}{3} )[/tex] ÷ [tex]( \frac{2}{3} )[/tex] [tex] w^{2} [/tex] = 12 ÷ [tex]( \frac{2}{3} )[/tex]
or
[tex]( \frac{3}{2} )[/tex] [tex]( \frac{2}{3} )[/tex] [tex] w^{2} [/tex] = 12 [tex]( \frac{3}{2} )[/tex]
[tex] w^{2} [/tex] = 18
Square root both sides to get rid of the squared on the w
[tex] \sqrt{w^{2} } [/tex] = [tex] \sqrt{18} [/tex]
w = 4.24

Evaluate a + b2 for a = 2 and b = 3. 8 11 25

Answers

a + b^2 for a = 2 and b = 3
= 2 + 3^2
= 2 + 9
= 11
answer
11

8

a+b2
replace the letter with it's number
2+3(2)
multiply 3 and 2
2+6
add
8

In the triangles below, ma + md = 90°. using the information given about the triangles below, determine how the triangles can be shown to be similar.

Answers

Find two numbers that arent the same that equal 90.

Answer:

The triangles are similar by AA

Step-by-step explanation:

How do you solve for x when x squared = 9?

Answers

If the squared number be 9 from a squared the x would = 18 right?

Which of these is false?
A) 21,730 < 22,341
B) 21,730 > 22,341
C) 22,341 > 21,730
D) 22,341 < 24,687

Answers

B. 21,730 is not greater than 22,341.

Final answer:

The false statement among the given options is B) 21,730 > 22,341. The greater than, less than symbols should be accurately used to compare two numbers. The other given statements are true.

Explanation:

The false statement in the given options is B) 21,730 > 22,341. This statement is saying that 21,730 is greater than 22,341, which is false. In mathematics, '<' symbol represents 'less than' and '>' represents 'greater than'. So, the statement B) is false because 21,730 is not greater than 22,341, but less.
Comparing the following two statements A) 21,730 < 22,341 and C) 22,341 > 21,730, we can see they are actually the same statement, restated in a different manner. Both statements are saying that 21,730 is less than 22,341 which is true.
The statement D) 22,341 < 24,687 is also true because 22,341 is less than 24,687.

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which pairs of angles are not always congruent when two parallel lines are cut by a transversal?

A. Vertical lines
B. Alternate exterior angles
C.corresponding angles
D. Consecutive interior angles

Answers

vertical lines are not always congruent when two parallel lines are cut by a transversal line

When two parallel lines are cut by a transversal vertical lines are not always congruent.

What are transversal?

A line that goes through two lines in the same plane at two different points is called a transversal. When determining whether two or more other lines in the Euclidean plane are parallel, transversals play a role. Different kinds of pairs of angles are created when two lines intersect a transversal: alternate angles, corresponding angles, consecutive exterior angles, and consecutive interior angles. If the two lines are parallel, Euclid's parallel postulate states that consecutive interior angles are supplementary, that corresponding angles are equal, and that alternate angles are equal.

Given to find the pairs of angles are not always congruent when two parallel lines are cut by a transversal,

when parallel lines are cut by a transversal some pair of angles are congruent like alternative exterior angle, corresponding angles and

Consecutive interior angles all the pairs are congruent and equal.

but When a transversal line cuts through two parallel lines, vertical lines are not always congruent.

Therefore vertical lines are not always congruent.

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Please help my brain is dead -_-
Lynn has an annual income of $17,500. she has $5,500 withheld as deductions. What is the amount of each paycheck if she gets paid biweekly?
please explain your answer i actually want to learn this THANKS

Answers

with out deductions the total will be 729.16. but with the deductions the income will be 500.

Ok, I hope I revive your brain honey! So annual we know, is a year, 12 months, 52 weeks, right? So what we do here now, as you mentioned the $5,500 deductions, subtract that right off the bat we get $12,000. Now we want to go ahead and divide 52 by 2. The reason is because it's bi-weekly; every 2 weeks. So, 52/2 = 26. Then what we do now is divide $12,000 by 26. We get a whole number but... IT HAS A DECIMAL! OH WHAT DO WE DO!. Well, we are going to round that decimal. So we have 461.538461538 as our decimal, so we want to round that to 461.54. She earns $461.54 biweekly. I hoped I help! ^-^

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