A mosquito is walking at random on the nonnegative number line. She starts at $1$. When she is at $0$, she always takes a step $1$ unit to the right, but, from any positive position on the line, she randomly moves left or right $1$ unit with equal probability. What is the expected number of times the mosquito will visit $0$ before the first time she visits $4$?
The expected number of times the mosquito will visit 0 before the first time she visits 4 is 3/4 by using concept of probability and geometric series.
Given that repeatedly throwing a fair tetrahedral die, trying to get a 4 (success) before getting a number from 1 to 3 (failure), which follows a geometric distribution.
To find the expected number of visits to 0 before reaching 4, analyze two cases:
success (reaching 4 before 0) and failure (reaching 0 before 4).By the given data, the probabilities of two cases are:
P(success) p = 1/4,
P(failure)=3/4.
The expected count of failures, X, can be found in terms of success probability p as
[tex]E[X]=\sum_{x=0}^{+\infty}[x(1-p)^xp][/tex]
On substituting p = 1/4 gives:
[tex]E(X) = 0(1/4)+1(3/4)(1/4)+2(3/4)^2(1/4)+3(3/4)^3(1/4)+.........[/tex]
On taking (1/4) gives
[tex]E(X) = 1/4[3/4+(3/4)^2+(3/4)^3+......+\infty]----(1)[/tex]
Consider [tex]3/4+(3/4)^2+(3/4)^3+......+\infty[/tex]
This forms a geometric series tends to infinity and the sum is given by :
[tex]S_\infty = a/(1-r)[/tex]
Here: a= 3/4
r = 3/4
Plugging these values into formula gives:
[tex]3/4+(3/4)^2+(3/4)^3+......+\infty = S_\infty[/tex]
[tex]S_\infty= 3/4/(1-3/4)[/tex]
On subtracting the denominator gives:
= 3/4/(1/4)
On taking reciprocal gives:
= 3/4 * 4
On simplifying gives:
= 3
Substituting these value into given equation 1 gives:
E(X) = 1/4*[3]
On multiplying gives:
E(X) = 3/4.
Therefore, the expected number of times the mosquito will visit 0 before the first time she visits 4 is 3/4 by using concept of probability and geometric series.
Learn more probability about here:
https://brainly.com/question/23846068
#SPJ4
An algebra class normally has y students, but today it is just 2/3 full. Express the number of students in class today terms of y.
Answer:
2/3y
Step-by-step explanation:
If the class usually has y students and has 2/3 today, it can be represented by 2/3y.
Since multiplying a number or variable by 2/3 makes it 2/3 of the amount, 2/3y will represent the people in the class.
So, in terms of y, 2/3y represents the number of students in class today.
expressions equivalent 10(2 + 3)-8.3 hurry extra points!
Answer:
41.7
Step-by-step explanation:
[tex]10(2 + 3) - 8.3 \\ \\ = 10 (5) - 8.3 \\ \\ = 50 - 8.3 \\ \\ = 41.7[/tex]
someone help plz it is appreciated very much
Answer:
y=x+6 is the correct answer:)
Step-by-step explanation:
ax + bx = 0
Solve equation for x
Answer:
you cant have two variables
Step-by-step explanation:
express 4,102/7 in decimal form
Answer:
586
Step-by-step explanation:
It would not be in decimal form because the number don't have a decimal so it would be a whole number
Answer: The answer is 586, so there is no decimal form
7. Given f(x) = 3x - 1, find f(2).
4
2
1
5
Answer:
5
Step-by-step explanation:
Solve for y
6 = 4x + 9y
Answer:
y=.44-.66
Step-by-step explanation:
hope this helps not 100 percent sure let me know in the comments.
Marisa has $26 in her purse. She pays $5 for lunch. Which expression represents this situation?
Answer: 26-5
Step-by-step explanation:
literally you take 5 aways from 26
Jordan solved the equation −7x + 25 = 48; his work is shown below. Identify the error and where it was made.
−7x + 25 = 48
Step 1: −7x + 25 − 25 = 48 − 25
Step 2: −7x = 23
Step 3: -7x/7= 23/7
Step 4: x = 23/7
Step 1: He should have added 25 to each side.
Step 1: He should have divided both sides by −7.
Step 3: He should have divided both sides by −7.
Step 3: He should have multiplied both sides by −7.
Answer:
step 3: he should have divided both sides by -7
Which represents the inverse of the function f(x) = 4x?
h(x) = x + 4
h(x) = x – 4
h(x) = three-quartersx
h(x) = one-quarterx
By definition, the correct answer is the last option: the inverse of the function f(x) = 4x is h(x)= [tex]\frac{1}{4}[/tex]x.
Definition of inverse functionThe inverse or reciprocal function of f(x) is called another function f⁻¹(x) that satisfies: If f(x)=y , then f⁻¹(y)=x.
To build or calculate the inverse function of any function, one of the ways to do it is to interchange the variables x and y, and use a combination of algebraic methods in order to isolate the variable "y".
Inverse of f(x)=4xBeing f(x)=y=4x, to calculate the inverse, in first place you interchange the variables x and y:
f(y)=x=4y
Isolating the variable y, you get:
h(x)=x÷4= [tex]\frac{1}{4}[/tex]x
Finally, the correct answer is the last option: the inverse of the function f(x) = 4x is h(x)= [tex]\frac{1}{4}[/tex]x.
Learn more about the inverse of a function:
https://brainly.com/question/13799722
Consider the expression. 6 · 60 · 6–3 Which statements are true about the expression? Check all that apply. The 6 without an exponent is equivalent to the 6 having a 0 exponent. The sum of the exponents is
Answer:
4. The expression has a value of 1/36 . True
5. An equivalent expression is (6)^5. (6)^- 7 True
Step-by-step explanation:
Not true. The 6 without an exponent is equivalent to the 6 having a 0 exponent.
Any number having an exponent zero has a value equal to 1.6 · (6)^0 · (6)^–3
= 6.1.1/216
= 1/36
= (6)^-2
2. The sum of exponents is 2.
False ( the sum of exponents is -2)
3.Multiply the exponents to solve the expression .
False when the bases are the same the exponents are added or subtracted.
4. The expression has a value of 1/36 .
True
5. An equivalent expression is (6)^5. (6)^- 7
True
Answer:
The last two answers d and e
Step-by-step explanation:
3) Jonathan purchased 120 pieces of candy for Valentine's Day. He
gives 2 pieces to each of his friends. When he finishes handing
out candy, he has 30 pieces left. How many friends did he give
candy to?
I think 45
Step-by-step explanation:
120-30=90
90 pieces are gone and divide that by two for each friend
90÷2=45 so he has 45 friends?
3 − 3k + 7k = 5b[tex]3 − 3k + 7k = 5b[/tex]
Answer:
k=-14
Step-by-step explanation:
Anya walked 7/10 km to the bank and then walked 3/4 km to the flower shop. What is the total distance Anya walked? Show your work. Write your answer as a mixed number.
Answer:
1 and 9/20
Step-by-step explanation:
add your fractions together 7/10 + 3/4
make them have the same denom 14/20 + 15/20
so its 29/20
to get the mixed fraction, divide 29/20 to get 1.45. The 1 is your whole number. Subtract 20 from 29 to get 9, which is what is remaining, and will go over 20.
the answer is 1 and 9/20
work:
7/10km = 14/20km
3/4km = 15/20km
15/20+14/20=29/20km
29/20 as a mixed number is 1 and 9/20.
Your friend thinks that the equation k-3.5 = 21 is a true statement. Is your friend correct? Explain.
Answer:
he is not correct because k could be equal to any whole number
there fore no matter what number you subtract 3.5 from it couldnt be a whole number (that includes 21)
Destiny has 10$ and Elijah has 5$. I give each person the same amount of money each week. This situation can be represented with: x + 10 = x + 5
How many solutions does this situation reperesent ? Please explain your reasoning
Answer:
I do believe that the answer is 0 solutions.
Step-by-step explanation:
x+10 =x+5
Subtract 5 from both sides, you get:
x+5=x
Subtract x from both sides, and you get:
5=0 which is NOT true. Also I maybe wrong, pls don't be mad at me.
Write the equation of the line in standard form
y
5
3
2
1
X
1
4
2
5
3
-1
-5
-4
-3
-2
-2-
-3
Answer:
(5,1)
(3,4)
(2,2)
(1,5)
There are 56 workers during each shift. The workers are split into teams of 14 each. How many work during a shift?
Answer:
4 teams
Step-by-step explanation:
To evenly distribute 14 into 56, you divide. 56/14 is 4.
Therefore the correct answer is 4 teams.
Hope I helped!!!
Use the table to find the ratio. Enter the ratio as a fraction in simplest form.
Color of socks white black blue brown
Number of socks 5 8 4 6
The ratio of blue socks to nonblue socks is-
Answer:
4/19
Step-by-step explanation:
Help!! I got this wrong last time lol
Answer:
A.
Step-by-step explanation:
when you distribute it you keep the subtraction sign and have to multiply 6 by 50 and then 6 by 1
The store bought a table for $200, and sold it for $350. What percentage was the markup? %
Answer: 175% or 75% more in price
Step-by-step explanation:
There was a 75% of markup in the price.
What is percentage?A percentage is a number that tells us how much out of 100 and can also be written as a decimal or a fraction.
Given that, The store bought a table for $200, and sold it for $350, we need to find the percentage of markup in the price,
percentage of markup in the price =
(final price - original price)/(original price)x100
final price = $350, original price = $200
Markup in price = $350-$200 = $150
percentage of markup in the price = 150/200x100 = 75%
Hence, There was a 75% of markup in the price.
For more references on percentage, click;
https://brainly.com/question/29306119
#SPJ2
I suck at math please do this for me I’ll give you anything
Answer:
Step-by-step explanation:
20:
The equation y=1.35x+10 models the cost of a cab ride, where y is the total cost of the ride in dollars and x is the number of miles driven. Which statement describes this model?
A. Customers pay $1.35 per-mile for the first x miles, and then $10 per mile afterwards.
B. Customers pay 10$ per-mile, and then $1.35 per mile afterwards
C. Customers pay $1.35 initially, and then another $10 for every mile traveled.
D. Customers pay $10 initially, and then another $1.35 for every mile travled
Answer:
C.
Step-by-step explanation:
X is the number miles driven so C. is the BEST answer choice.
Answer:
Its C
Step-by-step explanation:
Erica’s bank account increased from $1,200.00 to $1,500.00. By what percent did the amount of money in her bank account increase?
25% amount of money increased in her bank account.
Here,
Erica’s bank account increased from $1,200.00 to $1,500.00.
We have to find the percent of amount of money in her bank account increase.
What is Percent?
Percentage is a fraction or a ratio in which the value of whole is always 100.
Now,
Erica’s bank account increased from $1,200.00 to $1,500.00.
Increased money = $1,500 - $1,200 = $300
Percentage of increased money = [tex]\frac{300}{1200} * 100 = 25[/tex]
Hence, 25% amount of money increased in her bank account.
Learn more about the percent visit:
https://brainly.com/question/24304697
#SPJ6
Rickey has 7 over 8 cup of cereal in a bowl. He then gave two 1 over 4 cups of cereal from his bowl to his little sister. Which of the following best explains the amount of cereal left in Rickey's bowl?
Answer:
5/8 cup left
Step-by-step explanation:
7/8 - 1/4
1/4=2/8
7/8-2/8
5/8
Decide whether each of the following is greater than 1 or less than 1 and explain your answer.
1.) 1/2 ÷ 1/4 =
2.) 1 ÷ 3/4 =
3.) 2/3 ÷ 7/8 =
4.) 2 7/8 ÷ 2 3/5 =
Answer:
4.) 2 7/8 ÷ 2 3/5 =
1. Greater than 1
2. Greater than 1
3. Less than 1
4. Greater than 1
Step-by-step explanation:
I took the quiz
This system of equations is shown on the graph:
2y − 4x = 6
y = 2x + 3
Which statement about the system is true?
A. The system has no solution.
B. The system has a unique solution at (0,3).
C. The system has a unique solution at (1,5).
D. The system has infinitely many solutions.
Answer:
Option (D)
Step-by-step explanation:
System of equations has been given as,
2y - 4x = 6
y - 2x = 3 [Dividing both sides of the equation by 2]
y = 2x + 3 ------(1) [Slope-intercept for of the equation]
y = 2x + 3 ------(2)
Since, both the equations are same,
System of equations will have infinitely many solutions.
Therefore, Option (D) will be the correct option.
Answer:
d
Step-by-step explanation:
Jada plans to serve milk and healthy cookies for a book club meeting. She is preparing 12 ounces of milk and 4 cookies per person. Including herself, there are 15 people in the club. A package of cookies contains 24 cookies and costs $4.50. A 1-gallon jug of milk contains 128 ounces and costs $3. Let represent number of people in the club, represent the ounces of milk, represent the number of cookies and represent Jada's budget in dollars. Select all of the equations that could represent the quantities and constraints in this situation.
Jada plans to serve milk and healthy cookies for a book club meeting. She is preparing 12 ounces of milk and 4 cookies per person. Including herself, there are 15 people in the club. A package of cookies contains 24 cookies and costs $4.50. A 1-gallon jug of milk contains 128 ounces and costs $3. Let represent number of people in the club, represent the ounces of milk, represent the number of cookies and represent Jada's budget in dollars. Select all of the equations that could represent the quantities and constraints in this situation.
â m= 12(15)
n represents the number of people
in the club
b. 3m + 4.5c = 6
c. 4n =
m represents the ounces of milk
& 44.50) = C
c represents the number of
cookies
e b=2(3) + 3(4.50)
b represents Jada's budget in
dollars
The equations that could represent the quantities and constraints in this situation are:
a) m = 12(15)
c)4n = c
e) b = 2(3) + 3(4.50)
Step-by-step explanation:
Jada plans to serve milk and healthy cookies for a book club meeting
She is preparing 12 ounces of milk and 4 cookies per person
There are 15 people in the club
A package of cookies contains 24 cookies and costs $4.50
A 1-gallon jug of milk contains 128 ounces and costs $3
Let us represents number of people in the club by n
The the ounces of milk = m
The number of cookies = c
Jada's budget in dollars = d
y = 12(15)
She is preparing 4 cookies per person
4n = c
Since A package of cookies contains 24 cookies
She needs = 15 × 4 = 60 cookies
60 ÷ 24 = 2.5
Hence, approximately, she has to buy 3 packages of cookies
She needs = 15 × 12 = 180 ounces of milk
A 1-gallon jug of milk contains 128 ounces
180 ÷ 128 = 1.406
She needs to buy 2 A 1-gallon jug of milk
Note that: from the question
The cost of each jug of milk is $3
The cost of each package of cookies is $4.50
b represents Jada's budget in dollars
b = 2(3) + 3(4.50)
The equations that could represent the quantities and constraints in this situation are:
Options a, c and e are correct
WILL MARK BRAINLEST!!!!! THANK YOU! PLEASE SHOW ALL WORK NEEDED!
THE EQUATION IS a^5 b^5 + 5a^3 b^6 - 14ab^7 / ab^5. NOTE: ITS a^5 b^5 + 5a^3 b^6 - 14ab^7 DIVIDED BY ab^5
SIMPLIFY
Answer:
[tex] a^4 + 5a^2 b - 14b^2[/tex]
Step-by-step explanation:
[tex](a^5 b^5 + 5a^3 b^6 - 14ab^7) \div ab^5 \\ \\ = \frac{(a^5 b^5 + 5a^3 b^6 - 14ab^7) }{ab^5}
\\ \\ = \frac{a {b}^{5} (a^4 + 5a^2 b - 14b^2) }{ab^5} \\ \\ = a^4 + 5a^2 b - 14b^2[/tex]