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.
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If a video game was 10% off and the amount of the discount was $6 what was the original price?
Answer: the original price was $60! <3
Step-by-step explanation:
What do variables and function have in common
if kevin took 1/10 of an hour to use 1/2 of package of napkins. how many hours would it take to use 2 packages?
Answer:
2/5 hours
Step-by-step explanation:
We can write a proportion to solve
1/10 hour x hours
---------------- = -------------------
1/2 package 2 packages
Using cross products
1/10 * 2 = 1/2 x
1/5 = 1/2x
Multiply each side by 2
1/5 * 2 = 1/2x *2
2/5 =x
2/5 hours
Please show all work
Xavier ran 2.5 miles in 12 minutes. How long will it take him to run 1 mile?
Answer:
4.8 minutes
Step-by-step explanation:
2.5/2.5=1
so
12/2.5=4.8
Answer:
4.8 minutes per mile
Step-by-step explanation:
Let mi be miles
Let min be minutes
2.5mi = 12min
Divide by side by the mile to get the unit rate
2.5/2.5 = 12/2.5
You will get 1 = 4.8
Find an explicit rule for the nth term of the sequence.
-4, -8, -16, -32, ...
A) an = -4 • 2n - 1
B) an = 2 • -4n + 1
C) an = 2 • -4n
D) an = -4 • 2n
Answer:
An explicit rule for the nth term of the sequence will be:
[tex]a_n=-4\cdot \:2^{n-1}[/tex]
Thus, option (A) is true.
Step-by-step explanation:
Given the sequence
[tex]-4, -8, -16, -32, ...[/tex]
A geometric sequence has a constant ratio r and is defined by
[tex]a_n=a_0\cdot r^{n-1}[/tex]
Computing the ratios of all the adjacent terms
[tex]\frac{-8}{-4}=2,\:\quad \frac{-16}{-8}=2,\:\quad \frac{-32}{-16}=2[/tex]
As the ratio 'r' is the same.
so
[tex]r=2[/tex]
as
[tex]a_1=-4[/tex]
Hence, the nth term of the sequence will be:
[tex]a_n=a_0\cdot r^{n-1}[/tex]
substituting the values [tex]r=2[/tex] and [tex]a_1=-4[/tex]
[tex]a_n=-4\cdot \:2^{n-1}[/tex]
Therefore, an explicit rule for the nth term of the sequence will be:
[tex]a_n=-4\cdot \:2^{n-1}[/tex]
Thus, option (A) is true.
Solve F(x) for the given domain. Include all of your work in your final answer. Submit your solution.
F(x) = x2 + 2
F(x + h)=
Answer:
fx=2x+2
fx-2x=2
Step-by-step explanation:
x(f-2)=2
x=2/f/2✓marks
Answer:
F ( x ) = x^2 + 2
Domain = R
F ( x - h ) = ( x - h )^2 + 2xh + h^2 + 2
Si a/b=b/c=c/d=k ademas a/d=1/216 calcular b2/c2
pueden ayudarme con esto por favor, es urgente:(
Answer:
please mark me as brainlist
The value of the expression b²/c² is 46656.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
We can use the given equations to express a, b, c, and d in terms of k:
a/b = b/c = c/d = k
From a/d = 1/216,
we have:
a/d = k² / (c/d)
Substituting k = b/c and simplifying:
a/d = (b/c)² / (c/d)
a/d = b² / (c² x d)
Multiplying both sides by c².
(a/d) x c² = b² / d
Substituting k = c/d:
(a/d) x c² = b² / k
Substituting a/b = k and solving for b²/c².
a/b = k
a = k x b
b = a/k
b² = a²/k²
(b²/c²) = (a²/k²) / (a²/k² x (d/c)²)
(b²/c²) = 1 / (d²/k²)
Substituting k = c/d and simplifying:
(b²/c²) = d²
Substituting a/d = 1/216:
(b²/c²) = (216²)
Therefore,
The value of the expression b²/c² is 46656.
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The complete question is:
If a/b=b/c=c/d=k plus a/d=1/216 calculate b2/c2
Can you help me with this please, it's urgent?
17 out of 25 students carried blue mesh backpacks. What percent of the students had blue mesh backpacks?
Answer:
68
Step-by-step explanation:
multiply 17 by 4
Answer:
68%
Step-by-step explanation:
25 x 4= 100
17 x 4= 68
so 17/25 is equal to 68/100
Hope this helps!
I need HELPPPPP!!!!!!
Answer:
light blue
Step-by-step explanation:
SUPER EASY AND ILL GIVE BRAINLIEST
determine which of the following are functions
a. I and III only
b. II and IV only
c. II, III, and IV only
d. I, II, III and IV
Answer:
I and III only
Step-by-step explanation:
Answer:
2 and 5
Step-by-step explanation:
Make sure you use the vertical line to determine what is a function
A student collected monetary pledges for a fundraiser. One donor pledged to contribute $5 for each mile walked by the student during the fundraising walk up to a maximum of six miles.
A. is the situation continuous or discrete
B.write the domain and range of the situation
Answer:
A. The situation is discrete B. i. { x : 0 ≤ x ≤ 6; x ∈ Z} ii. { C = 5x : 0 ≤ C ≤ 30; C ∈ Z}
Step-by-step explanation:
A. The situation is discrete since we have integral values for the amount paid per mile walked. The amount per mile is $5 and is only paid if a complete mile is walked. So, it is a discrete situation.
B. i. Since 0 miles represents 0 distance and the student walks a maximum of 6 miles, let x represent the distance walked. So the domain is 0 ≤ x ≤ 6 where x ∈ Z where Z represent integers.
{ x : 0 ≤ x ≤ 6; x ∈ Z}
ii. Since at 0 miles the amount earned is 0 miles × $5 per mile = $ 0 and at the maximum distance of 6 miles, the amount earned is 6 miles × $5 per mile = $ 30, let C represent the amount donated in dollars. So the range is 0 ≤ C ≤ $ 30 where C = 5x.
{ C = 5x : 0 ≤ C ≤ 30; C ∈ Z}
Find the length of side x in simplest radical form with a rational denominator.
WILL GIVE BRAINLIEST!!!
Answer:
x=3
Step-by-step explanation:
The triangle has angles 30,60,90
In this type of right triangle, the ratio of the sides is 1:square root of 3:2
In this type of triangle, the square root of 3 is equal to the 1 in the ratio above because it is across from the angle 30
With this, we multiply the ratio at the top by the square root of 3
since x is across the angle 60, we multiply square root of 3 by the square root of 3 which equals 3.
I hope this makes sense
whoever hears this I want u to know that I am here for I will always be be and so will God. Things well get better I promise!! YOU have to go through the storm to get to the rainbow. TURN TO GOD he will always help u and he loves you and I do to and so does Jesus u got this. DONT GIVE UP and keep on pushing at the end it will all be worth it I promise AND GIVE YOUR LIFE TO JESUS he will help you
Answer:
im gay tho :)
Step-by-step explanation:
Answer:
atheists reading this :0
Step-by-step explanation:
this was a joke plz dont bully me
is 4/3 = 8/6 a proportional?
Answer:
its b
Step-by-step explanation:
b
Answer:
Yes 4/=8/6 are proportional
If you look at the first fraction 4/3 and multiply 2 by the denomenator and numerator it will equal to 8/6 . Now to switch it up 8/6 divided by 2 is 4/3 so yes the t2 fraction are proportional.
Step-by-step explanation:
4b + 6 = 2 - b + 4
b = -2
b = 0
b = 4
b = 6
Evaluate the expression 2(n + 1) - 5 using n=4
Answer:
5
Step-by-step explanation:
2(4+1)-5
2(5)-5
10-5
5
What is the slope of 3x-2y=7?
Answer:
The slope is -3/2
Step-by-step explanation:
Hope this helped have a good day!
The LA Dogers hit the most home runs in 2014. The number of home runs accounted for 6% of the entire major league Baseball home run count.If 583 total home runs were hit, then how many did the LA Dogers hit
Given:
Total number of home runs = 583
Home runs hit by LA Dogerse = 6% of the total home runs
To find:
The number of home runs hit by LA Dogers.
Solution:
We have,
Home runs hit by LA Dogerse = 6% of the total home runs
[tex]=\dfrac{6}{100}\times 583[/tex]
[tex]=\dfrac{3498}{100}[/tex]
[tex]=34.98[/tex]
[tex]\approx 35[/tex]
Therefore, LA Dogerse hits about 35 home runs.
2x to the power 2 minus 5x+6 X=-2
Answer:
=(x-2)(x-3)
Step-by-step explanation:
This is what I got. I hope this can help you.
A scientist measures the temperature of a chemical solution. At the start of the experiment, the solution is at a temperature of -14.06*C. TH decreases 2.9°C each hour. What is the temperature of the solution after 3 hours, rounded to the nearest whole degree?
Answer:
T(3) = -23°C
Step-by-step explanation:
Constant Rate of Change
Given an initial condition of a variable T, To and a constant rate of change m, it's possible to write a model to predict the value of T in time t:
[tex]T(t)=T_o+mt[/tex]
The initial temperature the scientist measures of a chemical solution is To=-14.06°C.
It's known the temperature decreases at a constant rate of -2.9°C each hour, thus the model is:
[tex]T(t)=-14.06-2.9t[/tex]
Evaluating at t=3 hours:
[tex]T(3)=-14.06-2.9\cdot 3[/tex]
[tex]T(3)=-14.06-8.7[/tex]
T(3) = -22.76°C
Rounding to the nearest whole degree:
T(3) = -23°C
What should the following equation be multiplied by in order to eliminate the fractions? x/2 + x/3 = 25/3
25
9
5
6
Answer:
6
Step-by-step explanation:
1 = 5x + 2; w = x^2 + 1
Can someone help me with this question?;(
Answer:
5x^3 + 5x+ 2x^2 + 2
Step-by-step explanation:
(5x+2)(x^2+1)
5x^3 + 5x+ 2x^2 + 2
Hi can someone help me please!
I’ll mark the first person to answer brainliest
1. Multiply using distributive property.
(4x - 2)(x - 3)
Please help me answer.
Answer: 4x-6
Step-by-step explanation: Combine like terms. 4x*x is 4x and -2*-3 is -6. That is how you find the answer.
Answer:
4x²-14x+6
Step-by-step explanation:
(4x · x - 4x ·3 - 2·x + 6) = 4x²-14x+6
What is the slope of the line that contains the points (4,3) and (2, 7)? A. - 5 B. 2 C. -2 O D. -5
Answer:
C. -2
Step-by-step explanation:
hope that helps! :)
s = ut + 1/2at squared
u = 10 a = -2 t = 1/2
Answer: 4.75
with u = 10, a = -2, t = 1/2
=> [tex]s=10.\frac{1}{2}+\frac{1}{2}. \frac{(-2).1}{4}=5-\frac{1}{4}=\frac{19}{4}=4.75[/tex]
Step-by-step explanation:
anyone stressed?? vent to me. and (so this will count as a question)
Laura earns $115 a month babysitting. If she saves all of the
money she earns in June and July and uses it to buy a bicycle
that cost $158, how much money will she have left?
A. $230,00
B. $43.00
C. $60.00
D. $72.00
Answer:72
Step-by-step explanation:
115+115=230
230-158=72
If you add the 115 a month that she earns from babysitting, then add both the months pay together, than subtract 158(cost of the bicycle) by the total pay, you should get 72$
Answer: D. $72
Step-by-step explanation:
If she earns $115 a month and June and July is a combination of two months then we will have to find the amount she earn toegther in June and July by multiplying 2 by $115.
2(115) = 230
She earned $230 in those months, and if the bicycle cost $158 , then we will have to subtract $158 from $230 to find her remaining amount.
$230 - $158 = $72
What is 35/4 simplified, or as a mixed number
Answer:
8 3/4
Step-by-step explanation:
Please help me BRAINLEST!
3x - 4y = 32
5x+2y = 10
Answer:
Point Form: ( 4 , − 5 )
Equation Form: x = 4 , y = - 5
Step-by-step explanation:
Solve for the first variable in one of the equations, then substitute the result into the other equation.
Point Form: ( 4 , − 5 )
Equation Form: x = 4 , y = - 5
Answer:
(4, - 5)
Step-by-step explanation:
3x - 4y = 32 ........ (1)
5x + 2y = 10 ....... (2)
(2) × 2 + (1)
13x = 52 ⇒ x = 4
3(4) - 4y = 32 ⇒ y = - 5
(4, - 5)
What is the same value as 40% of 84 ??
Answer:
33.6
Step-by-step explanation:
thats what 40% of 84 is x.
Answer: 33.6
explanation: Convert 40% to a decimal and multiply that number by 84