the limit of the ratio of the total sales to time is equal to the product of the arrival rate and the mean amount spent by a customer.
Let ti be the time between successive customers who are served. Then ti is the sum of the time spent by the customer being served (si) and the time until the next customer arrives (exponentially distributed with rate λ). Thus, we have ti ~ F + Exp(λ).
Now, let Ni be the number of customers who arrive during the i-th interval [ti-1, ti]. Then, Ni ~ Poisson(λ ti). Also, the total sales during this interval is the sum of the sales of the Ni customers who arrived during this interval. Therefore, the total sales during [ti-1, ti] is a random variable given by:
Si = ∑j=1 to N i Wj
where Wj denotes the random amount of money spent by the j-th customer. Since the Wj are independent and identically distributed, we have E(Si | Ni) = Ni μw.
Using the law of total probability, we have:
E(Si) = ∑k=0 to ∞ E(Si | Ni=k) P(Ni=k)
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= ∑k=0 to ∞ k μw P(Ni=k)
= λti μw
Now, let Tn = ∑i=1 to n ti be the time of the nth customer arrival. Then, W(tn) is the total sales up to time Tn. Therefore, we have:
W(tn) = S1 + S2 + ... + Sn
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= ∑i=1 to n Si
Taking the expectation of both sides and using the linearity of expectation, we get:
E(W(tn)) = ∑i=1 to n E(Si)
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= λ ∑i=1 to n ti μw
= λ Tn μw
Dividing both sides by tn, we get:
W(tn)/tn = (λ Tn μw)/tn
Now, taking the limit as tn → ∞, we get:
limt→∞ W(t)/t = λ μw
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One number is 6 less than 5 times the other number. Their sum is 60. Find the numbers.
Answer:
The numbers are 11 and 49.
Step-by-step explanation:
x = 5y - 6 This is just the first sentence written as an equation.
x + y = 60 This is just the second sentence written as an equation.
5y - 6 + y = 60 Substitute x for what you know it is equal to
6y - 6 = 60 Collect like terms
6y = 66 Add 6 to each side
y = 11 Divide each side by 6
x = 5 × 11 - 6 Substitute y for what you know it is
x = 55 - 6 Simplify by working out 5 × 11 = 55
x = 49 Subtract 6 from 55 to get 49
Substitute t = 3 and t = 6 to determine if the two expressions are equivalent.
3 (2 t + 5) 6 t + 15
Which statements are true? Select the three correct answers.
The value of both expressions when t = 3 is 33.
The value of both expressions when t = 3 is 23.
The value of both expressions when t = 6 is 41.
The value of both expressions when t = 6 is 51.
The two expressions are equivalent.
The two expressions are not equivalent.
Answer:
If t= 6
3 (2 x 6 + 5) 6 x 6 + 15
3 (12+5) 36 + 15
3 x 17 =51
= 51
The value of both expressions when t=6 is 51
When t = 3
3(2 x 3 + 5) 6 x 3 + 15
3 (6 +5) 18 + 15
3 x 11 =33
= 33
The value of both expressions when t= 3 is 33
Step-by-step explanation:
Step-by-step explanation:
Answer:
Explanation You Welcome Broski:It is A, D, and E Hope that is helpful...: ^ )
Also Give me a good rating to please
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9+9+9= (Forever)
999 Forever...PLS HELP MEEEEEE IM SO STUCK
Answer:
497 inches²
Step-by-step explanation:
Hi!
I have never done a problem like this in my life but I see exactly how it is meant to be solved. Lets try it out.
Let us first remind ourselves of the formulas we need for this.
Formula for a circle and the formula for a triangle.
Circle :
A = [tex]\pi[/tex] x r²
(or Area = pi x radius²) (Note that [tex]\pi[/tex] = 3.14)
Triangle :
A = b x h x 1/2
(or Area = base x height x 1/2)
Now lets see what the question wants from us and what we are given :
Gives us :
Diameter XY = 30 inches
YZ = 20 inches
XZ = 21 inches
And it wants the total area of the shaded regions to the nearest square inch. (Inches²)
Alright so first lets solve this triangle :
We need to do Base x Height x 1/2 :
Input your numbers given :
Base = 21in
Height = 20in
And lets multiply this out :
Base x Height x 1/2
21 x 20 x 1/2
21 x 20 gives us 420
Now we have :
420 x 1/2
Note that this is literally saying it wants half of 420. So we can actually just make it easier and do :
420/20
This gives us 210.
Great! Now we have the area of the triangle which is 210, this will be important later but for now lets move onto the circle.
Alright so we need radius to solve this but it really doesn't give us much about the circle.
But...
If you take a look at ∠YX you can see that it says 30in. This is actually the diameter of the circle and we can use this to find the radius of the circle.
The radius of a circle is 1/2 of the diameter.
And the diameter of a circle is 2 × the radius.
So in this case to find the radius we can actually take the 30inch diameter and divide it by 2 to find our radius.
30/2
=
15
Radius = 15inches!
Now lets look back to our wonderful circle formula.
A = [tex]\pi[/tex] x r²
or if we write it out :
Area = pi x radius²
So now lets plug in the radius we found and then solve to find the area of this circle.
Area = pi x 15²
(Don't forget the tiny 2 next to the 15!)
Now we can multiply this :
pi x 15²
=
706.858347058
Round to the nearest square inch :
707 inches²
(pi = [tex]\pi[/tex])
So now what we have is the area of both shapes. It is smooth sailing from this point on. Let us recap :
Triangle Area = 210 inches²
Circle Area = 707 inches²
Now we have to find the area of the shaded area which is really simple subtraction.
The shaded area is the circle but the triangle is overlapping this shaded area so all we have to do is subtract the triangles area from the circles area so all that will be left is the shaded area of the circle.
So we do :
Circles area - Triangles area = Our answer
707 - 210 = 497
There we go!
Our answer is 497 inches²
This took a minute I am sorry about that but I hope this helps!
If you have any other questions please let me know.
Could you help me please ?
Answer:
Step-by-step explanation: The quotient is 20
How many degrees is Angle 1?
1
1
30
80
Answer:
angle 1 is 30 degrees
Answer:
80 is the correct ansqer
Please help! I've looked everywhere!
Answer:
[tex]\frac{a^{2} }{4}[/tex]
Step-by-step explanation:
2[tex]\sqrt{2x}[/tex] = a
Divide both sides by 2.
[tex]\sqrt{2x}[/tex] = [tex]\frac{a}{2}[/tex]
Square both sides.
2x = ([tex]\frac{a}{2}[/tex])²
= [tex]\frac{a}{2}[/tex] × [tex]\frac{a}{2}[/tex]
2x = [tex]\frac{a^{2}}{4}[/tex]
What is the measure of arc HT?
Answer:
step 1. mHT = 2(74) = 148°. the arc measures twice the angle when crossing the circle.
A population of 30 deer are introduced into a wildlife sanctuary. It is estimated that the sanctuary can sustain 600 deer. The population would grow by 30 percent per year
Complete question :
A population of 30 deer are introduced into a wildlife sanctuary. It is estimated that the sanctuary can sustain 600 deer. The population would grow by 30 percent per year
how many after one year
how many after two years
Answer:
39 deers
51 deers
Step-by-step explanation:
The question can be expressed using the compounding rate formula:
A = P(1+r)^t
A = final population ; P = initial population ; rate, r = 30% = 0.3 ; t = time
After 1 year, t = 1
A = 30(1 + 0.3)^1
A = 30(1.3)^1
A = 39 deers
B.)
After 1 year, t = 2
A = 30(1 + 0.3)^2
A = 30(1.3)^2
A = 50.7
A = 51 deers approximately
Charlotte has 85 stickers. Her brother has x times more stickers than her. Write
an expression to show how many stickers her brother has.
?
Step-by-step explanation:
Her brother has 85 * x stickers.
if an object has a volume of 20 cubic inches and weights 28ounces what is the constant variation
Answer:
7/5 is the constant variation.
Hope this helps! Have a great day!
Please help for 18 points
Answer:
9 per game.
Step-by-step explanation:
45y/5x
I'm not so sure what the equation would look like
Answeerrrrr asapppooaoaoaoao please need helppppp
Answer:
1a. Yes
1b. No
1c. Yes
Step-by-step explanation:
Answer:
1a. 2/5 x 25 = 50/5 = 10 and 10 = 10 so yes
1b. 5 + 5 = 10 10 does not equal 15 so no
1c. 5 x 5 = 25 and 25 = 25 so yes
please Help me i'm timed
Answer:
X=28
Step-by-step explanation:
4x+248=360
112=4x
x=28
Answer:
28
Step-by-step explanation:
which of the follow expressions are equivalent to (3^4)^-2 • (3^5)^3
Answer:
3^7
Step-by-step explanation:
Answer:
3^7
Step-by-step explanation:
(3^4)^-2 • (3^5)^3 = 2187
3^7 = 2187
17 >n +4
I rlly need help now
Answer:
n=13
Step-by-step explanation:
Step 1: Flip the equation.
Step 2: Subtract 4 from both sides.
I need help on this homework
Answer:
The answer is y=-2x^2-8x+1
Step-by-step explanation:
I used an app called desmos and just plugged in the equation till i got the answer that looked like the image u gave.
Hope this helps
Sorry if not
Plz give brainliest
help help help quick
The question is in the picture
Hello please help me answer :)
( WILL GIVE BRAINLST)
Answer:
Answer is given
:) mark me brainliest
please help me on this will give you brainliest
The pet store has an abundance of birds and fish and is selling them at a great price there are 230 of these pets in the store the cost for a bird is $9 and the cost per fish is $4 the store sold all the pets in a weekend blow out sale and made $1060 how many of the pets were birds and how many were fish? Equation for pets? Equations for cost?
Answer:
a) How many of the pets were birds and how many were fish?
Number of birds = x = 28
Number of fish = y = 202
b) Equation for pets?
x + y = 230....... Equation 1
c) Equations for cost?
9x + 4y = 1060...... Equation 2
Step-by-step explanation:
The pet store has an abundance of birds and fish and is selling them at a great price there are 230 of these pets In the store the cost for a bird is $9 and the cost per fish is $4 the store sold all the pets in a weekend blow out sale and made $1060 how many of the pets were birds and how many were fish? Equation for pets? Equations for cost?
Let us represent:
Number of birds = x
Number of fish = y
The pet store has an abundance of birds and fish and is selling them at a great price there are 230 of these pets
x + y = 230....... Equation 1
x = 230 - y
In the store the cost for a bird is $9 and the cost per fish is $4 the store sold all the pets in a weekend blow out sale and made $1060
$9 × x + $4 × y = $1060
9x + 4y = 1060...... Equation 2
We substitute 230 - y for x
9(230 - y) + 4y = 1060
2070 - 9y + 4y = 1060
Collect like terms
- 9y + 4y = 1060 -2070
-5y = -1010
y = -1010/-5
y = 202
Solving for x
x = 230 - y
x = 230 - 202
x = 28
Therefore,
Number of birds = x = 28
Number of fish = y = 202
Leo's bank balances at the end of months 1, 2, and 3 are $1,700.00, $1,734.00, and $1,768.68, respectively. The balances form a geometric sequence. What will Leo's balance be after 8 months? Leo's bank balance will be $ after 8 months.
Answer:
i think it$1,991.82. this is what i got.
Step-by-step explanation:
Find the standard deviation of the data set below. Round to the nearest tenth,
6, 5, 2, 5,8
What is the slope of the line that passes through the points (-1,-10) and (-1,-2)?
Answer:
Infinite; no slopeStep-by-step explanation:
Because both points have -1 as X they are both located on the same line
This gives them no slope
Maricella plots two ordered pairs on the grid below.
On a coordinate plane, points are at (6, 2) and (8, 6).
The line segment is extended to cross both axes. What is the location of the y-intercept on the line?
(0, –22)
(0, –10)
(0, –5)
(0, 5)
Answer:
(0, -10)
If you graph the points and follow where the line would go, then it would hit these coordinates.
Answer:
(0,-10)
Step-by-step explanation:
How many more people like to swim than hike?
Show how you added or subtracted to find the answer
The number of people who likes to swim than hike is given by the equation A = 2 people
What is an Equation?Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.
It demonstrates that the expressions on the left and right sides are connected in the same way.
An equation has components like as coefficients, variables, operators, constants, terms, expressions, and the equal to sign. The "=" sign and terms on both sides are required when generating an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the number of people who likes to swim be s= 4 people
Let the number of people who likes to hike be h = 2 people
Let the number of people who likes to bike be b = 3 people
Now , the equation will be
The number of people who likes to swim than hike A = number of people who likes to swim - number of people who likes to hike
The number of people who likes to swim than hike A = s - h
The number of people who likes to swim than hike A = 4 - 2
The number of people who likes to swim than hike A = 2 people
Hence , the number of people who likes to swim than hike is A = 2 people
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suppose the company's cost per 1 gallon is $2.70 what is the markup if they sell each gallon at $3.20 then what is the markup if they sell each gallon at $3.50
Answer:
A= 50cents markup B=80 cents markup
Step-by-step explanation:
U just subtract the markup by 270 then bam
ppppppllease help meeeeee :)
WILL GIVE BRAINLIEST TO FIRST PERSON
The cost of a car rental is $40 per day plus $0.22 per mile. You are on a daily budget of $84. Write and solve an inequality to find the greatest distance you can drive each day while staying within your budget. Use pencil and paper. Find 2 other two-step inequalities with the same solutions.
Answer:
i think 24
Step-by-step explanation:
Answer:
$40 + $0.22x = $84
$0.22x = $44
x = 200 miles
The greatest distance you can travel is 200 miles
Brainly plz :))
When graphing a system of equations with INFINITE SOLUTIONS,
the SLOPES of the two lines will be__________.
Answer:
Step-by-step explanation:
Hgbuf7g