The expected waiting time is 1.2 minute
According the statement
We know that the kingman formula is
[tex]{ E(W) = \left ( \frac{p}{1-p} \right )\cdot \left ( \frac{ C_{a}^{2}+ C_{s}^{2} }{2} \right ) \cdot \mu_{s} }[/tex]
According to statement the mean value μs is 6 min.
Here the value of P is 6/36 = 1/6
And the value of ca and cs is 1
Substitute the values in formula then
[tex]{ E(W) = \left ( \frac{0.17}{1-0.17} \right )\cdot \left ( \frac{ 1^{2}+ 1^{2} }{2} \right ) \cdot \m6} }[/tex]
[tex]{ E(W) = \left ( \frac{0.17}{0.83} \right )\cdot \left ( 1 ) \cdot \m6} }[/tex]
[tex]{ E(W) = \left ( 0.20} \right )\cdot \left ( 1 ) \cdot \m6} }[/tex]
[tex]{ E(W) = 1.22[/tex]
So, the expected waiting time is 1.2 minute
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A rectangular plot is to be fenced off and divided into three parts/plots on land that borders a barn. If you do not fence the side along the barn, find the length and width of the plot that will maximize the area if you have 200 feet of fence. What is the largest area that can be enclosed
5000 square feet is the largest area that can be enclosed
It is given that a rectangular plot is to be fenced off and divided into three parts/plots on land that borders a barn there are and there is 200 feet of fence that is available.
One-fourth of the perimeter = 50
The other width also equals 50.
So the length of fencing = 200 - 50 - 50 = 100
So the area = 50 x 100 = 5000 square feet.
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Find a 95% confidence interval for the mean amount of time spent on this ride. Round the values in your confidence interval to two decimal places. The 95% percent confidence interval is
95% confidence interval is 1.96
A confidence interval is defined as the range of values that we observe in our sample and for which we expect to find the value that accurately reflects the population.
For 95% confidence interval, we will keep 95% area in the center and will divide the remaining area equally on both sides.
From Standard Normal table, P(-1.96 < Z < 1.96) = 0.95, i.e., there is a 95% probability that a standard normal variable, Z, will fall between -1.96 and 1.96.
Hence 95% percent confidence interval is 1.96
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Find the area of the shaded regions.
Answer:
Area = 84.8 cm²
Step-by-step explanation:
It appears that the line BO is equal to the radius. It also looks like the missing region is equal to 1/4 of the entire area. Therefore, to find the area of the shaded region, you need to (1) find the area of the entire circle and then (2) find the area of 3/4 of the circle.
Area of Circle:
r = 6 cm
A = πr²
A = π(6 cm)²
A = π(36 cm²)
A = 113 cm²
Area of Shaded Region:
Area (Entire Circle) x 3/4 = Area (Shaded Region)
113 cm² x 3/4 = 84.8 cm²
Given: AD∥BC and AB∥CD
Prove: AD≅BC and AB≅CD
Answer:
BC || AD and AB || CD (given)
∠BCA ≅ ∠DAC 2. As alt.interior angles with parallel lines
∠BAC ≅ ∠DCA 3. As alt.interior angles with parallel lines
AC ≅ AC (identity)
△ABC ≅ △CDA (ASA)
AB = CD (CPCT C)
x³/x=x²
FACTORISE this term .show the process as well.
first know it in a simple way
that,3-1=2 right so if we add base and numbers in power , because it has same base when x i.e x to the power 1 goes up
Step-by-step explanation:
x^3/x^1
now
x^3 *x^-1
x^3-1
x^2
proved
Simplify the following expression as a
monomial:
-8a8
———-
-2a7
Answer:
4a
Step-by-step explanation:
-8 / -2 = 4
a^8/a^7 = a^(8 - 7) = a
Answer: 4a
Two digit natural number whose sum is 5
When the tens place digit is x write in terms of x
The value of the given 2 digits number when the tens place digit is x write in terms of x is; 10x + y
How to find a two digit number?
We are given that the sum of a two digit number is 5.
Now, if the number is xy, then we can say that;
x + y = 5
Since x is the tens place digit, then we can say that the value of x is 10x and as such the value of the 2 digits is written as;
10x + y
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Find the measure of the angles indicated
Both angles have a measure of 125°.
How to find the measure of the angles?
Assuming the two horizontal lines are parallel, we know that the measure of the two indicated angles must be the same one.
Then:
-1 + 14x = 12x + 17
Now we need to solve this for x:
14x - 12x = 17 + 1
2x = 18
x =18/2 = 9
Now that we know the value of x we can replace it in any of the expressions for the angles:
-1 + 14*9 = 125°
Both angles have a measure of 125°.
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The number y of objects a machine produces is proportional to the time x (in minutes) that the machine runs. The machine produces five objects in four minutes.
a. Write an equation that represents the situation.
Hellllppp me please!!!!!!!!!!!
The equation that represents the situation will be 4y = 5x.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
The number y of objects a machine produces is proportional to the time x (in minutes) that the machine runs.
The machine produces five objects in four minutes.
Let y be the number of objects and x be the number of the minutes.
Then the equation that represents the situation will be
y = (5/4)x
4y = 5x
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Which of the following represents x = 1/3y written in general form?
The general form of the given equation is 3x-y=0.
The given equation is [tex]x=\frac{1}{3}y[/tex].
We need to write the given equation in a general form.
What is a general form of an equation?The general form of any equation contains the degree of variables in decreasing order. The general form of a linear equation is ax + b = 0.
That is, [tex]3x=y[/tex]
[tex]3x-y=0[/tex].
Hence, the general form of the given equation is 3x-y=0.
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please help me with math
The area of triangle BMN is 124.7 square centimeter.
What are similar triangles?Similar triangles are triangles that their corresponding angles are equal and the ratio of their corresponding lengths are equal. They are often similar When at least Two angles are equal or The ratio of any corresponding lengths are same.
Analysis:
AB = AC = BC = 50cm
AH = AC/2 = 50/2 = 25cm
From Δ ABH, using Pythagoras theorem to find BH.
[tex](BH)^{2}[/tex] = [tex](AB)^{2}[/tex] - [tex](AH)^{2}[/tex]
[tex](BH)^{2}[/tex] = [tex]50^{2}[/tex] - [tex]25^{2}[/tex]
[tex](BH)^{2}[/tex] = 2500 - 625
[tex](BH)^{2}[/tex] = 1875
BH = [tex]\sqrt{1875}[/tex] = 43.3cm
ΔBMN and BHC are similar,
so, BM/BH = MN/HC
BM/43.3 = 12/25
25BM = 12 X 43.3
BM = 519.6/25 = 20.78cm
Area of ΔBMN
= 1/2(MN)(BM) = 1/2 x 12 x 20.78 = 124.7 square centimeter
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Using a table of values, determine the solution to the equation below to the nearest fourth of a unit.
2-5x=2x - 3
=
OA. X 0.75
OB. x= -0.75
OC. x 1.25
OD. x= -1.25
2
The solution to the equation below to the nearest fourth of a unit is 0.75
Solving linear equationGiven the linear equation below expressed as:
2-5x=2x - 3
Collect the like terms
-5x - 2x = -3- 2
-7x = -5
Divide both sides by -7 to have:
-7x/-7 = -5/-7
x = 5/7
x = 0.75
Hence the solution to the equation below to the nearest fourth of a unit is 0.75
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Juan wants to change the shape of his vegetable garden from a square to a rectangle, but keep the same area so he can grow the same amount of vegetables. The rectangular garden will have a length that is 2 times the length of the square garden, and the width of the new garden will be 16 feet shorter than the old garden.
Answer:
The answer is 32
Step-by-step explanation:
Please help me with this geometry question, Im pretty sure you need to use SAS congruence rule
Congruent triangles are two or more triangles with the same length of sides and measure of internal angles. Thus the required proof is as shown below:
From the given diagram, it can be observed that:
AB = AC (similar property of two lines)
AC = AE (similar property of two lines)
Also,
m<A is a common angle to ΔABC and ΔADE
So that it can be concluded that;
ΔABC ≅ ΔADE (Side-Angle-Side property)
Thus since ΔABC ≅ ΔADE are congruent, then;
BC = DE (corresponding sides of congruent triangles)
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See below for the proof that sides BC and DE are congruent
How to prove the side lengths?The given parameters are:
AC = AE
AB = AD
∠BAD = ∠EAC
By the definition of congruence, side lengths marked with I are congruent and side lengths marked with II are congruent
From the attached figure, we have the following marks:
In triangle ABC,
AB = I and AC = II
In triangle ADE,
AD = I and AE = II
This means that two corresponding sides of ABC and ADE are congruent.
Since both triangles have a congruent angle, then the last corresponding sides are also congruent
i.e. BC = DE
Hence, sides BC and DE are congruent
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-8√147x simplify do you know how to answer this?
Answer:
-56√3x
Step-by-step explanation:
√147 = 7√3
-8(7√3x)
-56√3x
what is the relationship between the radius, surface area and volume of a cylinder?
Answer:
A cylinder's volume is π r² h, and its surface area is 2π r h + 2π r².
A drugstore sells vitamins in bottles with different pill counts. The price of each bottle is shown in the table below.
The price of one pill is approximately $0.04.
What is the price of one pill?Division is the mathematical operation used in grouping a number into equal parts using another number. The price of one pill can be determined by dividing the total cost of a number of pills by that number.
Price of one pill = cost of 50 pills / 50
$2.05 / 50 = $0.04
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3 men build a wall in 2 days.
How long will it take
a) 1 man
b) 2 men?
Please show working
Answer:
Step-by-step explanation:
Big clever stuff 100 men in 1 second tick tick boom
There are 210 rabbits at the farm. For every 5 gray rabbits, there are 2 white rabbits. How many white rabbits are at the farm
The number of white rabbits that are at the farm is 60
Calculating quantityFrom the question, we are to determine the number of white rabbits that are at the farm
From the given information,
There are 210 rabbits at the farm
and
For every 5 gray rabbits, there are 2 white rabbits
Then, we can write that
5x + 2x = 210
Where x is the number of groups of 5 gray rabbits and 2 white rabbits
Then,
7x = 210
x = 210/7
x = 30
The number of white rabbits is 2x
∴ Number of white rabbits = 2×30
Number of white rabbits = 60
Hence, the number of white rabbits that are at the farm is 60
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Therea re 8 kids at a birthday party. If there are 6 girls and 2 boys at the party, what draction of the kids are girls?
Answer:
3/4
Step-by-step explanation:
The total number of children is 8 and the number of girls is 6. This can be represented as 6/8.
You would then need to simplify...
6/2=3
8/2=4
which which lead you to 3/4!
Given the function g(x) = x^2 - 5x which statement is not correct ?
Hello,
g(x) = x² - 5x
g(-3) = (-3)² - 5 × 3 = 9 - 15 = - 6 ≠ 24 ⇒ not correct
g(-1) = (-1)² - 5 × (-1) = 1 - 5 = -4 ⇒ correct
g(5) = 5² - 5× 5 = 25 - 25 = 0 ⇒ correct
g(7) = 7² - 5 × 7 = 49 - 35 = 14 ⇒ correct
Lea wants to save money on a new computer. At the store near her, the computer she wants is listed at a regular price of $400.00.
On Saturday, the store will have a sale and discount the computer by 30%.
Shoppers who buy a computer that same Saturday before 9:00 a.m. will also receive an additional 10% off the sale price.
How much will Lea pay, without tax, when she buys the computer that Saturday before 9:00 a.m.?
Answer:
Step-by-step explanation:
you take 30% and 10% and turn them into decimal like so:
30/100=0.3
10/100=0.1
400.00(0.3)=120.00
120(0.1)=12
9r-4(-5r-5)<-9r+10+5
if a football player passes a football 4 feet off the ground with the velocity of 36 feet per second, how long will it take the football to hit the ground? Use the equation h=-16t^2+36t+4
The ball will hit the ground after 2.355 secs
Velocity of an objectThe velocity of an object the change of displacement with respect to time.
Given the function that represents the height of football ground
h(t) = -16t^2+36t+4
The ball will hit the ground at the point where the height h(t) = 0
Substitute
-16t^2+36t+4 = 0
16t^2-36t-4 =0
4t^2-9t-1= 0
Factorize
t = 9/8 + √97/8
t = 9/8 + 1.23
t = 2.355secs
Hence the ball will hit the ground after 2.355 secs
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What is the range of Y = l0g8X?
O all real numbers less than 0
O all real numbers greater than 0
O all real numbers not equal to 0
all real numbers
Step-by-step explanation:
all real numbers not equal to 0
all real numbers
Step-by-step explanation:
[tex]What \ is\ the \ range \ of \ y = log_8x?\\x > 0 \ or\ x\in(0;\infty).\\Answer: \ all \ real \ numbers \ greater\ than \ 0.[/tex]
The idea that you can empower players to seamlessly generate new content to a game continuously to keep the game fresh: Group of answer choices Loot boxes
User-generated content is the idea that you can empower players to seamlessly generate new content to a game continuously to keep the game fresh.
User-generated content (also known as UGC or consumer-generated content material) is original, emblem-particular content material created by customers and published on social media or other channels. UGC comes in many paperwork, inclusive of photos, films, opinions, a testimonial, or even a podcast.
User-generated content (UGC) has become an essential part of the content material advertising method within the present day era in which customers are prepared to rave about your products or services online. UGC refers to the content this is created through the users of a logo.
Types of User-Generated Content
Social media content.Reviews and testimonials.Blog posts.Video content (including live streaming and AR lenses/filters)Q&A Forums (including comments)Case studies.Learn more about User-Generated Content here https://brainly.com/question/20900221
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Multiply Conjugates Using the Product of Conjugates Pattern
In the following exercises, multiply each pair of conjugates using the Product of Conjugates Pattern
332. (5 − 3x)(5 + 3x)
Answer:
The product is the difference of squares is [tex]$$\left(5-3x\right)\left(5+3x\right)=25-9{{x}^2}$$[/tex]
Step-by-step explanation:
Explanation
The given expression is (5-3 x)(5+3x).We have to multiply the given expression.Square the first term 5. Square the last term 3x.[tex]$$\begin{aligned}&(5-3 x)(5+3 x)=(5)^{2}-(3 x)^{2} \\&(5-3 x)(5+3 x)=25-9 x^{2}\end{aligned}$$[/tex]
Create diagrams to represent the possible cases for common tangents between two circles. Your diagram can be created using multimedia sources or drawn by hand. They should not be copied and pasted from a website. Explain why your diagrams satisfy the given criteria.
No Common Tangents (10 points)
Diagram:
Justification:
The diagram to represent the possible cases for common tangents between two circles is as shown in the attachment.
How to Create Common Tangents?
A tangent line to a circle is defined as a line that touches the circle at exactly one point, never entering the circle's interior.
1. When one circle is in between another and one circle does not touch the other one, then tangent is not possible.2. When one circle is in between another and one circle touches the other one at a point inside the circle, then only one tangent is possible.3. When one circle intersects the other one, then two tangents are possible.4. When one circle touches the other one at a point outside, then three tangents are possible.5. When one circle neither intersects the other one nor inside the other one, then four tangents are possible.Thus, the diagram to represent the possible cases for common tangents between two circles are as attached below.
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A group of students and workers entering a metro station were asked whether they were riding the bus or the subway. The two-way table shows their answers.
How many people were polled?
A. 48
B. 69
C. 118
D. 166
Avery solves the equation below by first squaring both sides of the equation.
√z^2+8 = 1 -2z
What extraneous solution does Avery obtain?
z= ?
[tex]\left(\sqrt{z^{2}+8} \right)^{2}=(1-2z)^{2}\\\\z^{2}+8=4z^{2}-4z+1\\\\0=3z^{2}-4z-7\\\\0=(z+1)(3z-7)\\\\z=-1, z=\frac{7}{3}[/tex]
We know that if z=7/3, the right-hand side will be negative, which means it is an extraneous solution as square roots cannot be negative.