The expected waiting time to get a court is 8(k + 1).
What is expected time?
The projected time is simply the time frame in which the Project is anticipated to be finished. When the parties to the project contract are signing it, they will either mutually agree upon this time or decide it together with the participation of all the stakeholders, contractors, and clients.
They need to wait for k+1 pairs to finish before they can start.
Since the exponential distribution is memoryless, the expected time for a given pair to finish once started is 40 minutes, and there are 5 courts,
the expected time for any of the 5 courts to finish is 40/5=8 minutes, and so their expected waiting time is 8(k+1) minutes.
Hence, the expected waiting time to get a court is 8(k + 1).
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Simply the following expression. Show your work: 2(0.6x + 3/4 x + y)
Answer:
2.7x +2y
Step-by-step explanation:
Why because u distribute the 2 to get 1.2x + 1.5x + 2y. CBL and get
2.7x +2y
What is the slope of a line parallel to the line -1/2x=4y
Answer:
Step-by-step explanation:
Line 1: -3y = 2x + 6 Line 2: (2/9)y - 4 = (1/3)(x - 18)
A vegetable distributor knows that during the month of august, the weights of its tomatoes are normally distributed with a mean Of 0.62 lb and a standard deviation of 0.15.
A ) What percent of the tomatoes weight less than 0.77 lb?
B ) In a shipment of 8000 tomatoes can be expected to weight more then 0.32 lb?
C ) in a shipment of 3500 tomatoes how many tomatoes can be expected to weight from 0.32 lb to 0.92 lb
In a shipment of 3500 tomatoes can be expected to weight from 0.32 lb to 0.92 lb is 3340. When A vegetable distributor knows that during the month of august, the weights of its tomatoes are normally distributed with a mean Of 0.62 lb and a standard deviation of 0.15.
Define mean and standard deviation.A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed. In contrast, a high or low standard deviation indicates that the data points are, respectively, above or below the mean. A standard deviation that is close to zero implies that the data points are close to the mean. The standard deviation measures the degree of dispersion of a set of data. Each data point is compared to the average of all the data points, and standard deviation gives a determined value that indicates whether the data points are clustered together or dispersed. The standard deviation of a normal distribution indicates how far values deviate from the mean.
Given,
A vegetable distributor knows that during the month of august, the weights of its tomatoes are normally distributed with a mean Of 0.62 lb and a standard deviation of 0.15.
Normal variable of x = 0.32
Z = X - mean/ standard deviation
Z = 0.32 - 0.62/0.15
Z = -2
Now, normal variable of x = 0.92
Z1 = X - mean/ Standard deviation
Z1 = 0.92 - 0.62/ 0.15
Z1 = 2
Required area,
P(-2 ≤ z ≤ 2)
2P(0 ≤ z ≤2 )
2 × 0.4772
0.9542
Weight of 3500 tomatoes
3500 × 0.9542
3340
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How do you solve a function easy?
Function can be solved easily by f(x)= mx + c.
function
A function produces one output per input. Learn about function notation, tables of values, and more.
Function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
A function is uniquely represented by the set of all pairs (x, f (x)), called the graph of the function, a popular means of illustrating the function. When the domain and the codomain are sets of real numbers, each such pair may be thought of as the Cartesian coordinates of a point in the plane.
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Part B: Fill out the Problem-Solving boxes to talk yourself through the problem.
Two mountain bikers leave from the same parking lot and head in opposite directions on two different trials. The first rider goes 8km due East, then rides due south for 15km. The second rider goes 8km due West, then changes direction and rides 20 degrees west due North for 15km. (See the picture below.) Both riders have been traveling for 23km, but when they stopped, which one was further away from the parking lot?
Understand & Think (1 point): What is being asked in the problem? What do I know and what does it mean? What plan am I going to try?
Do/Answer (2 points): I will write out my response to the question, explaining my answer and what it means. I will explain why my answer makes sense.
Explanation of my answer why it makes sense:
PLEASE HELP AND TRY NOT TO MAKE IT SOUND SO COMPLICATED… THANKS AND MUCH APPRECIATED!!!
The first rider the displacement is, 17 km.
And the 2nd river the displacement is 20.22 km.
What is right triangle?
A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and other angles of the right triangle.
It is asked in this problem is who's displacement is greater (not distance) it means that the shortest distance of starting and ending point with direction from start and end.
Here we have two triangle with two arm know for both.
So we have to find the 3rd arm for both triangle.
Now we have for a right triangle
a^2 + b^2 = c^2
For other triangle we know the cosine law of triangle is,
a^2 + b^2 - 2ab cosθ = c^2
θ is the opposite angle of c
For the first rider the displacement is,
[tex]c = \sqrt{a^2 +b^2} = \sqrt{8^2 + 15^2} = 17 km[/tex]
For the 2nd river the displacement is
[tex]c = \sqrt{a^2 + b^2 - 2abcostheta}[/tex] θ = 120°
[tex]c = \sqrt{a^2 - b^2 - 2ab cos(120)} \\c = \sqrt{(8^2 + 15^2 - (2*8*15cos(120))} \\c = \sqrt{289 - 240 cos(120)} \\c = \sqrt{289- (-120)} \\c = \sqrt{409}\\ c = 20.22 km[/tex]
Hence, the first rider the displacement is, 17 km.
And the 2nd river the displacement is 20.22 km.
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Select all the correct answers.
Which expressions are equivalent to the given expression?
√80
O 160
04√10
0 4√5
80 %/
0 8√5
The expression that is equivalent to the given expression is 4√5.
What is simplification?
Simplifying procedures is one way to achieve uniformity in work efforts, expenses, and time. It reduces diversity and variety that is pointless, harmful, or unnecessary.
Here, we have
Given: √80
We have to find which expressions are equivalent to the given expression.
For this, we first evaluate all options and see which option is suitable for the given expression.
160 ≠ √80
4√10 = 16 ×10 = 160 ≠ √80
4√5 = 16 × 5 = √80
8√5 = 64 × 5 ≠ √80
Hence, the expression that is equivalent to the given expression is 4√5.
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During a stock clearance sale the shopkeeper gave a discount of 20% on sandals what will be the sale price of sandals if it’s marked price is rupees 560
Already ask and answered
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Can Someone Solve This By Using The Formula a^2+b^2=c^2
Answer: 24 cm
Step-by-step explanation:
51cm is the hypotenuse, so that it will be C in the equation!
45^2 + b^2 = 51^2
2025 + b^2 = 2601
b^2 = 576
b = 24 cm
y= 1/4 x+6 graph the line
Note that this line is in form y = mx + b, where b is the y intercept and m is the slope.
Y intercept is the value of y at x = 0
The function starts at y = 6
Slope is 1/4, meaning that for every 4 x the line travels, it goes up 1.
This is what the graph would look like:
(see image)
Hope this helps :)
If you need any more explanation, feel free to ask. If this really helps, consider marking brainliest.
- Jeron
a city has a population of people. suppose that each year the population grows by . what will the population be after years? use the calculator provided and round your answer to the nearest whole number.
After six years, the population will grow to 586,455 if compounded annually at a rate of 7.5%.
This is exactly like a compound interest problem where the interest rate is 7.5% compounded annually for 6 years.
If we use the compound interest formula A = P(1+r/n)nt where A is the end amount to be found, p = initial amount (p= 380,000), n = number of times the interest is compounded annually (n= 1) and t is the time in years (t=6)
A = 380,000(1 + .075/1)1(6)
A = 380,000(1.075)6
A = 586,454.58 people
Rounded to the nearest whole number
the population after 6 years should be
586,455 people
Hence we get the required answer.
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Your question is incomplete. Please find the missing content below.
A city has a population of 380,000 people. suppost that each year the population grows by 7.5%. what will be the population after 6 years.
If f (x) = 2 x + 5 and three-halves are inverse functions of each other and f(x)=2+5 what is
f-1(8)
The inverse function [tex]f^{-1}[/tex](8) = 3/2
What is an Inverse function ?A function that "undoes" another function is known as an inverse in mathematics. In other words, if f(x) produces y, then introducing y into the inverse of f produces x. An invertible function has an inverse, which is represented by the symbol.[tex]f^{-1}[/tex]
The function given is
f(x) = 2x + 5
We have to find the inverse
Let us consider f(x) as y
y = 2x + 5
Now by replacing x to y and y to x
x = 2y + 5
By solving for y and replacing f-1(x)
2y = x - 5
y = (x - 5)/2
[tex]f^{-1}[/tex](x) = (x - 5)/2
We have to find [tex]f^{-1}[/tex](8)
[tex]f^{-1}[/tex](8) = (8 - 5)/2 = 3/2
So
The inverse function [tex]f^{-1}[/tex](8) = 3/2
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a medical institution requests 1 g of bismuth-214, which has a half life of 20 min. how many grams of bismuth-214 must be prepared if the shipping time is 2 h?
Medical institution 64 grams of bismuth-214 must be prepared.
What is medical institution?A medical institution is a facility in which medical care is provided. It can be a hospital, clinic, nursing home, or other type of health care facility. Medical institutions provide a wide range of services including diagnosis, treatment, and preventive care. In addition to providing direct patient care, they also provide educational opportunities, research, and administrative services. Medical institutions are staffed by a variety of healthcare professionals such as doctors, nurses, allied health professionals, and administrative staff. They are responsible for providing quality care to their patients and ensuring the safety and wellbeing of their staff and visitors.
Given: 2 hours = 20 minutes
If each half life is 20 minutes, and 2 hours (120 minutes) go by,
then n = 6 ( [tex]\frac{120}{20}[/tex] )
The setup is as follows:
[tex]1g=m_{i}(\frac{1}{2}) ^{\frac{120}{20} }[/tex]
[tex]1g=m_{i}(0.015625)[/tex]
[tex]\frac{1}{0.015625} =64g[/tex]
Hence, 64 grams of bismuth-214 must be prepared if the shipping time is 2 hours.
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Please helpp 20 points
What graph goes to the inequality
x < 3 or x > 6
In photo
Answer: A :)
Step-by-step explanation:
let f be a function of two variables that has continuous partial derivatives and consider the points a(8, 3), b(12, 3), c(8, 10), and d(14, 11). the directional derivative of f at a in the direction of the vector ab is 4 and the directional derivative at a in the direction of ac is 15. find the directional derivative of f at a in the direction of the vector ad. (round your answer to two decimal places.) 18.16 incorrect: your answer is incorrect.
Therefore the directional derivative of f at a in the direction of the vector ad is grad F( x, y ) ×ad(u) =64/10
What is directional derivative ?Any function's rate of change at a given location in a fixed direction is known as its directional derivative. Any derivative is thought of in this way: as a vector form. It provides information on the function's immediate rate of variation.
Here,
The terms "directional derivative" and "gradient of a function" must be used in order to respond to this question.
Grad F(x, Y) = 64/10 ad(u)
A function's gradient is a vector with the following definitions:
Grad f(x,y) is equal to f(x,y)/x I + f(x,y)/y j.
where the definition of the directional derivative in the direction of ab is
Grad f(x,y) = Uab(u), where Uab is a unitary vector pointing in the direction of ab.
Consequently, Uab (u) = Uab/|ab|
If f (x,ydirectional )'s derivative in the direction of vector ab is 5, then.
A (7, 3), B (12, 3), and vector ab is then:
ab = [ 12 - 7 , 3 - 3 ] ⇒ ab = [ 5 , 0 ] as well as |ab| = (5)2 (0)2 |ab| = 5
a unitary vector in the direction of ab is:
ab(u) = 5×i/ 5 and according to equation (1)
δf(x,y) / δx × i × 5 × i / |5| = 5
δf(x,y) / δx × i × 5 × i = 25
δf(x,y) / δx = 5 then f( x,y ) = 5 × x + ????
We go on to calculate the component on j of f(x,y)
Following the same procedure
ac = ( 7 , 7 ) - ( 7 , 3 ) ⇒ ac = [ 0 , 4 ] |ac| = √(4)² + (0)²
|ac| = 4
In the direction of ac(u), the unitary vector is:
ac/|ac| = 4 × j / 4
Then :
j / 4 + f(x,y) / y = 4
16 is equal to f(x,y) / y j + 4 j.
both f(x,y) = -4y & f(x,y) / y = - 4
f(x,y) = 5 × I + 4 × j
Finally:
((15 - 7, 9 - 3)) as the vector ad ⇒ ad = ( 8 , 6 ) ( 8 , 6 )
a unitary vector in the direction of
ad(u) = (8 ×i + 6 ×j) / √ (8)² Plus (6)
² ⇒ ad(u) = (8 ×i + 6 ×j) /√ (8)² + (6) ²
ad(u) = (8 ×i + 6 ×j) /10
Currently, we have f (x, y) = 5 I + 4 j and ad(u) = 8 I + 6 j /10.
We can calculate the directional derivative of f(x,y) in the direction of ad with the use of equation (1)
grad F( x, y ) ×ad(u) = ( 5 × i + 4 × j ) × ( 8 ×i + 6 ×j ) /10
grad F( x, y ) ×ad(u) = 4 + ( 24/10)
grad F( x, y ) ×ad(u) =64/10
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Grey said he is thinking of a mystery number. The number is between 20 and 30, and it has exactly 3 factors. What is Grey's mystery number?
Answer:
25
Step-by-step explanation:
Let x be the mystery number.
The minimum number of factors a number can have is two:
1 and the number itself.(These numbers are called prime numbers).
If a number has exactly 3 factors, it must be an perfect square number since every perfect square has an odd number of factors and any number that is not a perfect square will have an even number factors..
Odd square numbers between 20 and 30:
25Factors of 25: 1, 5 and 25.
Therefore, Grey's mystery number is 25.
Proof:
Factors of 20: 1, 2, 4, 5, 10 and 20.Factors of 21: 1, 3, 7 and 21.Factors of 22: 1, 2, 11 and 22.Factors of 23: 1 and 23. (23 is a prime number)Factors of 24: 1, 2, 3, 4, 6, 8, 12 and 24.Factors of 25: 1, 5 and 25.Factors of 26: 1, 2, 13 and 26.Factors of 27: 1, 3, 9 and 27.Factors of 28: 1, 2, 4, 7, 14 and 28.Factors of 29: 1 and 29. (29 is a prime number)Factors of 30: 1, 2, 3, 5, 6, 10, 15 and 30.If x ≥ 0, then x+|x| =
The best and most correct answer is 2x greater then zero which satisfy the condition.
What is the absolute value function?The absolute value function is defined by the following piecewise rule, depending on the input of the function:
If x ≥ 0, then we need to find x+|x|
Since {x | x < 0} and {x | x > 0} there is no number that is less than zero and greater than zero at the same time.
WE need to add here;
x+|x| = 2x
Therefore, we can see that 2x is greater then zero which satisfy the condition.
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How to solve the following
9^2x+1 = 27^x-3
Answer:
To solve this equation, we can first rewrite it in a form that is easier to work with. We can do this by dividing both sides by 9^2, which gives us:
(9^2x+1)/9^2 = 27^x-3
We can then simplify the left side of the equation by taking the square root of both sides, which gives us:
3x+1/3 = 3^x-3
We can then rearrange the terms on the left side of the equation to get:
3x = 3^x-6
We can then subtract 3^x from both sides of the equation, which gives us:
3x-3^x = -6
We can then divide both sides of the equation by 3-3^x, which gives us the final solution:
x = -6 / (3-3^x)
This is the value of x that satisfies the original equation.
Step-by-step explanation:
What is the slope percentage of 1 12?
The slope percentage of the given ratio i.e. 1:12 is 83.33%.
You can determine the slope percentage by dividing the elevation change by the horizontal distance covered (sometimes called "the rise divided by the run") and multiplying the result by 100. The "run" assumes a flat surface - it doesn't account for elevation change when factoring in the actual distance traveled.
Example: let’s assume a mountaineer climbs 1,000 feet in altitude (the rise) and the horizontal distance measured on the map is 2,000 feet (the run).
thus, 1,000/2,000 = 0.5
Multiply 0.5 by 100 to derive the percent of the slope, which is 50%.
Hence, the slope percentage of 1:12 is = (1/12) x 100
= 8.33 x 100
= 83.33 %.
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The complete question is -
What is the slope percentage of 1:12?
under what conditions might someone be more rational? multiple choice question when provided likelihoods as percentages. when provided probability information. when provided frequency information. when provided less information.
The condition under which someone becomes more rational is when someone provided probability information.
Probability gives information about the likelihood that something will occur. For instance, weather patterns are used by meteorologists to predict the possibility of rain. Probability theory is utilized in epidemiology to comprehend the connection between exposures and the risk of health outcomes.
Everyday existence heavily relies on probability. In the analysis of political strategies, the determination of blood types, sports and gaming strategies, purchasing or selling insurance, online shopping, and online games.
Thus, having knowledge about probability makes someone more rational.
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It takes a cyclist 44 minutes to cycle a distance of 11 km. (a) How long will it take him to cycle a distance of (i) 45 km,
Answer:180 minutes
Step-by-step explanation:
Ethan buys a video game on sale. if the video game usually costs $39.99, and it was on sale for 20% off, how much did ethan pay? round to the nearest cent.
The required amount that Ethan have to pay is $32.
What is discount on sale?A sales discount is a marked down cost presented by a business on an item or administration. Figure out how to remember limits for solicitations. A deals rebate, likewise usually known as only a 'markdown' furnishes clients of a business with a diminished rate on at least one of the items or administrations being advertised.
According to question:We have,
Selling price = $39.99
Discount = 20%
20% of $39.99 = 20×$39.99/100
⇒ $7.99
So the payable amount for video game = $39.99 - $7.99
⇒ $32
Thus, required price is $32.
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Which congruence theorem can be used to prove △mlq ≅ △npq? aas sss asa sas
The SSS( Side-Side-Side) Congruance theorem can be used to prove that
△MLQ ≅ △NPQ.
So, The correct option is option (B).
We have given that,
The above figure shows three triangles .
Also, MQ = NQ
Q is mid point of Side LP .
or LM~= PN => LM = PN
we have to show that △MLQ ≅ △NPQ
Mid point is defined as a point which divide the side into to equal parts i.e if P is mid point of AB then AP = BP.
Using this fact , we have
LQ = QP --(1) ( because Q is mid point)
MQ = NQ (given)
LM = PN ( given)
That's we see that all three sides of triangle are
equivalents to corresponding sides of second triangle.
Therefore, these two triangles are congruent by SSS rule of congruance, i. e △MLQ ≅ △NPQ.
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Complete Question
Given: MQ = NQ; Q is the midpoint of LP; LM ≅ PN
Which congruence theorem can be used to prove △MLQ ≅ △NPQ?
a) AAS
b) SSS
c) ASA
c) SAS
How do you find the domain and range of a line graph?
The method to find the domain and range of the line graph is shown below .
In the question ,
we have to explain how we can find the domain and range of a line graph that is linear function .
we know that ,
Domain is the set of all possible input values , which produce a valid output from a particular function. It is set of all values for which the function is mathematically defined.
For Example ,
let the linear function be ⇒ f(x) = 2x + 1 ,
for the function every real number is a possible input .
thus , function's domain is all real numbers .
A line graph (shown below) , will extend forever in either y direction.
The range of linear function is all real numbers .
Therefore , the method to find the domain and range is explained above .
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in a row of five squares, each square is to be colored either red, yellow, or blue, so that no two consecutive squares have the same color. how many ways are there to color the five squares?
There are 4 ways are there to color the five squares
Given that
Reds cannot be placed close to one another per the regulations, so the three reds must be placed in squares 1, 3, and 5.
We can use either yellow or blue in Square 2. There is only one color remaining for square 4 after each of those decisions.
There are 4 ways.
Red Yellow Red Blue Red
Red Blue Red Yellow Red
Red Yellow Red Yellow Red
Red Blue Red Blue Red
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What is the equation of a line that is perpendicular to Y =- 3x 2?
The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. The equation of a line that is perpendicular to Y = -3x^2 is: X = -3y^2/2
The equation of a line that is perpendicular to a given line is found by changing the sign of the slope of the given line and taking the reciprocal of the slope.
The slope of the given line Y = -3x^2 is -3, so the slope of the line perpendicular to it is 3.
The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
Therefore, the equation of a line that is perpendicular to Y = -3x^2 is: x = 3y + b
We can now solve for the y-intercept, b, by substituting the point (0,0) into the equation:
x = 3y + b
0 = 3(0) + b
b = 0
Therefore, the equation of a line that is perpendicular to Y = -3x^2 is: x = 3y^2/2
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So you have a circle of sand going around a wooden door and buckets of soapy water. You need to ask for one more thing to torch this door. What could that be?
Answer:
Butane Gas
Step-by-step explanation:
When you add butane gas to soapy water, it reacts with a lighter/fire and will burst into flames. An example video should show up if you search for burning hand fire experiment online.
the formula gives the length of the side, s, of a cube with a surface area, sa. how much longer is the side of a cube with a surface area of 1,200 square inches than a cube with the surface area of 768 square inches? in. in. in. in.
The difference between the two lengths is 2.8284 inches
What is cube?
The six square faces of a cube, which has six sides that are all the same length, make it a solid object in three dimensions. One of the five platonic solids, it is additionally referred to as a regular hexahedron. Twelve edges, eight vertices, and six square faces make up the form. Given that the three-dimensional object is a square with equal-length sides, the lengths of the cube's length, breadth, and height are all the same. The edge, which is regarded as the edge's bounding line, divides a cube's faces along a shared border.
Cube's surface area is equal to 6 * (sides)2 where side2 = surface area / 6 and side = sqrt (surface area / 6)
The cube's 1200 square inch surface area is as follows:
side = (surface area / 6)
side = sqrt(1200/6)
size equals 14.1421 inches.
Using the 768-square-inch cube as an example:
side = (surface area / 6)
side = sqrt(768 / 6)
dimension is 11.3137 inches.
Hence the difference between the two lengths is 2.8284 inches
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Which graph increases most rapidly from its vertex?
Answer:
f(x) = 5x^(2)-3
Step-by-step explanation:
graph each equation
Let S be the part of the plane 2x + 1y + z = 2 which lies in the first octant, oriented upward. Find the flux of the vector field F = 1i + 1j + 3k across the surface S. F = 1i + 1j + 3k across the surface s2x + 1y + z = 2 which lies in the first octant, oriented upward. Find the flux of the vector field.
The flux of the vector-field F = 1i + 1j + 3k across the surface S is 2. We find out the flux of the vector-field using Green's Theorem.
Flux form of Green's Theorem for the given vector-field
φ = ∫ F.n ds
= ∫∫ F. divG.dA
Here G is equivalent to the part of the plane = 2x + 1y + z = 2.
and given F = 1i + 1j + 2k
div G = div(2x + 1y + z = 2) = 2i + 4j + k
Flux = ∫(1i + 1j + 3k) (2x + 1y + z) dA
φ = ∫ (2 + 4 + 2 ) dA
= 8∫dA
A = 1/2 XY (on the given x-y plane)
2x+4y =2
at x = 0, y = 1/2
y = 0, x = 1
1/2 (1*1/2) = 1/4
Therefore flux = 8*1/4 = 2
φ = 2.
Green's theorem has numerous applications. One method is to solve two-dimensional flow integrals, which state that the sum of fluid outflows from a volume equals the total outflow summed around an enclosing area.
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is 12 fl oz or 355 ml more