A small frictionless cart is attached to a wall by a spring. It is pulled 22 cm from its rest position, released at time t = 0, and allowed to roll back and forth for 5 seconds. Its position at time t is s = 22 cos (pi*t).A. What is the cart's maximum speed? When is the cart moving that fast? Where is it then? What is the magnitude of the acceleration then?B. Where is the cart when the magnitude of the acceleration is greatest? What is the cart's speed then?I cannot figure out part b.I have part a: which is 69.1 cm/sec
Answers
Answer:
a) 22π cm/s; on the odd half-second (t=0.5, 1.5, 2.5, 3.5, 4.5); at the rest position; zero
b) 22 cm from the rest position; zero
Step-by-step explanation:
Undamped simple harmonic motion is not complicated. Acceleration is a maximum where the applied force is a maximum, at the extremes of position. Since the position is extreme, the velocity is zero at those points. All of the energy is potential energy.
The speed is a maximum when the object is at the rest position, There is no applied force at that point, and no acceleration. All of the energy has been transformed to kinetic energy.
Part A:
The cart's velocity is given by the derivative of the position:
s'(t) = -22π·sin(πt)
This has a maximum magnitude (speed) of 22π ≈ 69.1 cm/s, as you have noted.
The speed is a maximum at the rest position. The cart is there on each odd quarter-period, at t=0.5, 1.5, 2.5, 3.5, 4.5 seconds.
The cart's acceleration is given by the derivative of the velocity:
s'' = -22π²·cos(πt)
On the odd quarter-period, the acceleration is zero.
Part B:
Acceleration is greatest when position is greatest (both are cosine functions). The speed of the cart is zero then (it is a sine function). The sine is at an extreme when the cosine is zero, and vice versa.
_____
The attached graph shows position, velocity, and acceleration (color coded).
To solve part b of the question, we need to find the point where the magnitude of the acceleration is greatest. This can be done by finding the derivative of the acceleration function and setting it equal to zero. The value of t that satisfies this equation can then be used to find the position and speed of the cart.
Explanation:In order to solve part b of the question, we need to find the point where the magnitude of the acceleration is greatest. We can do this by finding the derivative of the acceleration function and setting it equal to zero. The derivative of the acceleration function is given by: a'(t) = -22πsin(πt). Setting this equal to zero gives: -22πsin(πt) = 0. Solving for t, we find that t = 1/2.
Now that we have the value of t, we can plug it back into the position function to find the position of the cart when the magnitude of the acceleration is greatest. The position function is given by: s(t) = 22cos(πt). Plugging in t = 1/2, we get: s(1/2) = 22cos(π/2) = 0.
To find the cart's speed when the magnitude of the acceleration is greatest, we can plug t = 1/2 into the velocity function. The velocity function is the derivative of the position function, which is given by: v(t) = -22πsin(πt). Plugging in t = 1/2, we get: v(1/2) = -22πsin(π/2) = 22π.
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Related Questions
A rectangular piece of cardboard, 8 inches by 14 inches, is used to make an open top box by cutting out a small square from each corner and bending up the sides. What size square should be cut from each corner for the box to have the maximum volume?
Answers
Answer:
x = 1.64 in the size of the side of the square
Step-by-step explanation:
Let call x side of the square to be cut from cornes, then:
First side of rectangular base
L = 14 - 2*x
And the other side
d = 8 -2*x
Then Volume of the box
V(b) = L*d*x
V(x) = ( 14- 2*x ) * ( 8 -2*x)*x
V(x) = ( 112 - 28*x -16*x + 4*x² )*x ⇒ 4*x³ - 44*x² + 112*x
Taking derivatives on both sides of the equation we get:
V´(x) = 12*x² - 88*x +112
V´(x) = 0 ⇒ 12*x² - 88*x +112 = 0
A second degree equation, solvin it
3x² - 22*x + 28 = 0
x₁,₂ = [ 22 ± √484 - 336 ] / 6
x₁ = (22 + 12,17) /6 x₂ = ( 22 - 12.17 ) / 6
x₁ = 5.69 We dismiss this solution since it make side 8 - 2x a negative length
x₂ = 9.83/6
x₂ = 1.64
Then x = x₂ = 1.64 in
Answer:
1.64 in
Step-by-step explanation:
Find the angle that the line through the given pair of points makes with the positive direction of the x-axis
(1,4) and (-1,2)
Answers
Answer:
Therefore the angle that the line through the given pair of points makes with the positive direction of the x-axis is 45°.
Step-by-step explanation:
Given:
Let
A(x₁ , y₁) = (1 , 4) and
B( x₂ , y₂ ) = (-1 , 2)
To Find:
θ = ?
Solution:
Slope of a line when two points are given is given bt
[tex]Slope(AB)=\dfrac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Substituting the values we get
[tex]Slope(AB)=\dfrac{2-4}{-1-1}=\dfrac{-2}{-2}=1\\\\Slope=1[/tex]
Also Slope of line when angle ' θ ' is given as
[tex]Slope=\tan \theta[/tex]
Substituting Slope = 1 we get
[tex]1=\tan \theta[/tex]
[tex]\tan \theta=1\\\theta=\tan^{-1}(1)[/tex]
We Know That for angle 45°,
tan 45 = 1
Therefore
[tex]\theta=45\°[/tex]
Therefore the angle that the line through the given pair of points makes with the positive direction of the x-axis is 45°.
What postulate or theorem proves the two triangles are similar?
Answers
Answer:sas
Step-by-step explanation:
Answer:
SAS
IS THE ANSWER
Abby has a collection of 61 dimes and nickels worth $4.40. How many nickels does she have? Show steps
Answers
Answer:
34 nickels
Step-by-step explanation:
First, consider the value if they were all dimes. That would be 61×$0.10 = $6.10. Next, realize this is more than the actual amount by 1.70. Of course, replacing one of the 61 dimes by a nickel reduces the total amount by $.05, so we must have ...
$1.70/$0.05 = 34
nickels in the mix.
Abby has 34 nickels.
_____
Alternate solution methods
I like to solve these using number sense, as above. Equivalently, an equation can be written using n to represent the number of nickels. The total value is then ...
.05n + .10(61 -n) = 4.40
-.05n +6.10 = 4.40 . . . . . . eliminate parentheses
-.05n = -1.70 . . . . . . . . . . . subtract 6.10
n = -1.70/-.05 = 34
Hopefully, you notice some similarities between this solution and the one in words, above.
__
Often, you will see this sort of problem formulated using two equations.
n + d = 61 . . . . . . . . . . number of coins (d=#of dimes)
.05n +.10d = 4.40 . . . .value of coins
If we solve this by substitution, we can use d=61-n, and get ...
.05n +.10(61-n) = 4.40 . . . . . . looks like our equation in the previous section
By creating two equations for the total value of coins and the total number of coins Abby has, we can solve for both the number of dimes and nickels she holds. After doing the required calculations, we find that Abby has 34 nickels.
Explanation:The subject of this question is algebra and it involves solving a system of equations. This is a classic problem that can be solved using two equations because we have two unknowns: the number of dimes and the number of nickels.
Since each dime is worth 10 cents and each nickel is worth 5 cents, and total value of Abby's coins is $4.40 or 440 cents, we can write the value equation as:10d + 5n = 440 -- (Equation 1)Also, we know the total number of coins, which is 61, so we can write the count equation as:
d + n = 61 -- (Equation 2)We can now solve the system of equations using substitution or elimination method. Multiplying Equation 2 by 5 gives us:
5d + 5n = 305 -- (Equation 3)Subtracting Equation 3 from Equation 1, we get:
5d = 135, which simplifies to d = 27.Substitute d = 27 into Equation 2 to find n:
27 + n = 61, so n = 61 - 27 = 34.
So, Abby has 34 nickels.
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Use vectors to show that, for any triangle1 in R², the points2 that are 2/3 of the way from a vertex to the midpoint of the opposite side are all the same point. This point is called the centroid of the triangle.
True / False.
Answers
Final answer:
The statement is true; the centroid of a triangle is the point that lies 2/3 of the way from each vertex to the midpoint of the opposite side. The centroid is the same point for all three vertices, which can be shown using vector operations that equate to (A+B+C)/3 for a triangle with vertices A, B, and C.
Explanation:
The statement that points lying 2/3 of the way from a vertex to the midpoint of the opposite side for any triangle in ℝ² (the real number plane) are all the same point, and this point is called the centroid of the triangle, is True. To prove this, consider a triangle ABC with vertices A, B, and C. If M is the midpoint of side BC, N is the midpoint of side AC, and O is the midpoint of side AB, then the points two-thirds of the way from the vertices A, B, and C to the midpoints of the opposite sides, respectively, can be represented by the vectors (2M+A)/3, (2N+B)/3, and (2O+C)/3.
Applying the midpoint formula and vector addition, we find that these points are equivalent to (B+C)/3, (A+C)/3, and (A+B)/3 respectively, which, when simplified, all yield to (A+B+C)/3, illustrating that the points coincide and thus prove the existence of a single centroid.
In a geometric context, the centroid is the point where the triangle’s medians intersect, and it also serves as the triangle's center of mass. The centroid divides each median in a 2:1 ratio, with the larger portion being closer to the vertex. This property is intrinsic to triangles and can be demonstrated using vector algebra or geometric arguments.
Create an explicit equation for each recursively defined sequence below:
Answers
Part A
This is an arithmetic sequence with starting term a(1) = 17 and common difference d = -7.
a(n) = a(1) + d(n-1)
a(n) = 17 + (-7)(n-1)
a(n) = 17-7(n-1)
a(n) = 17-7n+7
a(n) = -7n+24 is the final answer========================================================
Part B
We have a geometric sequence here because we multiply by the same quantity (5) each time. This makes the common ratio be r = 5.
The starting term is t1 = 3
The nth term of this geometric sequence can be expressed as...
t(n) = t1*(r)^(n-1)
t(n) = 3*(5)^(n-1) is the final answerHow long would it take for a ball dropped from the top of a 576576-foot building to hit the ground? Round your answer to two decimal places.
Answers
Answer:
5.98 s
Step-by-step explanation:
576 ft = 576 / 3.28 = 175.56 m
Let g = 9.81 m/s2. The time it takes for the ball to fall from 165.56 m high to the ground is
[tex]s = gt^2/2[/tex]
[tex]t^2 = 2s/g = 2*175.56/9.81 = 35.8[/tex]
[tex]t = \sqrt{35.8} = 5.98 s[/tex]
A cable car can safely carry n people. There are already 3/4n people on the cable car. Only 12 more people can board the cable car before it becomes unsafe. How many people at most can the cable car carry? Write an inequality then solve
Answers
Answer:
The answer is 48 people.
Step-by-step explanation:
We can write the equation like following:
[tex]n=(3n/4)+12\\4n=3n+48\\n=48[/tex]
The cable car can carry 48 people at most.
n the sentence below identify the type of pronoun which the italicized word is.
It can stand by itself .
reflexive
intensive
interrogative
demonstrative
indefinite
relative
ITSELF is italicized
Answers
Answer:
Itself is a Reflexive Pronoun.
Step-by-step explanation:
The reflexive pronouns are words that end with prefixes "self or selves".When the object and the subject in the sentence are same then reflexive pronoun is used. That is It is to denote that the subject is doing something by or to itself .These reflexive pronoun can act either as a direct object or indirect object . It is preceded by the adverb, adjective, pronoun, or noun to which it refers to. They also allow us to point back to, or reflect on, the subject of the sentence with clarity. The nine English reflexive pronouns are
Myself Yourself Himself Herself Oneself ItselfOurselves Yourselves Themselves.A baseball is thrown at an angle of 30° with respect to the ground and it reaches the ground in 2 seconds. What is its initial velocity of baseball?
Answers
Answer:
The answer to your question is vo = 19.62 m/s
Step-by-step explanation:
Data
angle = α = 30°
time = t = 2 s
vo = ?
g = 9.81 m/s²
Formula
[tex]t = \frac{2vosin\alpha}{g}[/tex]
Solve for vo
[tex]vo = \frac{tg}{2sin\alpha}[/tex]
Substitution
[tex]vo = \frac{(2)((9.81)}{2sin 30}[/tex]
Simplification
[tex]vo = \frac{19.62}{2(0.5)}[/tex]
[tex]vo = \frac{19.62}{1}[/tex]
Result
vo = 19.62 m/s
Terry pays £635.71 a year on his car insurance. The insurance company reduces the price by 5.3%. How much does the insurance cost now? Give your answer rounded to 2 DP.
Answers
The insurance costs £602.02 now.
Step-by-step explanation:
Amount paid for car insurance = £635.71
Price reduce = 5.3%
Amount of reduce = 5.3% of amount paid
Amount of reduce = [tex]\frac{5.3}{100}*635.71[/tex]
Amount of reduce = [tex]0.053*635.71[/tex]
Amount of reduce = £33.69263
Rounding off to two decimal place
Amount of reduce = £33.69
Reduced price = Amount paid - Amount of reduce
Reduced price = 635.71 - 33.69 = £602.02
The insurance costs £602.02 now.
Keywords: subtraction, division
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Original price × (1 - reduction percentage) = Reduced price. £635.71 × (1 - 0.053) ≈ £602.97 (rounded to 2 DP).
let's break it down step by step:
1. Calculate the reduction amount:
Multiply the original price (£635.71) by the reduction percentage (5.3% or 0.053).
Reduction Amount = £635.71 * 0.053
2. Subtract the reduction amount from the original price:
Subtract the reduction amount from the original price to find the reduced price.
Reduced Price = £635.71 - Reduction Amount
Now, let's plug in the values:
1. Calculate the reduction amount:
Reduction Amount = £635.71 * 0.053
≈ £33.73763
2. Subtract the reduction amount from the original price:
Reduced Price = £635.71 - £33.73763
≈ £602.97237
Rounded to two decimal places:
Reduced Price ≈ £602.97
So, after the 5.3% reduction, Terry's car insurance costs approximately £602.97.
At 1:30 Marlon left his house to go to the beach a distance of 6.75 mi. He rode his skateboard until 2:15 and then walked the rest of the way. He arrived at the beach at 3:00. Marlins speed on his skateboard is 2 times his walking speed. Find his speed when skateboarding and when walking
Answers
Answer: his speed when skateboarding is 6 mph and when walking is 3 mph
Step-by-step explanation:
Let x represent Marlon's walking speed.
Marlins speed on his skateboard is 2 times his walking speed. This means that his skating speed would be 2x.
At 1:30 Marlon left his house to go to the beach a distance of 6.75 mi. He rode his skateboard until 2:15. This means that the total time he spent skating is 45 minutes = 45/60 = 0.75 hours
Distance = speed × time
Distance covered while skating would be
2x × 0.75 = 1.5x
He walked the rest of the way. He arrived at the beach at 3:00. This means that the time that he spent walking is 45 minutes = 0.75 hours.
Distance covered while walking would be
x × 0.75 = 0.75x
Total distance covered is 6.75 miles. Therefore
1.5x + 0.75x = 6.75
2.25x = 6.75
x = 6.75/2.25
x = 3 miles per hour
His skating speed = 2 × 3 = 6 miles per hour.
A right triangle has sides of length 3 feet, 4 feet, and 5 feet what is its perimeter? What is its area?
Answers
Answer:
Perimeter= 12 feet Area= 6 feet (squared)
Step-by-step explanation:
Perimeter= Adding all the sides together, that means it is 3+4+5= 12 feet
Area= Hight times base divided by 2. Because hight times base is area of a rectangle, and a right triangle (and all other triangles) is half of it. Because it is a right triangle, its hight must be 3 or 4, and base also 3 or 4. But no the same number twice, so 3*4=12, 12/2=6 feet (squared).
I hope that helped! =)
The exponential functions y=(1-25)^x-2/5. -10 is shown hraphed along woth the horizontal line y=115 their intersection is (a,115) start by using wht they give you for the point of intersection ans substitute that into the given equation
Answers
To find the point of intersection between the given exponential function and the horizontal line, substitute the y-value (115) into the equation and solve for x.
Explanation:To find the point of intersection between the exponential function y=(1-25)^x-2/5 and the horizontal line y=115, we can substitute the given y-value (115) into the equation and solve for x. By substituting y=115 into y=(1-25)^x-2/5, we can rewrite the equation as 115=(1-25)^x-2/5. This allows us to solve for x and find the x-coordinate of the point of intersection.
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To find the intersection point, substitute the y-coordinate (115) into the exponential function and solve for x using ln(1-25).
Explanation:To find the intersection point between the exponential function and the horizontal line, we substitute the y-coordinate of the intersection point (which is 115) into the given exponential function. We then solve for x.
Substituting y = 115 into the exponential function, we have (1-25)^(x-2/5) = 115. Taking the natural logarithm of both sides, we get (x-2/5)ln(1-25) = ln(115). Solving for x, we divide both sides by ln(1-25) and add 2/5 to get x = ln(115)/ln(1-25) + 2/5.
Therefore, the intersection point is (x, 115), where x = ln(115)/ln(1-25) + 2/5.
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Help: Simplifying inside parenthesis first
Answers
Answer:
4th one
Step-by-step explanation:
a^-2 goes down and become a^2 and
[tex] {a}^{2} \times {a}^{2} = {a}^{4} [/tex]
b^-1 goes up and become b
[tex] {b}^{2} \times {b}^{1} = {b}^{3} [/tex]
that why answer is 4th...mark me brainliest please
Find a function of the form
y=Asin(kx)+C or y=Acos(kx)+C whose graph matches this one:
Answers
Answer:
y = 2sin((π/7)x)
Step-by-step explanation:
The graph goes through (0, 0) and has a range of ±2. This matches a sine function with an amplitude (A) of 2 and a vertical offset (C) of zero.
The half-period is 7, so the value of k is such that 7k = π, or k = π/7.
The desired function is y = 2·sin((π/7)x).
A nationwide survey of 1000 adults found that 50% of respondents favored a plan to break up the 12 megabanks, which then controlled about 69% of the banking industry. Complete parts (a) and (b) below.
a. Identify the population and sample for this study.
b. Is the percentage provided a descriptive statistic or an inferential statistic? Explain your answer.
Answers
a. The population for the study is a total of 1000 adults, so the 50% that favored the plan made up a total of 500 people, since 500 is 1/2 (or 50%) of 1000.
b. The percentage provided is an inferential statistic. Inferential statistics are made by taking a sample of a population and using that sample as data used to make inferences/predictions. Since the percentage provided is a sample of a population being used to make a prediction, it is an inferential statistic.
The population is all adults in the nation, and the sample is the 1000 adults surveyed. The provided percentage is a descriptive statistic, as it summarizes data from the sample.
Explanation:In the context of this problem, the population refers to all adults across the nation, while the sample refers to the 1000 adults who were surveyed.
The percentage mentioned in the survey (50% in favor of breaking up the 12 megabanks) is a descriptive statistic. A descriptive statistic summarizes and represents data from a sample, which in this case is the surveyed group of 1000 adults. It does not aim to infer or predict facts about the larger population.
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An airplane flies horizontally from east to west at 320 mph relative to the air. If it flies in a steady 40-mi/hr wind that blows horizontally toward the southwest (45 degrees south of west). find the speed and direction of the airplane relative to the ground.
Answers
Answer:Speed of airplane= 43.18mi/he
Direction of the airplane relative to the ground=4.64°. Counter-clockwise rotation from west.
Step-by-step explanation: welovity/speed is represented as magnitudes of vectors.
Let A= the vector of the airplane
Let W= the vector of the wind
From the diagram,total vector F= A + w
F= 320+ 40cos45°I +0j) + (0i + 40sin46°)
F=320+28.28i+28.28j
To calculate the magnitude
/F/=root of A2 +w2
/F/=root320+40cos45°2+40sin45°2
/F/=root 1919.5168
/F/=43.18= speed
To calculate the direction of the airplane relative to the ground, use tan function because it is a right triangle as seen in the diagram
Tan x= opp/adj=40sin45/320+40cos45
Tanx=28.28/348.28
Tanx=0.091199
×=tan-1 0.091199
×=4.64
Over the summer Mr.Patel refilled a bird feeder 24 time using 6 cups of seeds each time.A bag of seeds holds 32 cups. How many bags of seeds did Mr.Patel use write an equation to represent the problem
Answers
Answer:
The equation representing the problem is [tex]x=\frac{24\times 6}{32}[/tex].
Mr. Patel used 5 bags of seeds.
Step-by-step explanation:
Given:
Number of times bird feeder refilled =24
Number of cups of seeds used each time = 6 cups
Number of seeds each bag holds = 32 cups.
We need to write the equation to represent the problem.
Solution.
Let the total number of bag of seed be 'x'.
First we will find the Total number of cups of seeds used.
Now we can say that;
Total number of cups of seeds used can be calculated by multiplying Number of times bird feeder refilled by Number of cups of seeds used each time.
framing in equation form we get;
Total number of cups of seeds used = [tex]24\times6 \ cups[/tex]
Now We know that;
1 bag holds = 32 cups
Total number of bags required = [tex]24\times6 \ cups[/tex]
So we can say that;
Total number of bags required is equal to Total number of cups of seeds used divided by number of seed hold by each bag.
framing in equation form we get;
[tex]x=\frac{24\times 6}{32}[/tex]
Hence the equation representing the problem is [tex]x=\frac{24\times 6}{32}[/tex].
On solving we get;
[tex]x=4.5[/tex]
Since bags cannot be bought in half or in decimal value.
Hence we can say Mr. Patel used 5 bags of seeds.
In triangle ABC, a = 2, c = 6, and cos B = . Find b.
Answers
Answer:
Use Law of Cosines, which is ß² = α² + c² - 2αccos(B) where <B is opp. to side ß.
Let α = 2, c = 6 and cos(B) = 1/6, so
ß = √(2² + 6² - 2(2)(6)(1/6))
= √(4 + 36 - 4)
= √36 = 6
Mike and Kim invest $18,000 in equipment to print yearbooks for school. Each yearbook costs $5 to print and sells for $15. How many yearbooks must they sell before their business breaks even?a. 1,100 yearbooksb. 1,200 yearsbooksc. 3,600 yearbooksd. 1,800 yearsbooks
Answers
Answer:
1800yearbook(D)
Step-by-step explanation:
Cost of printing a year book = $5
A year book is sold at $15
The profit on each year book = $15 - $5 = $10
Let y represent the number of year books sold for a break even to occur.
A break even occurs when the amount sold is equals the amount invested
10y = 18000
y = 18000/10
y = 1800 yearbooks
Rational Expressions
5n/15 + 7n/15
Answers
____________is the practice of putting students into specific curriculum groups based on their test scores and other factors.
Answers
Answer: Tracking is the practice of putting students into specific curriculum groups based on their test scores and other factors.
Tracking is the practice of grouping students based on their abilities and test scores. It involves sorting students into different curriculum groups. Ability grouping and tracking are used to place students on specific educational tracks.
Tracking is the practice of putting students into specific curriculum groups based on their test scores and other factors. This process involves classifying students based on academic merit or potential and is a formalized sorting system that places students on 'tracks' that perpetuate inequalities. Ability grouping and tracking are strategies used to group students according to their perceived abilities for educational purposes.
Which could be used to solve this equation? 3 1/5 +n =9
Answers
Answer:
A
Step-by-step explanation
You need to subtract the 3 1/5 from both sides, which gives you 29/5
Answer:
A
Step-by-step explanation:
You always to the opposite of the opporation already given.
Ernest and Gene have been saving coins every day for a sunny day in Arizona. Ernest has 8 more half dollars than Gene and no quarters. Gene has as many quarters as Ernest has half dollars, and each has 45 dimes. How many of each coin has each saved for the big day when $200 has been saved? Which of the following equations could represent the word problem if x is the number of half dollars that Gene has?a. 3x + 106 = 200
b. 125x + 916 = 20,000
c. 125x + 1,500 = 20,000
Answers
Answer:
1. Ernest has $82.5 and Gene has $117.5
2. c) 125x + 1500 = $20000
Step-by-step explanation:
If we mark Gene's half dollars with x, then it is given that Ernest has 8 more, which is x+8.
It is also given that Ernest has no quarters, but Gene has them as many as Ernest has half dollars, which is x+8.
And it is given that they both have 45 dimes each, which is $4.5 each.
Now, let's add up all these numbers:
Ernest: (x+8)•0.5 + 0•0.25 + 4.5 = 0.5x + 8.5
Gene: x•0.5 + (x+8)•0.25 + 4.5 = 0.75x + 6.5
They collected $200 together which means:
0.5x + 8.5 + 0.75x + 6.5 = $200
1.25x + 15 = $200
If we want to avoid decimal number, we can multiply whole equation with 100:
125x + 1500 = $20000
so, the correct answer is C.
Finally, to find x:
125x = 18500
x = 148
Ernest had 0.5x + 8.5 which is $82.5
Gene had 0.75x + 6.5 which is $117.5
Charles has already broken 14 eggs, and he's breaking eggs at a rate of 12 per minute. Louis has already broken 22 eggs, and he's breaking eggs at a rate of 10 per minute. How many minutes will it take Charles to have broken as many eggs as Louis?
Answers
Answer:
4 minutes - |12 x 4 = 48| |48 + 14 = 62| Charles = 62
10 x 4 = 40| 40 + 22 = 62
Step-by-step explanation:
If he has 14 all we have to do is keep multiplying 12 by x and 10 by x add them to their correct person until Charles has more eggs broken then Louis
An airline charges the following baggage fees: $25 for the first bag and $35 for the second. Suppose 54% of passengers have no checked luggage, 34% have one piece of checked luggage and 12% have two pieces. We suppose a negligible portion of people check more than two bags.
(a) Build a probability model, compute the average revenue per passenger, and compute the
corresponding standard deviation.
(b) About how much revenue should the airline expect for a flight of 120 passengers? With what
standard deviation? Note any assumptions you make and if you think they are justified.
Answers
Answer:
The average revenue per passenger = E(x) = $15.70
[tex]\sigma = \sqrt{\sigma^{2}} = \sqrt{398} \approx 19.95[/tex]
b)$1,884 ± $20
Step-by-step explanation:
a)
Refer attached fig for probability model,
i)The average revenue per passenger = E(x) = $15.70
[tex]\sigma^{2} = V[X] \sum _{x} (x-\mu )^{2} \times P(X=x)[/tex]
[tex]\sigma^{2} = (0-15.7)^{2} \times 0.54+(25-15.7)^{2} \times 0.34 +(60-15.7)^{2} \times 0.12[/tex]
[tex]\sigma^{2} = 133.1 + 29.4 + 235.5 = 398[/tex]
Standard Deviation = [tex]\sigma = \sqrt{\sigma^{2}} = \sqrt{398} \approx 19.95[/tex]
ii) average revenue per passenger = E(x) = $15.70
b) Revenue should the airline expect for a flight of 120 passengers
revenue = 120 * $15.70 = $1,884 ± $20 (or 19.95 rounded up)
use same σ
The average revenue per passenger is $15.2 and the standard deviation is $18.45. For a flight of 120 passengers, the airline may expect around $1824 with standard deviation of $202.33. We're assuming that each passenger's baggage habits are independent.
Explanation:To solve this, first we'll construct a probability model. Let X be a random variable denoting the revenue from each passenger. Then X can take three possible outcomes: $0 (with probability 0.54), $25 (with probability 0.34) or $60 (with probability 0.12).
The average revenue from each passenger E(X), also known as the expected value of X, is calculated as follows:
E(X) = 0*0.54 + 25*0.34 + 60*0.12 = $15.2
The standard deviation of X, denoted σ(X), is computed as follows:
σ(X) = sqrt[(0-15.2)^2*0.54 + (25-15.2)^2*0.34 + (60-15.2)^2*.12] = $18.45
Given this, for a flight of 120 people, the total expected revenue is 120*$15.2 = $1824 and the standard deviation of total revenue would be sqrt(120)*$18.45 = $202.33.
The underlying assumption here is that the baggage habits of passengers are independent, which is reasonable in this case.
Learn more about Revenue Expectation here:https://brainly.com/question/34340067
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What is the difference?
2x + 5/x 2 - 3x - 3x + 5/x3 - 9x - x + 1/x2 - 9
(x + 5)(x + 2)/x3 - 9x
(x + 5)(x + 4)/x3 - 9x
-2x + 11/x3 - 12x - 9
3(x + 2)/x2 - 3x
Edit: It's A
Answers
Answer:
The option [tex]\frac{(x+5)(x+2)}{x^3-9x}[/tex] is correct
The difference of the given expression is
[tex]\frac{2x+5}{x^2-3x}-(\frac{3x+5}{x^3-9x})-({\frac{x+1}{x^2-9})=\frac{(x+5)(x+2)}{x^3-9x}[/tex]
Step-by-step explanation:
Given expression is [tex]\frac{2x+5}{x^2-3x}-(\frac{3x+5}{x^3-9x})-({\frac{x+1}{x^2-9})[/tex]
To find the difference of the given expression as below :
[tex]\frac{2x+5}{x^2-3x}-(\frac{3x+5}{x^3-9x})-({\frac{x+1}{x^2-9})[/tex]
[tex]=\frac{2x+5}{x(x-3)}-(\frac{3x+5}{x(x^2-9)})-({\frac{x+1}{x^2-9})[/tex]
[tex]=\frac{2x+5}{x(x-3)}-(\frac{3x+5}{x(x^2-3^2)})-({\frac{x+1}{x^2-3^2})[/tex]
[tex]=\frac{2x+5}{x(x-3)}-(\frac{3x+5}{x(x-3)(x+3)})-({\frac{x+1}{(x-3)(x+3)})[/tex]
( using the formula [tex]a^2-b^2=(a+b)(a-b)[/tex] )
[tex]=\frac{2x+5(x+3)-(3x+5)-x(x+1)}{x(x-3)(x+3)}[/tex]
[tex]=\frac{2x^2+6x+5x+15-3x-5-x^2-x}{x(x-3)(x+3)}[/tex] (adding the like terms)
[tex]=\frac{x^2+7x+10}{x(x^2-9)}[/tex] ( by factoring the quadratic polynomial )
[tex]=\frac{(x+5)(x+2)}{x^3-9x}[/tex]
Therefore [tex]\frac{2x+5}{x^2-3x}-(\frac{3x+5}{x^3-9x})-({\frac{x+1}{x^2-9})=\frac{(x+5)(x+2)}{x^3-9x}[/tex]
Therefore the difference of the given expression is
[tex]\frac{(x+5)(x+2)}{x^3-9x}[/tex]
Therefore option [tex]\frac{(x+5)(x+2)}{x^3-9x}[/tex] is correct
Answer:
A
Step-by-step explanation:
Bacteria can multiply at an alarming rate when each bacterium splits into two new cells, thus doubling. If a single bacterium is discovered at 9 a.m. and doubles every hour, how many bacteria will there be at the end of the day (midnight)?
Answers
65,536 cells of bacterium
Answer: 135
Step-by-step explanation:
A community center has adopted two miles or 3520 wide of a highway to pick up trash along the side of the road falling tears are divided into 7 groups each group is a sign of equal length of Highway to clean up how many yards will each group clean up explained
Answers
Answer:
no it is 8 more so do it one more time and you will get the answer 352? fine the number
Step-by-step explanation: