the length of a staff meeting in hours is a random variable having the following probability density function 5(x-.5)^5 calculate the expected length of a staff meeting
Answers
The expected length of a staff meeting is approximately 12.5 minutes.
what is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
To calculate the expected length of a staff meeting, we need to find the mean of the probability density function given.
The formula for finding the expected value or mean of a continuous random variable with probability density function f(x) is:
E(X) = ∫ x f(x) dx over the range of the variable
Using this formula, we can find the expected length of a staff meeting as follows:
E(X) = ∫ x f(x) dx over the range of the variable
= ∫ 0 to 1 x \(5(x-0.5)^{5}\) dx (since the length of a meeting can't be negative)
= 5 ∫ 0 to 1 x\((x-0.5)^{5}\) dx
Now we can use integration by parts or substitution to solve the integral. For simplicity, we can use substitution, with u = x - 0.5 and du = dx:
E(X) = 5 ∫ -0.5 to 0.5\(5(x-0.5)(u)^{5}\) du
= 5 ∫ -0.5 to 0.5 \((u^6 + 0.5u^5)\) du
= 5 [(1/7)\(u^7\\\) + (1/10)\(u^6\)] evaluated at -0.5 and 0.5
= 5 [(1/7)\((0.5)^7\) + (1/10)\((0.5)^6\) - (1/7)\((-0.5)^7\) - (1/10)\((-0.5)^7\)]
≈ 0.2083 hours or 12.5 minutes
Therefore, the expected length of a staff meeting is approximately 12.5 minutes.
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Related Questions
Photo for the amounts and prices below!
Answer these questions with the information in the photo:
1) Tanya smokes 5 cigarettes a day. How much does she spend on cigarettes in a week?
2) If it takes Ben 1 week to smoke 10 cigarettes, how much money will he spend on cigarettes in one year?
3) Simone wants a handbag that is $168. She currently smokes two packs of cigarettes per week. If she stops smoking and saves that money, how long will it take her to buy the handbag?
4) If Libby smokes 2 packs of cigarettes per week, by how many days will her life be shortened after one year of smoking?
5) Mr Reynolds estimates that his smoking habit shortens his life by 98 minutes per day. How many cigarettes does Mr Reynolds smoke each day?
Please help! I got this all wrong last time even though it’s basic math :(
Answers
Answer:
below
Step-by-step explanation:
1) 35 cigarettes in a week
35/20 = 1,75 packs in a week
1,75 * 8 = 14 $(rounded in integers 2*8 = 16$
2) 52 weeks in a year
520 cigarettes in a year
520 / 20 = 26 packs
26 packs * 8 = 208 $ a year
3) 2*8 = 16$ a week
168/16 = 10,5 weeks
10,5 * 7 = 73,5 days
4) 52 * 20 * 2 = 2080 cigarettes in a year
2080 * 14 = 29120 minutes lost
29120 / 60 / 24 = 20,2 days lost
5) 98/14 = 7 cigarettes per day
How do you write 140% as a fraction, mixed number, or whole number?
Answers
The requried, 140% is equivalent to 7/5 as a fraction, 1 2/5 as a mixed number, and 2 as a whole number.
To write 140% as a fraction, we first recognize that "percent" means "per hundred," so 140% can be written as the fraction 140/100. We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor (GCF), which is 20:
140/100 = 7/5
To write 7/5 as a mixed number, we divide the numerator by the denominator and express the result as a whole number plus a fraction. In this case:
7 ÷ 5 = 1 with a remainder of 2
So 7/5 can be written as the mixed number 1 2/5.
To write 7/5 as a whole number, we can round it to the nearest whole number. Since 7/5 is greater than 1.5 and less than 2.5, it rounds to 2.
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If answered correctly and to be the first to answer gets big brain and
Help quick please
Answers
Hope this helps
For the system of equations shown, what is the value of x+y? 3x+y=−6−3x−4y=−12
Answers
Answer:
x + y = -12 + 30 = 18
Step-by-step explanation:
To solve this system of equations, we can use the elimination method. Multiplying the first equation by 3, we get:
9x + 3y = -18
Adding this to the second equation, we eliminate the x terms:
9x + 3y = -18
-3x - 4y = -12
-----------------
-y = -30
Solving for y, we get y = 30. Substituting this back into either equation, we can solve for x:
3x + 30 = -6
3x = -36
x = -12
Therefore, x + y = -12 + 30 = 18.
Mr. Newton wants to buy a shirt in Leavenworth Kansas that cost $20.The sales tax in Leavenworth is 8%. What would be the total price of the shirt after adding the sales tax?
Answers
First find the amount the price increased.
amount of change
= (percent change) x (starting value)
= (8%) x ($20)
= (0.08) x ($20)
= $1.60
(Remember to convert the percent to a decimal before multiplying.)
Now add the tax onto the price:
$20 + $1.60 = $21.60
The price, including sales tax, is $21.60.
I need help with geometry
Answers
Answer:
\(Points ~that ~lies~on ~the~sides~of ~the~triangle.\)
\(A)~(a,0)\)\(D)~\frac{a}{2}=\frac{b}{2}\)---------------------------
hope it helps...
have a great day!!
Answer:
Options A and D will be your answers
Step-by-step explanation:
hope it helps you...
this visual representation shows the sets of real numbers. which statement is true regarding the number sets? integers and rational numbers have no numbers in common. integers and rational numbers have no numbers in common. all rational numbers are also integers. all rational numbers are also integers. some integers are also rational numbers, but not all integers are rational numbers. some integers are also rational numbers, but not all integers are rational numbers. all integers are also rational numbers.
Answers
The statement "some integers are also rational numbers, but not all integers are rational numbers" is true regarding the number sets.
To understand the relationship between integers and rational numbers, it's important to understand the definitions of each set:
Integers: Integers are whole numbers (both positive and negative) and zero, without any fractional or decimal parts.
Rational numbers: Rational numbers are numbers that can be expressed as a fraction (ratio) of two integers, where the denominator is not zero.
Based on these definitions, we can conclude that:
All integers are rational numbers because they can be expressed as a fraction with a denominator of 1. For example, 3 can be written as 3/1, -5 can be written as -5/1, and 0 can be written as 0/1.
However, not all rational numbers are integers. Rational numbers include fractions, decimals that terminate, and decimals that repeat. These numbers may have a numerator and denominator that are not equal to 1. For example, 1/2, -3/4, and 0.25 are rational numbers, but they are not integers.
The statement "some integers are also rational numbers, but not all integers are rational numbers" is true. While all integers are rational numbers, not all rational numbers are integers.
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A survey conducted in 2005 found that the State of Louisiana was the happiest State in the United States. The survey was completed before Hurricane Katrina destroyed most of New Orleans and the surrounding area. The information quality for this survey is probably not:
Answers
The information quality of the survey is not reliable for understanding the current happiness level in the state.
The information quality for this survey is likely outdated and not
representative of the current state of Louisiana, particularly after the
devastating impact of Hurricane Katrina in 2005.
The survey was conducted before the hurricane, which significantly
affected the region, including the mental health and well-being of its
residents.
Thus, the survey's results may not accurately reflect the current level of
happiness or satisfaction among Louisiana residents.
Therefore, the information quality of the survey is not reliable for
understanding the current happiness level in the state.
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use the shooting method to solve 7d^2y/dx^2 -2dy/dx-y x=0 with the boundary conditions (y0)=5 and y(20)=8
Answers
The shooting method is used to solve the second-order ordinary differential equation 7d^2y/dx^2 - 2dy/dx - yx = 0 with the boundary conditions y(0) = 5 and y(20) = 8.
To solve the differential equation using the shooting method, we convert it into a system of two first-order equations. Let y = y0 and z = dy/dx, where z represents the derivative of y with respect to x. Then, we have the following system:
dy/dx = z
dz/dx = (2z + yx) / 7
By specifying the initial condition y(0) = 5, we have y0 = 5. To find the appropriate initial condition for z, we use the shooting method. We start by assuming an initial condition for z, say z0, and solve the above system of equations from x = 0 to x = 20. We compare the value of y at x = 20 with the desired boundary condition y(20) = 8.
If the value of y at x = 20 is greater than 8, we adjust the initial condition z0 and repeat the process. If the value is less than 8, we increase z0 and repeat. By iteratively adjusting the initial condition for z, we find the appropriate value that satisfies y(20) = 8.
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If f(x) has a y-intercept at 3 and x-intercepts at 2 and −4, and if
g(x) = −2f(−2x), what are the intercepts of g(x)?
Answers
Answer:
Step-by-step explanation:
The y-intercept of g(x) is 3 * -2 = -6.
To find the x-intercepts of g(x), we need to find the values of x that make g(x) equal to 0. Since g(x) = -2f(-2x), this means we need to find the values of x that make f(-2x) equal to 0. Therefore, we can find the x-intercepts of g(x) by solving the equation f(-2x) = 0 for x.
Since the x-intercepts of f(x) are at 2 and -4, this means that the equation f(x) = 0 has solutions at x = 2 and x = -4. Substituting these values into the equation f(-2x) = 0, we get:
f(-2(2)) = 0
f(-4) = 0
and
f(-2(-4)) = 0
f(8) = 0
Therefore, the x-intercepts of g(x) are at x = -2 and x = 4. These are the only intercepts of g(x) that we can determine for certain.
y = 2/3 x-1
y = -1/3 x + 2 System of equation
Answers
Answer:
See Below
Step-by-step explanation:
y= 2/3x - 1
y= -1/3x +2
Use substitution
2/3x -1 = -1/3 +2
+1/3 +1/3
x-1 = 2
+1 +1
x = 3
Plug that in
y = 2/3(3/1) -1
3 cancel out leaving it with
y = 2-1
y = 1
(3,1)
describe all solutions of ax0 in parametric vector form, where a is row equivalent to the given matrix.
Answers
All solutions to ax0 in the parametric vector form can be written as x = -3[1, 0]. This equation defines a line in the space of the free variables x3 and x4, and any point on this line will be a solution to ax0.
The parametric vector form of a solution to ax0 is given by the equation x = tv, where t is a parameter, and v is a vector composed of all the free variables in the matrix. For example, if the given matrix is:A = [ 1 2 3 4 | 0] [ 5 6 7 8 | 0] .Then the parametric vector form of a solution is given by x = tv, where t is a parameter and v is a vector composed of the free variables x3 and x4, like so: v = [x3, x4] = [1, 0].Therefore, the parametric vector form of the solution will be x = t[1, 0]. This equation defines a line in the space of the free variables x3 and x4, and any point on this line will be a solution to ax0.To find all solutions, we need to solve for t. This can be done by replacing x3 and x4 with the equation in the given matrix. For example, if we plug x3 and x4 into the first equation in the given matrix, we get 1*t + 2*0 +3*1 + 4*0 = 0 Which simplifies to t = -3. Therefore,all solutions to ax0 in the parametric vector form can be written as x = -3[1, 0]. This equation defines a line in the space of the free variables x3 and x4, and any point on this line will be a solution to ax0.
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Use the divergence theorem to compute the net outward flux of the vector field f across the boundary of the region d. F= 32-x,x - 5y,7y +9z
Answers
Using the divergence theorem we can compute that the outward flux of the vector field is 16π .
The outward flux of F over the solid cylinder and z = 0 is
∫∫F·ds = ∫∫∫ DivF dv
F = 2xy² i + 2x²y j + 2xy k
Div F = D/dx (2xy²) + D/dy (2x²y )
Div F = 2y² + 2x²
In cylindrical coordinates dV = rdrdθdz and as z = 0 the region is a surface ds = r·dr·dθ
Using the parametric form of the surface equation
x = rcosθ y = r sinθ and z = z
Div F = 2r² sin²θ + 2r²cos²θ
∫∫∫ DivF dv = ∫∫ [2r²sin²θ + 2r²cos²θ] × rdrdθ
∫∫ 2r² [sin²θ + cos²θ] × rdrdθdz ⇒ ∫∫ 2r³ drdθ
Integration limits
0 < r < 2 0 < θ < 2π
2∫₀² r³ ∫dθ
(2/4) × (2)⁴ × 2π
The divergence theorem, commonly known as Gauss' theorem or Ostrogradsky's theorem, is a theorem that connects the flow of a vector field across a closed surface to the field's divergence in the volume enclosed.
In more detail, the divergence theorem states that the surface integral of a vector field across a closed surface, sometimes referred to as the "flux" through the surface, is equal to the volume integral of the divergence over the region inside the surface.
Therefore the flux is 16π .
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Classify the quadric surface. 4x2 - y2 - z2 = 1 a. hyperbolic paraboloid b. elliptic cone c. Hyperboloid of two sheets d. hyperboloid of one sheet e. ellipsoid
Answers
The given equation (4x² - y² - z² = 1) is classified under Hyperboloid of two sheets.
What is Hyperboloid equation?
When a hyperbola is rotated around one of its axes, an open surface is created that is known as a hyperboloid. The surface's general equation is written as (x²/ a²) + (y² / b²) - (z² / c²) = 1
if the surface's transverse axis is along the x axis, its centre is at the origin, and a, b, and c are its primary semi-axes.
As per question given that,
here is the equation of the quadratic surface is,
4x² - y² - z² = 1
Thus surface is a hyperboloid of two sheets.
The sketch of this quadratic surface is the sketch in the 2nd option which is shown below.
i.e. in the upper right corner.
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solve the equation show steps -2m+4m+5=3
Answers
(-2m+4m)+(5)=3
2m+5=3
2m+5-5=3-5
2m=-2
2m/2=-2/2
m=-1
1. you combine -2m and 4m that equals 2m
2.you subtract 5 from both sides and that gives you 2m=-2
3. you divide both sides by two and it gives you -2/2 which is equivalent to -1
HELP me guys i am illiterate
Find the unknown angles
Answers
Answer:
90°
Step-by-step explanation:
X=180°-(45°+45°){being square property}
X=180°-90°
X=90°
simplify the expression
Answers
Here are clues for a puzzle involving two numbers.
Seven times the first number plus six times the second number equals 31.
Three times the first number minus ten times the second number is 29.
PART A
What are the two numbers?
Answers
Answer:
the first number is 5 1/2the second number is -1 1/8Step-by-step explanation:
The relations describing the two numbers can be written as equations. First, we need to assign variables: let x and y represent the first and second numbers, respectively.
The given relations are then ...
7x +6y = 31
3x -10y = 29
__
Such a system of equations can be solved many ways. One that is usually convenient is to use a graphing calculator. It tells us ...
the first number is 5 1/2the second number is -1 1/8
please help with math question to earn brainliest and points
Answers
Answer:
11 and 12
Step-by-step explanation:
If the square root of X equals 3.4, then 3.4 times 3.4 equals 11.56. So the two integers is 11 and 12.
100 pts.
help please hurry
Highschool Algebra
Answers
Answer:
B
Step-by-step explanation:
Take the second equation for example, just solve like there is an equal sign.
13x+25< -1
13x<-26
X '='-2
X<-2
Answer:
B
Step-by-step explanation:
ssacar Los factores semejantes y dividir por 113
2. The following set of count readings was made in a gradient-free γ-ray field, using a suitable detector for repetitive time periods of one minute: 18,500;18,410; 18,250;18,760;18,600;18,220;18,540;18,270;18,670;18,540. (a) What is the mean value of the number of counts? (b) What is its standard deviation (S.D.)? (c) What is the theoretical minimum S.D. of the mean? (d) What is the actual S.D. of a single reading? (e) What is the theoretical minimum S.D. of a single reading?
Answers
The inflection point of f(t) is approximately t = 3.73.
(a) To determine if the function f(t) = -0.425t^3 + 4.758t^2 + 6.741t + 43.7 is increasing or decreasing, we need to find its derivative and examine its sign.
Taking the derivative of f(t), we have:
f'(t) = -1.275t^2 + 9.516t + 6.741
To determine the sign of f'(t), we need to find the critical points. Setting f'(t) = 0 and solving for t, we have:
-1.275t^2 + 9.516t + 6.741 = 0
Using the quadratic formula, we find two possible values for t:
t ≈ 0.94 and t ≈ 6.02
Next, we can test the intervals between these critical points to determine the sign of f'(t) and thus the increasing or decreasing behavior of f(t).
For t < 0.94, choose t = 0:
f'(0) = 6.741 > 0
For 0.94 < t < 6.02, choose t = 1:
f'(1) ≈ 14.982 > 0
For t > 6.02, choose t = 7:
f'(7) ≈ -5.325 < 0
From this analysis, we see that f(t) is increasing on the intervals (0, 0.94) and (6.02, ∞), and decreasing on the interval (0.94, 6.02).
(b) To find the inflection point of f(t), we need to find the points where the concavity changes. This occurs when the second derivative, f''(t), changes sign.
Taking the second derivative of f(t), we have:
f''(t) = -2.55t + 9.516
Setting f''(t) = 0 and solving for t, we find:
-2.55t + 9.516 = 0
t ≈ 3.73
Therefore, The inflection point of f(t) is approximately t = 3.73.
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en una escuela hay 520 alumnos el 40 por ciento son niñas y el 60 por ciento son niños cuantos y cuantas niñas hay
Answers
Answer:
niños=312 y niñas=208
Para obtener el por ciento de este problema debes que:
520×0.4 y 520×0.6 Esto nos da 40% de Las niñas que como dije es: 520×0.4=208 niñas y 60% de niños : 520×0.6=312
true or false 1+6=5+2 true or false ? ;-;
Answers
Answer: True
Step-by-step explanation: both equal 7
1 + 6 = 7
5 + 2 = 7
it has to be 20 characters long so i’m typing here
15. What is the area of the triangle?
15.5m
9.9 ft
Answers
Answer:
153.45
Step-by-step explanation:
15.5 x 9.9 = 153.45
Which of the following are properties of the linear correlation coefficient?
a. If r is close to 0, then little or no evidence of any relation between the explanatory or response variable exists.
b. The linear correlation coefficient is always between−1 and 1. That is,−1≤r≤1.
c.The correlation coefficient is resistant.
d. A linear correlation of −0.742 suggests a stronger negative association between two variables than a linear correlation of −0.472.
e. A linear correlation of 0.639 suggests a stronger linear relation between two variables than a linear correlation of −0.639.
f. If r=−1, then a perfect negative linear relation exists between the two variables.
Answers
Among the options given in the question, the following are the properties of the linear correlation coefficient:
The linear correlation coefficient is always between−1 and 1. That is,−1≤r≤1.
A linear correlation of −0.742 suggests a stronger negative association between two variables than a linear correlation of −0.472.
If r=−1, then a perfect negative linear relation exists between the two variables.
Properties of linear correlation coefficient:
Linear correlation coefficient is a value calculated from given data and used to measure the strength of linear relationship between two variables, for instant between x and y variables.
The sign of this coefficient (r) indicates the direction linear relationship will take between x and y. Below are some properties of the linear correlation coefficient:
The value of r lies between -1 and 1 inclusiveThe sign of r indicates the direction of the linear relationship between x and yThe size of r indicates the strength of the linear relationship between x and yNow, the properties of the linear correlation coefficient among the given ones in the question are:
b. The linear correlation coefficient is always between−1 and 1. That is,−1≤r≤1.
d. A linear correlation of −0.742 suggests a stronger negative association between two variables than a linear correlation of −0.472.
f. If r=−1, then a perfect negative linear relation exists between the two variables.
Hence, options b, d and f are correct.
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PLEASE HELP! I WILL GIVE BRAINLIEST!!
Answers
Answer:
using the law of sines m<A is 36 approximately.
3. if the 90% confidence limits for the population mean are 34 and 46, which of the following could be the 99% confidence limits a) (36,41) b) (39,41) c) (30,50) d) (39,43) e) (38,45) 4. given that the population standard deviation is 7500 and a 95% confidence level. what should be the sample size if we want the margin of error to be m
Answers
a) Option D, (39,43) could be the 99% confidence limit.
b) The determined minimum sample size is 166.
a) For a given sample size, the confidence interval is just the range of values including the real population mean. The confidence interval is interpreted as follows:
The real population mean are contained in around 95% of the estimated confidence intervals.
The breadth of the interval and the confidence level (including 95% or 99%) have a positive connection.
As the confidence level rises, the range of both the confidence interval expands, implying that the lower limit of the interval shrinks and the top bound of the interval expands.
Option B is the correct one among the available possibilities since it entirely follows the pattern. When compared to a 99% confidence interval, 33 should be less than 34, and 46 is more than 43.
b) s = Standard Deviation = $7,500 m = Margin of Error = $1,500 z = Empirical z-score at 95% CI = 2.575
The random sample for a 95% confidence interval is calculated as follows:
= (Z × s)² ÷ m²
= (2.575 × s)² ÷ m²
= (2.575 × 7500)² ÷ (1500)²
= 165.76
≈ 166
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the event containing the outcomes belonging to a or b or both is the __________ of a and b.
Answers
The event containing the outcomes belonging to a or b or both is the union of a and b.
Let us consider two sets a and b, and say events or the elements in set a are: (x, y, z), and the elements in set b are: (o, p, q)
The union of these two sets will give:
aUb=(x, y, z, o, p, q)
Now, a union of two sets (denoted by U), for our case a and b, is the set or event containing the elements belonging to a or b or both the elements in a and b altogether.
Thus, the even containing the outcomes belonging to a or b or both in a and b altogether is the union of a and b.
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given the system y=-1/2x-1 and -1/4x+y+4=0 write the solution to the system on the space provided below as an ordered pair
Answers
The solution to the system of equations as an ordered pair is (4, -3).
We are given a system of linear equations in two variables. The first equation is y = (-1/2)x-1. The second equation is (-1/4)x+y+4 = 0.
We need to find the solution of the system of equations. We will use the substitution method to solve for the values of "x" and "y".
y = (-1/2)x - 1
(-1/4)x + y + 4 = 0
Substitute the value of "y" from the first equation into the second equation.
(-1/4)x + (-1/2)x - 1 + 4 = 0
(-3/4)x+3 = 0
(3/4)x = 3
x = 4
Substitute the value of "x" back into the first equation to get the value of "y".
y = (-1/2)x - 1
y = (-1/2)4 - 1
y = -2 - 1
y = -3
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Which line plot displays a data set with an outlier?
Please no guessing or malfunctions, you will get 100 points, but can you do it honestly and answer the question? Please and thank you!
Answers
Answer: I think the answer is A
Step-by-step explanation:
An Outlier is any number that doesn't "Match" with the rest. In this case, the data points range from 3-13. However, most points are between 3-8. The point on the 13 seems to be out of place especially considering that the range between 3-8 is 5. Even though the range is also the same between 8-13, the problem says "outlier" in the singular form. Therefore, my answer is A.